Innovation & Society
Statistics and Data Science for Evaluation and Quality
Editors: Giovanna Boccuzzo, Enrico
Bovo, Marica Manisera, Luigi Salmaso
University of Padova Casa della Gioventù Brixen - Bressanone June 25-27, 2025
First edition: June 2025
ISBN 978 88 5495 849 4
© IES 2025 - Statistical Methods for Evaluation and Quality
2025 Cleup sc
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via G. Belzoni 118/3, Padova (t. +39 049 8753496), Italy
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No part of this book may be translated or copied in whole or in part without written permission of the authors, except for brief excerpts in connection with reviews or scholarly analysis.
IES 2025 - Innovation & Society: Statistics
and Data Science for Evaluation and Quality
BOOK OF SHORT PAPERS
Editors: Giovanna Boccuzzo, Enrico Bovo,
Marica Manisera, Luigi Salmaso
Book of Short Papers
2025 Conference of the 12th Scientific Meeting of the Statistics
for the Evaluation and Quality of Services Group of the Italian
Statistical Society (SVQS)
IES 2025 - Innovation & Society: Statistics and Data Science
for Evaluation and Quality University of Padova
Casa della Gioventù, Brixen - Bressanone
June 25-27, 2025
Program Committee
Chair: Marica Manisera University of Brescia
Ana Maria Aguilera University of Granada - Sociedad de Estadistica Rosa
Arboretti Giancristofaro University of Padova
Francesca Bassi University of Padova
Matilde Bini European University of Roma (ISBIS) Eugenio Brentari
University of Brescia
Mario Bolzan University of Padova
Ida Camminatiello University of Campania ‘L. Vanvitelli’ Maurizio
Carpita University of Brescia
Carlo Cavicchia Erasmus University Rotterdam Giulia Cavrini Free
University of Bozen-Bolzano Roy Cerqueti University of Rome ‘La
Sapienza’ Enrico Ciavolino University of Salento
Elisa Cisotto Free University of Bozen-Bolzano Corrado Crocetta University of Bari ‘Aldo Moro’ Antonello D’Ambra University of Campania ‘L. Vanvitelli’ Pierpaolo D’Urso University of Rome ‘La Sapienza’ Tonio Di Battista University of Chieti-Pescara ‘G. D’Annunzio’ Simone Di Zio University of Chieti-Pescara ‘G. D’Annunzio’ Marta Disegna University of Padova
Michele Gallo University of Naples ‘L’Orientale’ Claudiu Herteliu Bucharest University of Economic Studies Salvatore Ingrassia University of Catania
Michele La Rocca University of Salerno
Christophe Ley University of Luxembourg (President of the Lux embourg Statistical
Society)
Caterina Liberati University of Milano ‘Bicocca’ (ISBIS) Rosaria
Lombardo University of Campania ‘L. Vanvitelli’ Antonio Lucadamo
University of Sannio
Ambra Macis University of Brescia
Paolo Mariani University of Milano ‘Bicocca’ Antonella Massari
University of Bari
Fabrizio Maturo University Mercatorum
Matteo Mazziotta ISTAT
Fatmir Memaj University of Tirana
Tullio Menini University of Naples ‘L’Orientale’ Rodolfo Metulini
University of Bergamo
Stefania Mignani University of Bologna
III
Fabrizio Ruggeri CNR - IMATI
Silvia Salini University of Milano
Pasquale Sarnacchiaro University of Naples ‘Federico II’ Kozeta
Sevrani University of Tirana and INSTAT Violetta Simonacci
University of Naples ‘Federico II’ Rosaria Simone University of
Naples ‘Federico II’ Anna Simonetto University of Brescia
Amalia Vanacore University of Naples ‘Federico II’ Vedat Verter Queen’s
University Smith School of Business Marika Vezzoli University of Brescia
Maurizio Vichi University of Rome ‘La Sapienza’ Emma Zavarrone
IULM University
Local Organizing Committee
Co-Chair: Giovanna Boccuzzo University of Padova
Co-Chair: Luigi Salmaso University of Padova
Erika Banzato University of Padova
Elena Barzizza University of Padova
Pietro Belloni University of Padova
Nicolò Biasetton University of Padova
Enrico Bovo University of Padova
Riccardo Ceccato University of Padova
Pierdomenico Duttilo University of Padova
Alberto Molena University of Padova
Maurizio Nicolaio University of Padova
Manuela Scioni University of Padova
Margherita Silan University of Padova
Francesco Trolese University of Padova
IV
Scientific Committee of the group of the Italian Statistical Society on Statistics for the Evaluation and Quality of Services - SVQS
Maurizio Carpita University of Brescia
Pietro Amenta University of Sannio
Matilde Bini European University of Rome
Antonello DAmbra University of Campania ‘L. Vanvitelli’ Luigi D’Ambra
University of Naples ‘Federico II’
Paolo Mariani University of Milan ‘Bicocca’
Marica Manisera University of Brescia
Monica Palma University of Salento
Pasquale Sarnacchiaro University of Naples ‘Federico II’
SVQS Thematic Area Leads
Matilde Bini European University of Rome
Eugenio Brentari University of Brescia
Maurizio Carpita University of Brescia
Carlo Cavicchia Erasmus University Rotterdam
Roy Cerqueti University of Rome ‘La Sapienza’
Enrico Ciavolino University of Salento
Antonello D’Ambra University of Campania ‘L. Vanvitelli’ Tonio Di Battista
University of Chieti-Pescara ‘G. D’Annunzio’ Michele Gallo University of
Naples ‘L’Orientale’
Salvatore Ingrassia University of Catania
Marica Manisera University of Brescia
Paolo Mariani University of Milan ‘Bicocca’
Stefania Mignani University of Bologna
Pasquale Sarnacchiaro University of Naples ‘Federico II’
Editors
Giovanna Boccuzzo University of Padova Enrico Bovo University of Padova Marica Manisera University of Brescia Luigi Salmaso University of Padova
VI
Preface
Statistical thinking and data-driven methodologies are essential to understanding contem porary challenges and driving innovation in several sectors. Since 2009, the Innovation and Society (IES) biennial conference, organized by the Group of Statistics for the Evaluation and Quality of Services (SVQS) of the Italian Statistical Society (SIS), has served as a key venue for advancing research in statistical methods applied to evaluation and quality.
The 12th edition, titled “Innovation & Society: Statistics and Data Science for Evaluation and Quality” took place from June 25 to 27, 2025, at the Bressanone-Brixen campus of the University of Padova. This year’s conference reinforced the role of statistics and data science as key tools for evaluating complex phenomena and ensuring quality in a variety of fields, in eluding education, healthcare, environment, public administration, finance, tourism, sports, and beyond.
The scientific program was particularly rich, featuring 3 plenary lectures, 44 invited ses sions, 6 contributed sessions, one special plenary lecture and a round table Co-organized by The Italian (ISTAT) and Albanian (INSTAT) National Statistical Institutes. In total, 199 contributions were presented within invited and contributed sessions. The event also saw the highest international participation in the history of IES, with contributions from the Austrian and Luxembourg Statistical Societies, among others.
Three distinguished keynote speakers enriched the program with plenary lectures: Fabrizio Ruggeri, Christophe Ley, Werner Muller. In addition, a special plenary session featured two prominent invited talks by Fortunato Pesarin and Narayanaswamy Balakrishnan, further enhancing the depth and breadth of the scientific discussions.
The conference also hosted the Young Statisticians Award, which attracted 36 high-quality submissions, showcasing the energy and creativity of early-career researchers working at the intersection of statistics and real-world evaluation problems.
The short papers in this volume highlight the wide spectrum of topics discussed at IES 2025, and testify to the evolving role of statistics and data science in producing knowledge and supporting decision-making in complex systems.
We are sincerely grateful to all authors, session chairs and discussants, session organizers, re viewers, and participants. We also warmly thank our institutional partners for their support: Italian Statistical Society (SIS), SVQS Group, DMS StatLab of the University of Brescia, Departments of Statistical Sciences and of Managements and Engineering of the University of Padova, Ósterreichische Statistische Gesellschaft (Austrian Statistical Society), Interna
VII
tional Society for Business and Industrial Statistics (ISBIS), European Network for Business and Industrial Statistics (ENBIS).
We hope this volume will serve as a source of inspiration and a valuable reference for re searchers working at the interface of statistics, data science, and the evaluation of quality in contemporary society.
Marica Manisera
Chair of the Program Committee
Giovanna Boccuzzo
Co-chair of Local Organizing Committee
Luigi Salmaso
Co-chair of Local Organizing Committee
Maurizio Carpita
Coordinator of the SVQS Group
VIII
Contents
Plenary Sessions 1 Unsupervised Statistical Tools for Anomaly Detection: The Case of Healthcare Frauds
F.Ruggeri	2New data science
breakthroughs in sports (medicine)
C.		Ley	2	A unifying approach to the Behrens-Fisher problem
F. Pesarin	3	Recent challenges in optimal design of experiments (dedicated to the memory of H.P. Wynn) W.G. Muller	4
Invited session IPS01 - CLADAG - Advances in statistical modeling of educational data 5 Combining multiple imputation and variable selection for the analysis of Invalsi test data
S. Bacci, E. Dreassi, L. Grilli, and C. Rampichini	6 A latent class model for item responses and response times
D.		Spinelli, F. Pennoni, F. Bartolucci, and G. Vittadini	13	Exploring factors affecting gender gap in university student performance M. La Rocca, M. Niglio, M. Restaino, and M.P. Vitale	19
Invited session IPS02 - SIS-ySIS - Advanced Methods for Assessing Environmental Im pact and Green Innovation 27 Clustering Hierarchical Disjoint Principal Component Analysis for Environmental Impact Assessment of Food Products
M. Bottazzi Schenone, M. Vichi 	28	Spatiotemporal clustering of GHGs emissions in Europe: exploring the role of spatial component
C. Morelli, P. Maranzano, and P. Otto	36
Invited session IPSOS - Evaluation in transportation and mobility: different points of view 45
IX
Greenhouse gas emissions and audit fees in the transportation and logistic sector R. Santonastaso, R. Macchioni, and A. DAmbra	46	The
environmental assessment of sustainable vehicular transport through the Life Cycle Analysis (LCA) methodology applied to a vehicle
L. Della Ragione, and G. Meccariello	54 Towards a more accurate prediction of aircraft passenger discomfort by integrating temporal analysis of seat-interface pressure with static passenger anthropo metric features
A. Vanacore, and A. Ciardiello	62
Invited session IPS04 - Functional data analysis in action 71 Fuzzy clustering of NPL recovery curves
A.		Carleo, and R. Rocci	72	Enhancing survival learning from time-to-event data with functional random sur vivai forest
G.		Loffredo, E. Romano, and F. Maturo	79 Leveraging Functional Diversity in Statistical Ensemble Learning for Robust Func tional Data Classification
D.		Riccio, F. Maturo, and E. Romano	86 Forecasting carbon emissions from electricity generation: classical vs functional methods
P. Duttilo, and F. Lisi	93
Invited session IPSOS - SIS-SDS - Statistics and data science for sustainable science 101 Learning from Crowds: Model-Based Approaches with a Novel Discriminant Anal ysis Method
A. Cappozzo	102 Multi-state
Markov-switching for extreme summer temperatures modelling G. Di Credico, V. Gioia, and F. Pauli	108 Bayesian Modelling for Forensic Evaluation of Handwritten Loop Characters L. Tzai, I. Ntzoufras, F. Taroni, and S. Bozza	116 A copula-based hidden semi-Markov model for toroidal data
M. Mingione, and F. Lagona	123
Invited session IPS06 - Frailty in Aging Populations 131 Measuring frailty in the elderly: an indicator based on a combination of classifiers P. Belloni, and S. Rebottini	 	132	Where to age happily: a quantitative assessment of Age-Friendliness in the districts of three Italian cities
L. Schiavon, and M. Stivai	140	Χ
CONTENTS
Social Frailty and Healthcare Utilization Among Community-Dwelling Older Adults in Europe
E. Cisotto, A. Donno, G. Cavrini, and G. Boccuzzo	147
Invited session IPS07 - Well being: humans and algorithms 155 Assessing the impact of Active and Assisted Living technologies on older adults’ psychosocial well-being: there is room for improvement
A. Bodini, A. Brancaccio, C.G. Leo, P. Mincarone, V. Recchia, and M.R. Tumolo. 	156	RAISE Math: An Adaptive
Approach to Middle School Mathematical Proficiency A. Brancaccio, and A. Bodini... 	163 Thermal Comfort Monitoring of Urban Areas: A
Spatio-Temporal Jump Model Approach F.P. Cortese, and A. Pievatolo	170	Assessing the
SAFEty of Machine Learning Models
E. Raffinetti, and A. Spelta	178
Invited session IPSOS - Advancing Social Sustainability: Approaches and Frameworks 187 The CARESWELL Project on professional well-being in elderly care L. Salaris, N. Tedesco, M. Abate, G.M. Milanese, A. Spera, and G. Tricarico 188 Tourism and Economic Growth in Basilicata: The Impact of Matera’s European Capital of Culture M.G. Grassia, M. Marino, R. Cataldo, S. Paesano, R. Mazza, D. Sacco, and A. Stavolo	196 SustVIS: bridging Corporate Reporting and actionable sustainability insights A. Forciniti, and E. Zavarrone 	204
Invited session IPS09 - Interplay between multimorbidity and frailty: implications for health and aging 211 Sensitivity Intervals for a Frailty Indicator based on partially ordered set theory
M. Nicolaio, M. Silan, and G. Boccuzzo	212 On
longitudinal study of chronic diseases multimorbidity patterns at older ages L.H.K.
Dang, N. Caranci, G. Roli, R. Rettaroli, and R. Miglio 	220 Measuring frailty
through the multimorbidity network
E. Banzato, and G. Boccuzzo	228
Invited session IPS10 - Assessing Young Students’ Academic Performance: Insights from Recent Studies on Digital and Mathematical Competence 237 Digitalization and Digital Competences. Towards a Measurement Model at the End of Compulsory Schooling
S. Ercolanoni, and M. Gui	238	XI
Investigating inequalities in digital skills of Italian students based on ICILS data L. Bungaro, M. Matteucci, and S. Mignani	245	Measuring Digital
Competencies in Secondary Education: A First-Phase Investi gation of Standardized Assessment and Certification Models
P. Falzetti, P. Giangiacomo, and R. Ricci 	252	Evaluating Student Performance: Unveiling the Impact of School’s Economic, So cial, and Cultural Status with Regression Discontinuity
P. Sannino, C. Davino, and R. Romano	258
Invited session IPS11 - Advances in Functional Data Analysis and Applications 267 Multivariate functional data analysis to monitor, evaluate and classify engineering failures
C. Yildirim, A.M. Franco-Pereira, and R.E. Lillo	268 Partially observed functional data: a general model
M.C. Aguilera-Morillo, M. Durban, and P. Hernàndez-Amaro	276 Basis expansion approaches for penalized functional ICA with applications in neu roscience A.M. Aguilera, and M. Vidal	281 New Perspectives on Explainability Tools for Functional Random Forests F Maturo, and A. Porreca	288
Invited session IPS12 - Futures Studies and Statistics 295 Policy analysis with generative pre-trained transformers: the future of north-eastern Italian families
Y. Calleo, M. Scioni, S. Di Zio, M. Marozzi, and M. Bolzan 	296 A classification of Delphi outputs in scenario development adopting a network based fuzzy clustering
Y. Calleo, M. Bolzan, and S. Di Zio 	303	Predicting and Preventing gender-based violence: A strategic framework for long term change E. Zavarrone, and Ε. Forciniti	311 A spatio-temporal forecasting model for the State of the Future Index of European countries
L.S. Alaimo, Y. Calleo, and S. Di Zio	319
Invited session IPS13 - Digital Statistics and Official Data: Innovation, Quality, and Challenges 327 Ensuring Data Quality in Population and Housing Census in Albania: Challenges and Solutions in the Digital Transformation Era
E.		Dhuli, and K. Sevrani	328 XII
CONTENTS
Household income and academic outcome: A register-based analysis of Italian stu dents
L. Coppola, D. Ichim, and I. Siciliani	334 Improving official statistics: the new Audit internal procedure at Istat. Description and findings M.F. Loporcaro	341	Introducing Al in
Istat: Responsibility and Innovation
S. Letardi, and F. Orecchini	348
Invited session IPS14 - Advances in Statistical Learning from High-Dimensional Data 355 Different dimension reduction approaches for estimating the functional regression model
H. Ortiz Alcalà, C. Acal, M. Vidal, and A.M. Aguilera	356
Augmented Functional Random Forests: Robust Classifier Construction and Con ditional Importance of Functional Principal Components
F.		Maturo, and A. Porreca	363 Functional Clustering for Survival Curves
M. De Lucia, E. Romano, and F. Maturo 	370
Invited session IPS15 - BDsports - Sport Statistics 379 Fitting Bayesian and frequentist football models in R via the footBayes package L. Egidi, and R. Macri Demartino	 	380 Improved prediction of 100-meter sprint records
G.		Fonseca, F. Giummolè, M. Lambardi di San Miniato, and V. Mameli .. . 387 The role of basketball shooting trajectories in predicting shot success A. Macis, M. Sandri, and P. Zuccolotto	393	Exploring the Role of Kinematic Variables in Determining Match Outcomes in Serie A: A Statistical Approach A. Lucadamo, P. Troiani, F. Laterza, C. Savoia, M. Bertollo, D. Pompa, S. Pacillo, P. Amenta, and L. Greco	401
Invited session IPS16 - ISBIS - Statistical Modeling for New Economic and Social In sights 409 Exploring Spatial Disparities and Gaps in Transportation and Mobility through Airbnb Reviews: A Sardinian Case Study
L. Frigau, G. Contu, Μ. Ortu, and F Mola 	410
Web-Scraped Data for MSMEs Economic Analysis: Insights on Innovation and Bankruptcy
C. Bottai, L. Crosato, and C. Liberati	418 Invited session
IPS17 - Sustainable tourism for territorial development 427 XIII Multidimensional Statistical Indicators For The Analysis Of Sustainable Tourism P. Perchinunno, A. Massari, S. L’Abbate, A.M. D’Uggento, and C. Crocetta . 428 Tourism and territories: a multilevel analysis in Italy
L.S. Alaimo, Ε. di Bella, and S. L’Abbate	435
Sustainable Tourism Indicators: A Classification Proposal from the SDGs Perspec tive V. Tomaselli and M.D. Giammanco	442
Invited session IPS18 - New methods and applications for the analysis of survey data 449 A distance-based consensus measure for analyzing ternary preferences A. Albano, J.L. Garcia-Lapresta, A. Plaia, and M. Sciandra	450	Lost in Noise: When cleaning up clouds the picture. Fuzzy topic modeling and robust low-rank decomposition
A.		Calcagni, A. Sciandra, and A. Tuzzi	458	Assessing Latent Structure in Questionnaire Data: an integrated approach between Consensus Bayesian Networks and Community detection
P. D’Urso, L. DeGiovanni, L. Federico, and V. Vitale	465
Composite Likelihood Inference for Simultaneous Clustering and Dimensionality Reduction in the Chinese Longitudinal Healthy Longevity Survey
M. Ranalli, R. Rocci, and A. Maruotti	473
Invited session IPS19 - Luxembourg Statistical Society - Statistically Enhanced Learning 479 Estimation of match abilities for tennis players via a maximum likelihood approach
H. Bartmann, A. Groll, and R. Michels	480	Variable ranking and data reduction in GLM domain
F. Giordano, M. Niglio, and M. Restaino	488
Invited session IPS20 - Advances in multivariate permutation methods 495 Advances in Cluster Analysis: a permutation approach to cluster validation E. Barzizza, N. Biasetton, and R. Ceccato	496 A Nonparametric Approach for Robust Product Ranking
E.		Barzizza, and R. Ceccato	503 Comparing
Multiple Samples under Heteroscedasticity: a Multivariate Permutation Solution E.	Barzizza, N. Biasetton, and R. Ceccato	510 Nonparametric Time Series Screening for Bitcoin and Gold Volatility G. Feo, F. Giordano, and S. Milito	518
Invited session IPS21 - Measuring latent traits and perceptions for social innovation 527 Streaming entropy for dynamic modelling in psychological measurement M. Angelelli,

528

O.C.G. Gelo, and E. Ciavolino

XIV

CONTENTS
Low-Rank Analysis of Topic Quality: Comparing LDA, CTM, and Fuzzy-LSA methods
A.		Calcagni	535	A Penalized
Complexity Prior for the Measurement Error of Covariates in Small Area Models
D.		Battagliese, A. Pollice, S. Arima, and B. Liseo	543 Patient satisfaction and healthcare quality perception: an explorative textual anal ysis
C. Valentino, M. Aria, M. Angelelli, and E. Ciavolino	551
Invited session IPS22 - Advances in the Modelling of Spatio-Temporal Data 559 Transition Models for Precipitation Climatology Estimation
N. Umlauf, and R. Stauffer	560	Spatial and
Spatiotemporal Volatility Models: A Review
P. Otto, O. Dogan, S. Ta§pinar, W. Schmid, and Α.Κ. Bera	568 Signature Lasso for Fractional Brownian Motion Processes
A. Mohaddes, F. lafrate, and J. Lederer	575
Invited session IPS23 - Reporting violence against women: statistical tools and some pitfalls 583 A Territorial Analysis of Factors Affecting Access to Support Centers for Violence Against Women in Apulia
C.		Calculli, L. Cefalo, and A. Pollice	584	A Bayesian dynamic model for the analysis of 1522 helpline data
S. Polettini, S. Arima, and A. Farcomeni	591
Under-reported data: a simulation study about parameter sensitivity G. Panunzi, S. Polettini, and S. Arima	599
Invited session IPS24 - SIS-DIAS - Data science to measure environmental sustainability 607 Working with composite indicators to measure environmental sustainability M. Ciommi, F. Mariani, G. Polinesi, and M.C. Recchioni	608	Assessing CO2 emissions from electricity generation: a methodological review and comparative analysis
M. Bertolini, P. Duttilo, and F. Lisi	616
Invited session IPS25 - BDsports - Sport statistics: methods and applications 623 A New Dataset for Exploring Actions of Italian Football Matches
M. Cefis, R. Metulini, and M. Carpita	624	A Financial
Instrument Indexed to Football Players Performance
G. Dello loio, and M. Cefis	631	XV
Towards Smarter Player Scouting: Learning Football Player Embeddings with Vari ational Autoencoders (VAEs)
G.		Fantuzzi, L. Egidi, and N. Torelli 	637 On the relationship between passing-related features and the result of offensive actions in football
R. Ievoli, L. Palazzo, R. Rondinelli, and G. Ragozini	645
Invited session IPS26 - Advanced methods in Labour Market 653 Dynamics of IT and Digital Professional Profiles in Italy: An analysis of the tra jectories of required soft skills
P. Mariani, A. Marietta, D. Pirotta, and M. Zenga	654
Hospitality and Tourism Activities in the Italian Provincial Labour Market P. Mariani, and M. Zenga	661	Gender Diversity in Life Sciences Firms: A Data Integration Approach L. Benedan, C. Colapinto, P. Mariani, L. Pagani, and M. Zenga	668 Gender inequality in the workplace: a comparative analysis of Italian companies through the definition of composite indicators
A. Gattulli, M. Antonicelli, I. De Turi, and M. Posa	674
Invited session IPS27 - New methods for university assessment in teaching and research 683 Research assessment in Italy: the recent experience and the way forward M. Malgarini, and S. Sarlo	684 Insights into the Italian university system: analyzing standardized indicators I. Camminatiello, and R. Lombardo	691 Can the dimension of a university affect the assessment of the performance? A.M. D’Uggento, V. Ricci, and E. Toma	 	698
Invited session IPS28 - ENBIS - Handling uncertainty and complexity in modern decision making and smart applications 707 A Bayesian model for measurements by counting
F. Pennecchi, and W. Bich	708 The benefits of classification: a system operational perspective Y.N. Marmor	716	A Scalable and
Cost-Effective Approach for Disease Detection in Smart Agriculture: the case of Xylella Fastidiosa
A. Vanacore, A. Ciardiello, L. Uccello, G. P. Auricchio, and A. Izzo 	723
Invited session IPS30 - High dimensional data analysis for evaluating sustainable devel opment 731 Identity Spline and LASSO Regression for Analysing Italian Poverty R. Lombardo, M. Musella, and I. Camminatiello	732
XVI
CONTENTS
Evaluation of Synthetic Indicators: a new method based on functional data analysis L.S. Alaimo, F. Fortuna, and A. Naccarato	739	From Data
Collection to Knowledge in Health: Turning Scientific Production into Practical Decision-Making Tools
M. Aria, C. Cuccurullo, L. D’Aniello, M. Spano, and C. Alabiso 	746
Invited session IPS31 - Statistical methods for measuring the sustainability 755 Toward a Sustainable Society: assessing legal progress of LGBT rights with func tional data analysis
F.		Fortuna, A. Naccarato, and A. Trezzini	756 Advanced multidimensional spatial clustering for sustainable transport assessment V. Distefano and S. Deiaco	763	Quantile-Based Hidden Markov
Graphical Models for PM10 Pollution Analysis: A Perspective on Air Quality in Northern Italy
B. Foroni, L. Merlo, L. Petrella, and N. Salvati 	770
Invited session IPS32 - Austrian Statistical Society - Effectively Using Relevant Infor mation for Statistical Inference 779 How to efficiently analyse data in rare diseases research: Accounting for individual variability of the primary outcome over time G.	Zimmermann	780	Random Reward Phase-Type Distributions with Applications in Employee Devel opment S.	Pauli, and A. Futschik 	787	How to best analyze randomized experiments with very small samples S.L. Grùninger, R. Furrer, and F. Frommlet	793	Nonparametric Analysis of Tourism Data for Optimizing Sustainable Transport Services at Airport Salzburg
M. Kiefel, and D. Lahnsteiner	800
Invited session IPS33 - Statistics and geometry with applications 809 An improved TDA-based algorithm for the isomorphism problem of orthogonal arrays
R.		Fontana, and M. Guerra	810	A geometrical approach to research assessment
B.		Cappelletti-Montano, S. Columbu, S. Montaldo, and M. Musio	818 Impact of zero-patterns in the dependence of three-way binary tables R. Fontana, E. Perrone, and E Rapallo	826	Three dimensional Bernoulli generators and their dependence structure R. Fontana, and P. Semeraro	 	833
Invited session IPS34 - Nonparametric methods and applications 841 XVII
Statistical Analysis of the Italian pension system: a nonparametric approach M. Giacalone, G. Piscopo, S. Marra, and C. Marciano 	842	Impact assessment of big music events with a focus on the food service industry: a nonparametric test for linear models
M. Borghesi	849	Local Inference for Data Giants
G. Cattani, M. Scholz, and S. Sperlich	856 Time series comparisons with application to electricity market
S. Bonnini, and Μ. Borghesi	863
Invited session IPS35 - Statistics and Al to support sustainability in agro-ecosystems 871 Quantitative Tools for Evaluating Biological Processes in Vineyard Agroecosys terns: BIOPASS® and QBS-ar
M. Tonni, P. Donna, M. Donna, I. Ghiglieno, L. Valenti, and G. Gilioli...872 Impact of meteorological conditions, canopy shading and leaf removal on yield, must quality, and norisoprenoid compounds content in Franciacorta sparkling wine
S. Carlin, I. Ghiglieno, G. Cola, U. Vrhovsek, L. Valenti, M. Garcia-Aloy, and F. Mattivi	880 Leveraging Remote Sensing and Artificial Intelligence to Monitor Biodiversity in Wine-sector and Semi-Natural Urban Environments
G. Tariku, I. Ghiglieno, A. Simonetto, I. Serina, and G. Gilioli	887 Measuring supply chain sustainability: a structured multilevel framework F. Demaria, F. Bertacchini, U. Kocollari, and M. Cavicchioli	894
Invited session IPS36 - Business Intelligence for Official Statistics: Tools for Improving Quality 903 Artificial intelligence and methodological innovations in the statistical process: a GSBPM perspective
G. Ascari 	904	Business
Intelligence for assessing Istat HR processes
A. Dentini, and M. Mazziotta	912	The
Importance of Business Intelligence in Monitoring Organizational Effective ness: Analysis of some organizational structures in Istat
S. Demofonti, and S. Pifferi 	920	Statistical indicators on public administration employees: what support from Busi ness Intelligence?
G. Cinquegrana, R. Fantozzi, and I. Screpante	928
Invited session IPS37 - Statistical methods for traffic and the environment 935 XVIII
CONTENTS
Assessing Predictive Performance of Time Series Copula Models in Traffic Flow Analysis
S.S. Guerini, and R. Metulini	936 Traffic
Restrictions and Air Quality: A Counterfactual Matrix Completion Analysis of Milan’s Area C
R. Adam, F. Biancalani, and R. Metulini	944 Characteristic-based clustering of traffic flow time series with complex seasonality M. Carpita, R. Metulini, and M. Migliorati	952	Graph Neural
Networks for Traffic Accident Risk
G. Cantaluppi, J. Lin, G. Valena, and D. Zappa 	959
Invited session IPS39 - MICS - Data-Driven Strategy, Management, and Technical De velopment for ‘Made in Italy’ Products 967 The VABSA framework: a Value- and Attribute-Based Sentiment Analysis of con sumer perceptions
N. Biasetton, R. Ricciardi, and N. Arghistani	968 Group-specific document embeddings: An application to User-Generated Content F. Alberti, R. Ricciardi, and M. Manisera	975 Model-Based
Clustering of Multivariate Rating Data to Evaluate Consumer Per ceptions on Sustainability
M. Ventura, J. Jacques, and P. Zuccolotto	983
Permutation-Based Multivariate Chi-Square Test: A Case Study
M. Disegna, A. Fanesi, and L. Salmaso 	991
Invited session IPS40 - Advancing Sustainability in Healthcare 999 Early dementia recognition with Digital Linguistic Biomarker
L. Altieri, and G. Gagliardi	1000	Inequalities in adherence to the diabetes guidelines in the migrant population at the regional level
M. Arcaio, A. Allotta, S. Scondotto, and M. Ferrante 	1007
Research excellence and patient perception: investigating the impact of AHSCs’ scientific output
A. Gnasso, D. Sacco, L. Celardo, M.A. Smecca, C. Alabiso, and M. Spano . 1014
Invited session IPS41 - Multivariate tools for Sustainability 1021 Identifying optimal candidate models of classification trees with weak bias K. Hayashi, and R. Inose	 	1022 A Synthetic Green Indicator and Its Role in Green Bond Pricing
P. Galfrascoli, E. Ossola, and G.S. Monti	1029 Sustainability in sports: a three-decade scientific review
L. Palazzo, Τ. Menini, V. Simonacci, and M. Gallo 	1036 XIX
Do SMEs really walk the talk? A textual analysis of sustainability reporting in Italy
A. Sarra, B. lannone, M. Di Giampietro, A. Evangelista, and Τ. Di Battista 1043
Invited session IPS42 - Tourism and sustainability 1051 New approaches for innovative tourism promotion among artificial intelligence and the metaverse
V. Santarcangelo, M. Giacalone, A. Romano, and G. Piscopo 	1052	A proposal for daily mortality indices related to the official measurement of pollu tants S. Cervellera, M. Giacalone, M. Longobardi, G. Piscopo, and C. Cusatelli . . 1060 An ultrametric composite indicator for ranking the environmental sustainability performance of Italian provinces
I. Ariante and P. Sarnacchiaro	1067
Invited session IPS43 - Data Analytics for Mobility Domains 1073 Quality Key Factors in the Public Transportation Scenario
S. Porcu, and F. Marcello	1074 A review and future directions in big data subsampling
R. Arboretti and A. Molena	1082 Regulating Spatial Fairness in a Tripartite Micromobility Sharing System via Re inforcement Learning
M. Cederle, M. Fabris, and G.A. Susto	1089 Overcoming Computational Challenges in Two-Stage Multi-path Traveling Sales man Problem via Neural Networks
X. Chou, L. di Marco, and E. Messina	1097
Contributed Session CPS01 - Statistical methods and models for student mobility, per formance, and resilience 1105 Dropout rates in Italian universities: a comparison of online and traditional uni versities
C.		Usala, G. Lombardi, and A. Priulla	1106 Navigating Academic Waters: Exploring the Trends of Switching Students in Higher Education V. Tocchioni, S. Milone, G. Lombardi, and A. Petrucci	1114 Evaluating the Impact of Teachers Characteristics and Practices on High School Students’ Performance
I. Moreschini, N. Brancaccio, I. Sulis, and M.P. Vitale	1121 Optimizing goodness of fit of mixture models with uncertainty for rating data: a case study on academic distress
R. Simone	1129 XX
CONTENTS
Bayesian Downscaling of INVALSI Data with Small Area Estimation D. Battagliese, and A. Pollice	1137 Academic
Resilience Among Low ESCS Students in Italy A. Pisu, I. Sulis, and M. Porcu	1145
Contributed Session CPS02 - Statistical modeling for economic and social studies 1153 Assessment of the diversity of housing expenditures of households in Polish regions M. Sadko, and B. Pawelek	1154	Linking Income and
Housing Poverty: A Comprehensive Analysis Using Integrated Fuzzy and Relative Approach
M. Cwiek, P. Ulman, and M. Sadko	1161 Disability and Economic Disparities in Europe: A 2023 Comparative Analysis P. Ulman, and A. Walgga	1168 Social Protection and Household
Food Security: Evidence from Ethiopia’s PSNP Program
S.T. Mengesha, E. Stanghellini, and M. Genback	1175
Supportive Obligations among Nuclear and Extended Kin: A Vignette Study M.F. Morabito, M. Tosi, and V. Tocchioni	1182 Material deprivation in
Europe: a comparative analysis of the phenomenon through demographic parameters M. Antonicelli	1189
Contributed Session CPS03 - Statistical modeling for environmental, social, and eco nomic challenges 1197 Model confidence set for air pollution time series models
G. Zammarchi, and Y. Kawasaki	1198 Risk map for female genital mutilation/cutting
S. Golia, D. Carrillo, P. Farina, L.E. Ortensi, and E. Ripamonti 	1205 Is Time Well Spent in Later Life? Understanding Life Satisfaction Through Daily Time Reallocation Across Activities
M. Salierno, A. Donno, and M.L. Tanturri	1212 Adaptive
Bayesian Spatial Modeling of Economic Resilience to Environmental and Climate Shocks
A. Pacifico	1220 Exploring Peer
Effect in Educational Choices: The Missing Tie A. Pacca, and G. Giordano 	1228	If I say bread... What comes to your mind?
S. Nascetti, D. Doglio, F. Ciesa, D. Delvai, P. Selle 	1235
Contributed Session CPS04 - Advances in statistical methodology and computational techniques 1243
XXI
A comparative analysis of machine learning algorithms for predicting probabilities of default
A.I. Cristescu, and M. Giordano	1244 Segmenting the spatial distribution of the adjusted dissimilarity index to detect residential segregation of foreigners in Campania
R. Simone, and F. Benassi	1251
Extreme-value copulas: a note on comparing models for tail-risk events A. Gatto, S. Perazzini, F.M.L. Di Lascio	1258 On a generalized stochastic
Bass model
G. Albano, A. Barrera, V. Giorno, and F. Torres Ruiz 	1266 On
CTA-PLS corrections applied on sports performance
M. Angelelli, M. Cefis, E. Ciavolino, and Maurizio Carpita 	1273 Skew-normal finite mixture models for change-point detection in time series M. Forti, A. Nigri, and H. Shang	1280
Contributed Session CPS05 - Statistical and computational methods for mobility, tourism, and risk analysis 1287 Generative Al for traffic scenarios: a GCN-VAE model
M. Carbonera, M. Ciavotta, and E. Messina	1288 A
Markov chain approach to investigate the Tourists movements: the case of Sar dinia
G. Contu, L. Frigau, M. Ortu, and F. Mola	1296 Identifying
corruption risk profiles in public procurement over emergency periods: a latent class - Item Response Theory approach
S. Del Sarto, M. Gnaldi, and N. Salvini 	1303
Classification and Forecasting of Foreign Tourists Using Time Series from Mobile Phone Networks
R. Rossetti, and Y. Sagaert	1310 Denoising and Forecasting Model for Structural Health Monitoring of Bridges: A Case Study in Brescia
L. Biazzo, and L. Fenga 	1318 The cost of isolation: how insularity affects European transport cost
G. Zammarchi and P. Mattana 	1326
Contributed Session CPS06 - Advances in text mining and visualization of complex data 1333 A Novel Metric for Enhancing Online Review Relevance in E-commerce
L. Stracqualursi, and P. Agati	1334	The
APP-LIC-IT data visualization tool
G. Cantaluppi, D. Zappa, M. Rho, and J. Vera Bacigalupo 	1341	XXII
CONTENTS
From Self-Perception to Feedback: Mapping Sustainability-Oriented Self-Descriptions to Airbnb Reviews
M. Ortu, G. Contu, and L. Frigau	1349	Natural Language
Processing for Data Analysis: an application on the well-being S. Boi, N. Tedesco, M. Romano, and L. Salaris	1356	Constructing fair and comprehensive dataset of online opinions for human annota tions: considerations and challenges dealing with Italian content
A. Cucco, E. del Gobbo, L. Fontanella, S. Fontanella, and L. Ippoliti 	1363 The Impact of Inappropriate Emergency Admissions in the Autonomous Province of Bolzano: Challenges and Insights
Μ. Bonetti, G. D’Orio, and C. Seghieri	1370	XXIII
Plenary Sessions
•		Fabrizio Ruggeri - Unsupervised Statistical Tools for Anomaly Detection: The Case of Healthcare Frauds
•		Christophe Ley - New data science breakthroughs in sports (medicine) ·
Fortunato Pesarin - A unifying approach to the Behrens-Fisher problem
•		Werner G. Muller - Recent challenges in optimal design of experiments (dedicated to the memory of H.P. Wynn)
1
Unsupervised Statistical Tools for Anomaly
Detection: The Case of Healthcare Frauds
Fabrizio Ruggeri
Italian National Research Council, Milano, Italy
Chair: Giovanna Boccuzzo
Abstract The research is motivated by the increased interest in detecting possible frauds in healthcare systems. We propose some unsupervised statistical tools (Lorenz curve, concen tration function, sum of ranks, Gini and Pietra indices) to provide efficient and easy-to-use methods aimed to signal possible anomalous behaviours. A more sophisticated method, based on Bayesian co-clustering, is presented as well.
New data science breakthroughs in sports
(medicine)
Christophe Ley
Department of Mathematics, University of Luxembourg, Esch-sur-Alzette,
Luxembourg
Chair: Marica Manisera
Abstract In this presentation, I will give an overview of recent developments in the world of sports and sports medicine rendered possible by a crafty usage of data science and Artificial Intelligence. Different sports will be covered (handball, football, wheelchair basketball, etc.), and different topics will be treated, such as tactical analysis, outcome prediction, injury risk estimation. Concrete links with the sports world, in particular athletes and coaches, will be discussed, and an outlook on open challenges provided. The talk is meant to take the listener on a stroll along this vibrating combination of sports and science.
Plenary Sessions
A unifying approach to the Behrens-Fisher
problem
Fortunato Pesarin
Department of Statistical Sciences, University of Padova, Padova, Italy
(joint with: Elena Barzizza, Riccardo Ceccato, Luigi Salmaso)
Chair: Maurizio Carpita
Abstract Traditionally, the Behrens-Fisher problem regards the testing of equality of two means, irrespective of equality of two unknown variances, in a two-sample normal data. It is well known that this problem cannot admit any finite-sample exact solution. So, all available papers on the subject matter are designed to improve approximations in specific circumstances. Based on properties of permutation tests, in the paper we provide:
1)		an exact solution under the condition that two CDFs do not cross (as typically occurs when a treatment, the expected random effect of which is either positive or negative, is randomized to units);
2)		an approximate solution, suitable when two CDFs may cross (as typically occurs on obser vational studies), under the condition that two distributions are symmetrically distributed around their median (when no distributional symmetry is assumed, suggestions are provided to symmetrize rank transformations of two data distributions);
3)		an exact weak solution in the general case, based on permutation comparison of two fre quencies of data smaller than the pooled median.
A concise simulation study is provided to evaluate the results. Also, hints are provided for extending all solutions to the multidimensional case.
References
Pesarin, F. (1997). An almost exact solution for the multivariate Behrens-Fisher problem. Metron, LV. 85-100.
Pesarin, F. (2001). Multivariate Permutation Tests: with Applications in Biostatistics. Wiley & Sons, Chichester, UK, Chapter 10, 305-328.
3
Recent challenges in optimal design of
experiments (dedicated to the memory of
H.P. Wynn)
Werner G.MOIIer
Institute of Applied Statistics, Johannes Kepler University, Linz, Austria
Chair: Luigi Salmaso
Abstract This talk is dedicated to the memory of Henry Philip Wynn, who died on 2nd of November of last year. Henry was a towering figure in British and International Statistics and a giant in the field of (optimal) experimental design. He devised what we now call the Fedorov-Wynn algorithm for optimal design construction and coauthored the seminal paper on computer simulation experiments, which currently holds at over 11000 citations.
He was also a warmhearted and affectionate person, a collaborator and dear friend. I will briefly recapitulate our joint work on approximate Bayesian computation design (ABCD) as a modern and flexible tool for design generation. In the second part I shall present three recent challenges for the optimal design of experiments. Their solutions were inspired by Henry’s computational algebraic attitude towards statistics.
4
Invited session IPS01 -
CLADAG - Advances in
Organiser: Michele La Rocca, Rosaria Simone
Chair: Rosaria Simone
Discussant: Diego Battagliese
•		S. Bacci, E. Dreassi, L. Grilli, and C. Rampichini - Combining multiple imputation and variable selection for the analysis of Invalsi test data
•		D. Spinelli, F. Pennoni, F. Bartolucci, and G. Vittadini - A latent class model for item responses and response times
•		M. La Rocca, M. Niglio, M. Restaino, and M.P. Vitale - Exploring factors affecting gender gap in university student performance
5
Combining multiple imputation and
variable selection for the analysis of
Invalsi test data
Silvia Bacci1, Emanuela Dreassi1, Leonardo Grilli1, Carla Rampichini1
Department of Statistics, Computer Science, Applications, University of
Florence, Firenze, Italy
6
Invited session IPS01 - CLADAG - Advances in statistical modeling of educational data
Combining multiple imputation and variable selection for the analysis of Invalsi test data
Silvia Bacci, Emanuela Dreassi, Leonardo Grilli, Carla Rampichini
Abstract Large-scale assessment data, such as those collected in Italy by Invalsi, typi cally include several student background variables, which can be exploited as predictors in modelling student achievement. Unfortunately, the student background variables are usu ally affected by missing values, posing serious challenges to the model selection procedures. As a further complication, many of the predictors are variables with unordered categories. This paper proposes combining multiple imputation and variable selection methods in a set ting with categorical predictors. In particular, we implement multiple imputation by chained equations (MICE). At the same time, for variable selection, we exploit an innovative method based on the knockoff filter, where the knockoff copies are generated using a sequential pro cedure suitable for unordered categories. Once the student background variables have been selected, we fit a random intercept model to analyse the determinants of the Invalsi math score at grade 5. The proposed approach is computationally feasible and highly flexible.
Keywords: education, knockoffs, multilevel data, missing data
1.		Introduction
Selecting the covariates in a statistical model is a challenging task which can be accomplished with several methods, such as fit indexes (e.g. BIC) and lasso [1]. However, traditional variable selection methods do not explicitly control for the error rates of the selection process [2]. To overcome this limitation, the knockoff filter [3] has been proposed to perform the selection while controlling for the false discovery rate (FDR), i.e., the probability including irrelevant covariates.
The classical knockoff methodology has been developed for continuous predictors with out missing values. This is a severe limitation in applications, for example, in large-scale assessment data, where most predictors are categorical with non-negligible rates of missing values. To overcome that limitation, Xie, Chen, von Davier and Weng [4] recently proposed an approach to apply knockoffs in a missing data setting, allowing for continuous, binary and ordinal predictors. They exploit derandomised knockoffs [5] and integrate out missing values with an EM algorithm. Their approach is groundbreaking and highly efficient, but the following limitations restrict its applicability: (i) the missing data are assumed to be generated under a restrictive version of the MAR assumption [6], known as Stronger MAR (SMAR), according to which the probability of missingness depends only on non-null vari ables, namely variables with a non-null regression coefficient in the model for the outcome; (ii) the model is based on a multivariate normal distribution generating binary and ordinal variables via thresholds; thus other kinds of variables (e.g. unordered categorical, counts) are not admitted.
In the following, we sketch our proposal to overcome the above limitations and outline
7
the results of the application to the analysis of Invalsi survey data.
2.		The multiple imputation sequential knockoff method
We propose a flexible approach to deal with variable selection in missing data settings by combining multiple imputation and variable selection via sequential knockoffs. In fact, mul tiple imputation is a general method to analyse data with missing values generated by MAR mechanisms, and sequential knockoffs have been recently proposed [7] to handle both contin uous and categorical variables by a sequential generation scheme.
Specifically, for p available predictors X1, ..., Xj,..., Xp the knockoff is randomly sampled from a normal distri bution when X is a continuous variable and from a multinomial distribution when X is a categorical variable. The mean and variance of the normal distribution and probabilities of success of the multinomial distribution are estimated through a sequential procedure: for
j = 1,... , p, the predictor X is regressed on the remaining predictors X- and on the knockoffs generated in the previous steps [X1,..., X-il- The model for the knockoff gen eration is a penalised linear model if Xj is continuous and a penalised multinomial logit model if X is categorical. The sequential knockoff method has been recently optimised by introducing a preliminary step based on the graphical lasso [8]. Once the knockoffs are generated, the knockoff filter is applied in the usual way [3] by fitting a linear model with lasso and comparing the regression coefficients β jand β j0^ the original variable Xj and the corresponding knockoff copy XI - respectively. To avoid dependency of the results on ran dom fluctuations, the knockoffs are generated multiple times according to the derandomised method [5]. Categorical variables with K categories enter as a set of Κ - 1 dummies linked together by the group lasso [9], so the entire set of dummies is either selected or discarded.
Combining multiple imputation and variable selection entails carrying out variable selec tion provisionally for each imputed dataset, then summarising the results to decide about the inclusion of each variable into the final model. Specifically, our proposal is based on the following steps: (i) multiple imputation of the missing data via chained equations; (ii) application of the knockoff filter to each imputed dataset; (iii) identification of the selected variables by choosing a proportion ps such that a variable is included in the final model if selected in a proportion of imputed dataset greater or equal to ps. Once the variable selection process is concluded, the model of interest is fitted on the imputed datasets using the set of selected variables.
A simulation study, not reported here, based on the setting of Xie, Chen, von Davier and Weng [4], demonstrates that our proposal performs similarly to theirs. Yet, it is characterized by greater flexibility, allowing applications in a wide range of settings. A difficulty with our approach is that, while it controls the FDR for each imputed dataset, the FRD of the final selection depends on ps, as each variable is ultimately selected if it is provisionally selected in at least ps* 100% of the imputed datasets.
A higher minimal proportion ps reduces the probability of a variable being ultimately selected, decreasing the expected number of false discoveries (i.e., non-null variables wrongly selected) and thus the FDR. Therefore, a conservative choice would be to set the minimal
8
Invited session IPS01 - CLADAG - Advances in statistical modeling of educational data
proportion to 1, i.e. ultimately select only variables selected in all the imputed datasets. However, this choice could lead to a final FDR much lower than the target one at the cost of a reduction of the ability of the procedure to correctly identify non-null variables, leading to a potentially low True Positive Rate (TPR). In the absence of theoretical results, the minimal proportion ps can be chosen based on simulation studies. The study we carried out suggests ps = 0.8. This is a key issue deserving further investigation with theoretical developments and simulation studies in different settings.
3.		Application to Invalsi data
We focus on data from the Invalsi sample survey of the year 2022-23 on pupils in grade 5, corresponding to the last year of primary school. The dataset includes 16,828 students nested in 501 schools.
Specifically, the outcome is the achievement in mathematics, a latent ability measured by a set of dichotomously scored items and estimated by the Rasch model. The average sample score in math is 191.82 points, with a standard deviation of 41.07.
The dataset includes several background variables about the students, such as gender, siblings, material well-being, parent’s educational level and job condition. Most background variables have missing values, ranging from 1.6% to 26%.
We aim to model the relationship between the math score and the background variables. To this end, we select the variables using the multiple imputation sequential knockoff method outlined in Section . Specifically, we implement Multiple Imputation by Chained Equations with 10 imputed datasets using the mice package of R [10]. For each imputed dataset, the predictors are selected using the sequential knockoff procedure [7], as implemented in the R package knockofftools [8] with PFER set at 2 (PFER is the expected number of false discoveries, namely irrelevant variables wrongly classified as relevant).
Table 1 shows, for each predictor, the proportion out of the 10 imputed datasets in which it has been provisionally selected by the lasso applied to the original variables (penultimate column) and by the sequential knockoff method (last column). Setting the minimal propor tion for ultimately selecting a predictor at ps = 0.8, as suggested by our simulation study, it turns out that the sequential knockoff method selects 23 out of 31 predictors (it is reassuring to note that any choice of ps between 0.4 and 0.9 would have selected the same variables). There is an agreement with the group lasso on the original variables except for three pre dictors. Even if the results are close, the lasso has the drawback of not controlling for the number of false discoveries.
The predictors selected by the sequential knockoff method (namely, those with an entry greater or equal to 0.8 in the last column of Table 1) are used in a linear model for the math score with a random effect to account for the clustering of pupils into schools. The model is fitted separately on each imputed dataset, combining the results with Rubin’s rules.
The results, not shown here due to space constraints, are generally in line with the literature. Mothers’ and fathers’ education have similar effects, monotonically increasing from compulsory to master’s or more. On the other hand, the effects of occupation are
9
much greater for the father. The items about material well-being (listed in Table 1 with the headline "At home, you have") are positively associated with the math score with some exceptions; interestingly, possessing a personal tablet or a smartphone has a negative effect, likely due to the distracting role of those devices. The stronger predictor is the number of books at home, which is an indicator of the cultural environment.
Acknowledgments
This research has been financed by (i) PRIN 2022 Call (D.D. 104/2022) by the Italian Min istry of University and Research (MUR) - Project "Latent variable models and dimensional ity reduction methods for complex data" (Project No. 20224CRB9E, CUP B53C24006320006); (ii) European Union, Next Generation EU, National Recovery and Resilience Plan, Invest ment Partenariato Esteso ΡΕ8 "Conseguenze e sfide dell’invecchiamento", Project Age-lt (Ageing Well in an Ageing Society, PE8-B83C22004800006).
10
Invited session IPS01 - CLADAG - Advances in statistical modeling of educational data
Table 1: Variable selection with lasso (penalty parameter chosen by BIC) and sequential knockoff: proportion selected over 10 imputed datasets. INVALSI grade 5 sample survey, year 2022-23. Variable Levels lasso knock. Male 1=yes, 0=no 1 1 # brothers ordinal, 5 levels 1 1# sisters ordinal, 5 levels 1 1 At home, you have:
quiet space 1=yes, 0=no 1 0.9 computer 1=yes, 0=no 1 1 personal desk 1=yes, 0=no 0.7 0.3 software 1 =yes, 0=no 0 0 internet connection 1 =yes, 0=no 1 1 personal room 1=yes, 0=no 1 1 classical books 1=yes, 0=no 0 0 artworks 1=yes, 0=no 0 0 technical manuals 1=yes, 0=no 0 0 dictionary 1=yes, 0=no 1 1 personal tablet 1=yes, 0=no 1 1 smartphone 1=yes, 0=no 1 1# books ordinal, 5 levels 1 1 Student origin, language
Student born in Italy 1=yes, 0=no 1 1 Immigrant staus 1=native; 2=1st gen imm.; 3=2nd gen imm. 0 0 Italian language at home 1=yes, 0=no 1 1 Dialect spoken at home 1=yes, 0=no 1 1 Italian used with friends 1=yes, 0=no 1 1 Parents
Father born in Italy 1=yes, 0=no 0.4 0.2 Mother born in Italy 1=yes, 0=no 0 1 Father’s
education 1 =comp., 2=high sch., 3=college, 4=master+ 1 1 Mother’s education 1=comp.,
2=high sch., 3=college, 4=master+ 1 1 Father’s occupation 1=unenpl. 2=manager, clerk
3=self-employed 1 1 4=blue coll. 5=professional 6=housew., retir.
Mother’s occupation 1 =unenmpl. 2=manager, clerk 3=self-employed 1 1 4=blue coll.
5=professional 6=housew., retir.
Student career
Nursery school (for pupils aged 3-5 years) 1=yes, 0=no 1 1 Regular student 1=yes, 0=no 1 1 School weekly hours>30 1=yes, 0=no 1 0 School area 1=NW; 2=NE; 3=Cent.; 4= South; 5= S-lsl. 1 1
11
References
[1]		R. Tibshirani. Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society, Series B, 58:267-288, 1996.
[2]		J. Taylor and R. J. Tibshirani. Statistical learning and selective inference. Proceedings of the National Academy of Sciences, 112:7629-7634, 2015.
[3]		E. Candès, Y. Fan, L. Janson, and J. Lv. Panning for gold: Model-X knockoffs for high dimensional controlled variable selection. Journal of the Royal Statistical Society, Series B, 80:551-577, 2018.
[4]		Z. Xie, Y. Chen, M. von Davier, and H. Weng. Variable selection in latent variable models via knockoffs: an application to international large-scale assessment in educa tion. Journal of the Royal Statistical Society Series A, 00:1-25, 2023.
[5]		Z. Ren, Y. Wei, and E. Candès. Derandomizing knockoffs. Journal of the American Statistical Association, 118:948-958, 2023.
[6]		R. J. A. Little and D. Β. Rubin. Statistical Analysis with Missing Data. 2nd. Wiley Series in Probability and Statistics. Wiley, 2002.
[7]		M. Kormaksson, L. J. Kelly, X. Zhu, S. Haemmerle, L. Pricop, and D. Ohlssen. Se quential knockoffs for continuous and categorical predictors: with application to a large psoriatic arthritis clinical trial pool. Statistics in Medicine, 40:3313-3328, 2021.
[8]		M. R. Zimmermann, M. Baillie, M. Kormaksson, D. Ohlssen, and K. Sechidis. All that glitters is not gold: type-1 error controlled variable selection from clinical trial data. Clinical Pharmacology & Therapeutics, 115:774-785, 2024.
[9]		M. Yuan and Y. Lin. Model selection and estimation in regression with grouped vari ables. Journal of the Royal Statistical Society Series B: Statistical Methodology, 68:49- 67, 2006.
[10]		S. van Buuren and K. Groothuis-Oudshoorn. mice: Multivariate Imputation by Chained Equations in R. Journal of Statistical Software, 45:1-67, 2011.
Invited session IPS01 - CLADAG - Advances in statistical modeling of educational data
A latent class model for item responses and
response times
Daniele Spinelli1, Fulvia Pennoni1, Francesco Bartolucci2, Giorgio Vittadini1
Department of Statistics and Quantitative Methods, University of
Milano-Bicocca, Italy
2Department of Economics, University of Perugia, Italy
A latent class model for item responses and response times
Daniele Spinelli, Fulvia Pennoni, Francesco Bartolucci, Giorgio Vittadini
Abstract We illustrate a latent class item response theory model designed to analyze both response accuracy and response times within the framework of computer-based tests admin istered in the educational setting. The model extends the generalized linear item response theory framework, in which response accuracy and response times are modeled indepen dently and linked through cross-relations, by incorporating a flexible latent class structure. In this article, we outline the methodological approach. The forthcoming application of the model will evaluate item difficulties and students’ abilities using a sample of grade 10 stu dents involved in the INVALSI Mathematics test administered during the 2017-2018 school year.
Keywords: INVALSI data, Item Response Theory, Latent Class, Response Accuracy, Re sponse Times
1.		Introduction
The National Institute for the Evaluation of the Education and Training System (INVALSI) is a public research institution tasked with systematically assessing the overall quality of the educational system in Italy. INVALSI yearly administers standardized tests to evaluate students’ skills and learning outcomes in Italian, Mathematics, and English. These tests are conducted across grade levels 2, 5, 8, 10, and 13. An analysis of these data can be found, among others, in [1]. For grades 8, 10 and 13, INVALSI employs computer-based tests that enable the collection of data on both response accuracy and response times. While INVALSI currently applies a Rasch model to analyze response accuracy, response times are not yet modeled. However, modeling response times along with accuracy gives more complete information on items and test takers. Indeed, this information is useful to improve test design, item selection, and identification of patterns in response behavior [2].
In the item response theory literature, Bungaro et al. [3] used a Bayesian joint hierarchi cal model [2, 4] that defines separate submodels for responses and response times to analyze the INVALSI Mathematics test data for grade 10 students. In the present paper, we use the same dataset and estimate a model that incorporates latent classes to capture different levels of the students’ abilities in terms of both accuracy and speed.
2.		Model
Let Yij denote the binary response variable equal to 1 for a correct response provided by individual i - 1, . . . , η to item j = 1, . .., r and to 0 otherwise, and let Tij be the corre sponding response time. The random vectors of responses and response times for individual i are denoted by Y;= (Y11, ..., Yr) and T = (T1, ..., Tir) and, in general, realizations of random variables and vectors are denoted by lower case letters.
In the present framework we adopt a discrete latent variable approach [5] assuming
Invited session IPS01 - CLADAG - Advances in statistical modeling of educational data
existence of a latent variable U, with k levels, corresponding to latent classes, for every individual i so that variables Yij and Tij are conditionally independent given U;. Moreover, as in the Rasch model, we assume that the conditional distribution of every Y given U,= u is of Bernoulli type with success probability
e
Pju =e u~Pj
1 + e°-8, j = 1,..., r,
where 9 is the ability level of individuals in latent class u and βj is the difficulty level of item
j. We also assume that the conditional distribution of Tij given U = u is of exponential type
with parameter
E u T,
where ξυ is the speed of individuals in class u and TiS a corresponding parameter referred to item j. For every individual i, the conditional distribution of T and Y given U = u has density	A Uy
Ajue jut P 11
Y	■ (1 - n\1-yj 7lux'MIU/’
Vi) - J=1
while the corresponding density, that is, the density of the manifest distribution, is
1
, XK
f(t, y) =	,
u= Tfty;),
where TTy = p(U; = u) is the weight of latent class u. Given the observed data collected in the vectors t; and yi,i = 1,... , n, under the assumption of independence between individuals, the proposed model has log-likelihood
. Xn	log f(t, y), (1)
where φ is the vector of all model parameters.
2.1		Expectation-Maximization Algorithm for Parameter Estimation
To maximize e(q), we suggest the Expectation-Maximization (EM) algorithm [6]. The
complete-data log-likelihood corresponding to (1) is	
γ X"u=1 775 — {\Φ) - /=1	Ziulog(^) +	
+	7=1	Is
0=1	ZiuX/=1		
Xn +	7=1
Χκ	u=1
or
Ziu X 7-1	L(@u -j)-
Iog(1 + e°,-d)	(&-- ti^u-h (2)	
		+		

where Ziu is a binary indicator variable for the event U, = u, given the observed data and the current value of the parameters. The EM algorithm alternates the following two steps
until convergence:
15
•		E-step: compute the expected value of the complete-data log-likelihood. This amounts to substitute each Ziuin (2) with the corresponding posterior expected value
Ziu =πΜ, Yi)
f (t, y)
The resulting function is denoted by (o).
•		
Z iu·

M-step· maximize f(d) with respect to φ to update the model parameters. As the three terms at the right-hand side of (2) have zero cross-derivatives, they can be maximized separately. Specifically, for the class weights we have an explicit solution, that is:
For the parameters involved in the model for the response probabilities, it is necessary to use an iterative algorithm that maximizes Vn X"u=1	zLX)= 1	- log(1 +
X i= 1 e°b-6 )];

/-1
3. Data
Ziu X/=1

similarly, to update the parameters involved in the model for the response time we adopt an iterative algorithm that maximizes
(§ -1- t,e5-).
u =1
The model outlined in the previous section will be applied to analyze the responses
provided by a sample of grade 10 students during the 2017-2018 school year. The test
bank includes

Figure 1: Distributions of the number of correct responses and of the total test time.
16
Invited session IPS01 - CLADAG - Advances in statistical modeling of educational data
Variable Proportion
Year of Birth 1999 (or earlier) 0.007
2000 0.037
2001 0.133
2002 0.751
2003 0.072
Sex Male 0.528
Female 0.472
Place of Birth Italy 0.926
EU 0.026
Other 0.047
Location North - West Italy 0.202
North - East Italy 0.211
Central Italy 0.195
Southern Italy 0.292
Islands 0.099
Table 1: Descriptive statistics of the observed demographic characteristics of the students.
143 items, which are used to generate 12 test forms, each comprising 35 items administered to the students. The INVALSI Mathematics test sample includes 41,405 students. The median number of correct responses is 17 out of 35, while the median test duration is 64.50 minutes; the linear correlation coefficient between the number of correct responses and total test duration is 0.40. Figure 1 shows the empirical distributions of the number of correct responses and total test time. Table 1 summarizes the main observed demographic characteristics of the students.
4.		Final Remarks
The application of the latent class item response theory model to the INVALSI Mathematics test data is expected to complement the work of Bungaro et al. [3] by identifying unobserved homogeneous clusters that represent distinct ability patterns for both accuracy and response times. For instance, a latent group might exhibit high accuracy with low response time, while another may demonstrate low accuracy and low response time. The proposed model gener alizes the model in [7] by incorporating response times, providing a more flexible alternative to methods that assume bivariate normality for time-ability and response-ability, such as the one proposed in [8].
17
References
[1]		Francesco Bartolucci, Fulvia Pennoni, and Giorgio Vittadini. Assessment of school performance through a multilevel latent Markov Rasch model. Journal of Educational and Behavioral Statistics, 36:491-522, 2011.
[2]		Wim J Van der Linden. A hierarchical framework for modeling speed and accuracy on test items. Psychometrika, 72:287-308, 2007.
[3]		Luca Bungaro, Marta Desimoni, Mariagiulia Matteucci, and Stefania Mignani. Jointly exploring mathematics ability and speed in large-scale computer-based testing. Statis tical Methods & Applications, 33:1429-1450, 2024.
[4]		Jean-Paul Fox and Sukaesi Marianti. Joint modeling of ability and differential speed using responses and response times. Multivariate Behavioral Research, 51:540-553, 2016.
[5]		Francesco Bartolucci, Silvia Pandolfi, and Fulvia Pennoni. Discrete latent variable
models. Annual Review of Statistics and its Application, 9:425-452, 2022.
[6]		Arthur P. Dempster, Nan M. Laird, and Donald B. Rubin. Maximum likelihood from incomplete data via the EM algorithm (with discussion). Journal of the Royal Statis tical Society. Series B, 39:1-38, 1977.
[7]		Francesco Bartolucci, Silvia Bacci, and Michela Gnaldi. MultiLCIRT: An R package for multidimensional latent class item response models. Computational Statistics & Data Analysis, 71:971-985, 2014.
[8]		Dylan Molenaar, Daniel Oberski, Jeroen Vermunt, and Paul De Boeck. Hidden Markov item response theory models for responses and response times. Multivariate Behavioral Research, 51:606-626, 2016.
Invited session IPS01 - CLADAG - Advances in statistical modeling of educational data
Exploring factors affecting gender gap in
university student performance
Michele La Rocca1, Marcella Niglio1,
Marialuisa Restaino1, Maria Prosperina Vitale2
1Department of Economics and Statistics, University of Salerno
2Department of Political and Social Studies, University of Salerno
19
Exploring factors affecting gender gap in university student performance Michele La Rocca, Marcella Niglio, Marialuisa Restaino, Maria Prosperina
Vitale
Abstract In recent years, exploring the determinants that can influence student achieve ment in higher education has received much attention. Empirical studies have found that the most important factors affecting student performance are sociodemographic characteristics and attitudes, family context, high school grades, social interactions among peers, and geo graphical areas. This contribution investigates university students’ performances, aiming to capture the presence of the gender gap. University performance is measured by the number of ECTS credits students earn during the first year, representing an essential stage of their career path. Starting from a cohort of students enrolled in degree programs offered by an Italian university, the primary purposes are to estimate the probability of getting at least a certain number of credits at the end of the first year as well as to capture if there are any differences in performance between male and female also investigating the factors affecting these results. Secondary data obtained from the Italian National Student Archive are used to estimate statistical models that catch the effect of contextual and individual factors on student performance.
Keywords: students’ performance, gender gap, regression models, machine learning
1.		Introduction
Forecasting student performance and success is an increasingly important goal in educational domain (from primary school to university) and is a significant challenge for higher education institutions (HEIs).
Several contributions investigate how various approaches, such as deep learning paradigms, machine learning, and Educational Data Mining (EDM) techniques, may improve the com prehension and prediction of students performance [1, 2].
Different attributes and factors are associated with predicting students’ performance and success [3]. For the Italian higher education system, the studies can be distinguished into two main groups: a) those that account for students’ social and demographic characteristics (among others, [4]); and b) those that account for their previous school performance and/or psychological and subjective features (among others, [5]).
Moreover, [5] underlined that the impact of the determinants varies (in terms of extent and direction) according to the context (economic, social, political, demographic, etc.). The data collected on educational processes can be analyzed by the EDM methods. They can be used i) to evaluate the activities of successful students and those who are at risk of failure, ii) to develop corrective strategies for improving the student’s academic performance, identifying slow learners, and reducing the risk of failure and/or dropout, and iii) to assist educators in the development of pedagogical and teaching methods.
Thus, an early prediction of (in)success may include assessment methods to support students by proposing appropriate corrective strategies and policies in this field [6].
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Invited session IPS01 - CLADAG - Advances in statistical modeling of educational data
Given this framework, in this work, we will focus on analyzing and predicting the stu dents’ performance in bachelor’s degrees. The student’s performance is measured by fixing a threshold on the total number of gained credits (ECTS) after the first academic year. The chosen threshold is associated with that requested for computing the indicators in the An nual Review Report by the Italian National Agency for the Evaluation of Universities and Research Institutes (ANVUR), and it is equal to 40 ECTS. Thus, the focus is to estimate and predict the probability of having at least 40 ECTS by the first academic year. Moreover, an associated task is determining which background students’ characteristics might influence their performance and detecting whether a gender gap exists in reaching the threshold of 40 ECTS among the disciplinary areas/courses of study.
Given that several statistical models and techniques are used for studying the student’s performance, the primary purpose is to assess whether (and which) statistical models should have a better performance for predicting academic success. Then, a secondary purpose is to evaluate whether the profile of a student at the beginning of his/her academic career is predictive of his/her success.
The manuscript is structured as follows. Section 2 describes the education data used for the analysis. The statistical models implemented for analyzing students’ performance are also briefly outlined. Finally, Section 3 concludes by showing the main results of the data analysis.
2.		Data and methods
The data used in this analysis are drawn from MOBYSU.IT [7]1 database. It is a longitudinal dataset on university careers from 2008 to 2022 and includes several details on students’ socio-demographic characteristics and high school performance. This dataset is merged with the INVALSI (National Institute for the Evaluation of the Education and Training System) [7] database, which contains the results of tests that are administered annually to students at five educational levels (grades 2, 5, 8, 10, and 13) to evaluate their proficiency in mathematics, Italian language skills, and English reading and listening skills.
Our analysis concerns 4,507 students who enrolled in one of the bachelor and single-cycle degrees offered by the University of Salerno (located in the South of Italy) in the academic year 2019-2020 (and, consequently, received their diplomas in 2018-2019).
The variables considered as potential features for studying and predicting the students’ performance are listed below:
•		total number of university credits (ECTS) gained by the first academic year, which ranges from 0 to 60;
1The data used in this study have been processed in accordance with the RESEARCH PROTOCOL FOR THE STUDY “From high school to the job placement: analysis of university careers and university mobility from Southern to Northern Italy" among the Ministry of University and Research, the Ministry of Education and Merit, the University of Palermo as the lead institution, and the INVALSI Institute. The reference researcher is Maria Prosperina Vitale.
21
•		course of study where students have enrolled, that is represented by disciplinary areas, a categorical variable with four categories (Arts, Literacy, Education; Economics, Law, Social; Health, Agriculture, Veterinary; Stem);
•		gender of the enrolled student (male and female);
•		age at enrollment, transformed into a binary variable that takes value 1 if the year of enrollment is equal to the year of diploma. This variable captures whether a student has a (ir)regular path during high school;
•		high school diploma, categorized as Classical diploma, Scientific Diploma, Professional Diploma, Technical Diploma, Teaching Diploma, Other Diploma;
•		high school final mark, which ranges from 60 to 101, where 101 identifies “100 cum laude”;
•		province where the student resides, a categorical variable with 6 categories (Salerno, Avellino, Napoli, Caserta, Benevento, Outside Campania);
•		distance (in km and minutes) between the city of residence and the university2;
•		Far-away students, obtained by combining the distance in minutes and province of residence. It is a categorial variables with 9 categories: Salerno < 30/> 30 minutes, Avellino < 30/> 30 minutes, Napoli < 30/> 30 minutes, Caserta, Benevento, Outside Campania;
•		the Economic, Social and Cultural Status (ESCS) of student, class, and high school3;
•		type of diploma of students’ parents, with 4 categories (Middle school diploma or lower; High school diploma; Professional qualification, Degree);
•		INVALSI test score for Italian for the 13th grade;
•		INVALSI test score for Mathematics for the 13th grade;
To obtain a homogeneous set of students consistent with our research goal, we filter the data by removing students: i) who are not enrolled for the first time at university; ii) who have missing data in the potential features; iii) who have non-zero ECTS in the enrollment (for some unspecified reasons); iv) who have more than 60 ECTS, that is a standard number of ECTS for the first year or the academic regulation of the course of study (due to some errors in the database); v) who have a foreign high school diploma (because the diploma mark is missing; vi) who do not have the ESCS; and vii) who do not have the INVALSI test score (for mathematics and Italian).
Since the variable of interest for our aims is binary and takes value 1 if the student has at least 40 ECTS at the end of the first academic year and 0 otherwise, we want to predict the probability of reaching the threshold, given a vector of student characteristics x: Pr(Y = 1|x).
2The data on the distance between all pairs of Italian towns is downloaded from the ISTAT website, and is available at https://www.istat.it/it/archivio/157423
3https://www.invalsiopen.it/indicatore-escs-valutazione-equa/
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Invited session IPS01 - CLADAG - Advances in statistical modeling of educational data
Table 1: Measure of performance for the three statistical models.
Logistic Tabnet Random Forest
Accuracy
Estimate 0.7253 0.7020 0.6858
c.i. - lower 0.6862 0.6621 0.6455
c.i. - upper 0.7620 0.7397 0.7242
AUC
Estimate 0.7807 0.7019 0.7212
c.i. - lower 0.7411 0.6563 0.6780
c.i. - upper 0.8203 0.7475 0.7644
Sensitivity or TP-rate
Estimate 0.9211 0.9181 0.8772
c.i. - lower 0.8872 0.8838 0.8376
c.i. - upper 0.9473 0.9449 0.9100
Specificity or TN-rate
Estimate 0.4140 0.3581 0.3814
c.i. - lower 0.3474 0.2941 0.3162
c.i. - upper 0.4829 0.4262 0.4499
The vector of covariates includes Diploma Mark, (Ir)regular career, High school type, Gender, Disciplinary areas, Far-away students, ESCS score, math test score, Italian test score. The statistical models considered for estimating the probability of success are the logistic regression [8], random forest [9], TabNet (Deep Neural Network for Tabular Data) [10], and their performance is compared by some accuracy measures.
3.		The main results The dataset considered for the analysis consists of 54.27% female students and 45.73% male students. Moreover, 21.41% of students attended a course in the disciplinary area of “Arts, Literacy, Education”, 33.30% are students in “Economics, Law, Social”, 12.80% belong to “Health, Agriculture, Veterinary”, and the remaining 32.48% are STEM students.
Then, regarding the event of interest Υ , more than 62% of students earned at least 40 ECTS at the end of the first academic year.
We recall that the aim is twofold. First, we assess whether (and which) statistical models should perform better in predicting academic success. Second, we evaluate whether a student’s profile at the beginning of his/her academic career predicts his/her success.
For the first aim, Table 1 shows the accuracy measures (accuracy, AUC, sensitivity and specificity) computed for the three models (logistic regression, random forest and Tabnet), revealing that logistic regression outperforms the other two by looking at the accuracy, AUC and sensitivity (that is the probability of classifying correctly the true positive, i.e. students with at least 40 ECTS). At the same time, Tabnet has a better performance in terms of specificity (that is, the probability of classifying correctly the true negative, i.e. students with less than 40 ECTS), which is lower than the other two. However, the difference in the performance of the three techniques is not so marked, given that their AUC values are greater than 0.70, underlining a fair performance.
For the second aim, the model formulation also considered the interaction between the
23

(c). Logistic regression
Figure 1: Variable importance for a) Random Forest, b) Tabnet, c) Logistic regression

students’ characteristics and gender to assess whether a gender gap exists in their academic performance. For capturing the relevance of covariates, their importance for the three models is shown in Figure 1, where the top ten covariates are displayed. The order of the important variables changes according to the model, concluding that each model seems to capture different aspects of academic success.
24
References
[1]		Liu Y., Huang Z., and Wang G. Student learning performance prediction based on online behavior: an empirical study during the covid-19 pandemic. PeerJ Computer Science, 9:e1699, 2023.
[2]		M. Ya gci. Educational data mining: prediction of students’ academic performance
using machine learning algorithms. Smart Learning Environments, 9:2-19, 2022.
[3]		Amirah Mohamed Shahiri, Wahidah Husain, and Nur’aini Abdul Rashid. A Review on Predicting Student’s Performance Using Data Mining Techniques. Procedia Computer Science, 72:414-422, 2015.
[4]		Grilli L., Rampichini C., and Varriale R. Statistical modelling of gained university credits to evaluate the role of pre-enrolment assessment tests: An approach based on quantile regression for counts. Statistical Modelling, 16:47-66, 2015.
[5]		Adelfio G., Boscaino G., and Capursi V. A new indicator for higher education student performance. Higher Education, 68:653-668, 2014.
[6]		Waheed H., Hassan S.U., Aljohani N.R., Hardman J., Alelyani S., and Nawaz R. Pre dieting academic performance of students from VLE big data using deep learning models. Computers in Human Behavior, 104:106189, 2020.
[7]		MOBYSU.IT. Database MOBYSU.IT, Italian university students’ mobility. The Ital ian Ministry of University and Research agreement with Palermo (responsible scien tifico), Cagliari, Florence, Naples-Federico II, Sassari, Siena and Turin universities. Source: ANS-MIUR/CINECA. 2016.
[8]		Collet D. Modelling Binary Data. 2nd ed. Chapman & Hall/CRC: Boca Raton, USA, 2003.
[9]		Trevor Hastie, Robert Tibshirani, and Jerome Friedman. The Elements of Statistical Learning. Springer Series in Statistics. Springer New York Inc., 2001.
[10]		Sercan Omer Arik and Tomas Pfister. TabNet: Attentive Interpretable Tabular Learn ing. http://arxiv.org/abs/1908.07442, 2020.
26
Invited session IPS02 -
SIS-ySIS - Advanced Methods
for
Assessing Environmental
Impact and Green Innovation
Organiser: Giorgia Zaccaria
Chair: Marco Mingione
Discussant: Federico Pasquale Cortese
•		M. Bottazzi Schenone, and M. Vichi - Clustering Hierarchical Disjoint Principal Com ponent Analysis for Environmental Impact Assessment of Food Products
•		C. Morelli, P. Maranzano, and P. Otto - Spatiotemporal clustering of GHGs emissions in Europe: exploring the role of spatial component
27
Clustering Hierarchical Disjoint Principal
Component Analysis for Environmental
Impact Assessment of Food Products
Mariaelena Bottazzi Schenone1, Maurizio Vichi1
1Department of Statistical Sciences, Sapienza University, Piazzale Aldo Moro
5, Rome, Italy
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Invited session IPS02 - SIS-ySIS - Advanced Methods for Assessing Environmental
Impact and Green
Innovation
Clustering Hierarchical Disjoint Principal Component Analysis for Environmental
Impact Assessment of Food Products
Mariaelena Bottazzi Schenone, Maurizio Vichi
Abstract This study evaluates the environmental impacts of food production by propos ing a new methodology named Clustering Hierarchical Disjoint Principal Component Analy sis that allows for a deep understanding of multivariate data and simplifies their interpreta tion by using clustering and a hierarchical set of Specific Composite Indicators (SCIs) that arrive to a General one (gCI). In fact, by utilizing data encompassing 43 food items, the research constructs SCIs for environmental dimensions such as land use, water consumption, and greenhouse gas emissions, which are synthesized into a gCI representing the overall foods environmental impact. The methodology also identifies significant clusters of food items, re vealing variations in environmental burdens and offering insights into sustainable dietary choices. The proposed methodology aims to guide policy and consumer decisions towards reduced environmental footprints in food production.
Keywords: Environmental impact, food sustainability, composite indicators, clustering
1.		Introduction
The environmental impacts of food production are a pressing global concern, encompassing challenges such as climate change, biodiversity loss, water scarcity, and land degradation. For this reason, the body of scientific literature on this field has grown more than tenfold over the past 15 years.
For our analysis, we will employ data from the Our World in Data study of [1] on greenhouse gas emissions, land use, water consumption, and eutrophying emissions for a set of 43 food items.
The current state-of-the-art in environmental impact assessment relies heavily on method ologies such as Life Cycle Assessment (LCA). LCA is widely recognized as a robust tool for evaluating the cradle-to-grave environmental impacts of food production, capturing processes from raw material extraction to end-of-life disposal. However, while LCA excels at providing granular insights, it often struggles to present results in a form that is accessible to policy makers and consumers, especially when dealing with multi-dimensional environmental data. Composite indicators, by aggregating multiple dimensions into a single metric, may help in this direction. However, traditional approaches to composite indicators’ construction, such as weighted summation, may oversimplify the complex interdependencies between environ mental variables, which may show a hierarchical and multi-dimensional nature. Innovative methodologies like Hierarchical Disjoint Principal Component Analysis [2] have emerged to address these gaps. HDPCA introduces a framework that separates variables into a hi erarchical structure of disjoint components, enabling both reflective (shared variance) and formative (distinct variance) modeling approaches. Building on these developments, this study introduces the Clustering Hierarchical Disjoint Principal Component Analysis (CHD PCA), with the goal of assessing the environmental impact of food systems. CHDPCA
29
extends HDPCA by incorporating clustering directly into the analysis, facilitating the si multaneous identification of Specific Composite Indicators (SCIs) for distinct environmental dimensions and the aggregation of these into a General Composite Indicator (gCI) repre senting overall environmental impact. The clustering component further reveals patterns in food production, offering actionable insights for sustainable dietary and policy decisions.
2.		Methodology
This section describes the proposed CHDPCA methodology. Given a (n x J) data matrix X, it aims to cluster units into K groups and construct a (n x 1) vector g representing a gCI, which is obtained through a mixed reflective and formative approach.
HDPCA [2] is a method for hierarchical dimension reduction, where Q disjoint principal components are constructed to maximize the variance of disjoint subsets of observed vari ables. The methodology builds a hierarchy of disjoint components, starting from a more granular level of specific components and aggregating them into higher-order ones, ulti mately leading to a general component (g). A key feature of HDPCA is its ability to model both reflective (components reflecting shared variance) and formative (components formed by uncorrelated variables) relationships at different levels of the hierarchy. A critical aspect is its flexibility to test correlations at each hierarchical level, transitioning between reflective and formative models based on correlations’ statistical significance. The HDPCA can be formally specified by Q - M + 1 simultaneous equations
X = Y,VB,+ Eqq = Q,...,M,(V)
where M is the first bottom-up level of the hierarchy at which the correlation among dis joint principal components turns out to be not statistically significant. If M = 1, the hierarchy is reflective; if M > 1 (up to Q), the hierarchy is reflective/formative. Ma trices V2 are (J χ q) membership matrices defining a partition of the J observed vari ables into q groups, each one represented by a (disjoint principal) component. They are subject to the binary and row stochasticity constraints, and they must be nested, i.e. Vg-1 = [Va \ (vq-1(q) Vq(q), Vq-^q-V)], where Vg-1(q-1) = Vq-1(q) + Vq(q) and with v3(b) denoting the a column of V2. Matrices B4 are diagonal matrices of order J, whose di agonal elements b (q), j = 1,... , J, represent the unique loading of each observed variable on the corresponding disjoint principal component according to Vq. They must be semi orthogonal: V B BNg = I,. Finally, Yg are the (η χ q) component score matrices. On the whole, the equations of model (1) aim at reconstructing the data matrix by means of a decreasing number of disjoint principal components Y0 = XB V2 q = M,..., Q, linked by the semi-orthogonality constraint.
The choice of M is critical to determine the remaining hierarchical levels of the model. Indeed, M € [2, Q] is the first bottom-up level at which no statistically significant correla tion occurs among the disjoint principal components. Suppose the correlation among the M disjoint principal components results to be not statistically significant. In that case, the
30
Invited session IPS02 - SIS-ySIS - Advanced Methods for Assessing Environmental Impact and Green
Innovation
remaining part of the hierarchy is modeled via multiple linear regression, i.e. following a formative approach. HDPCA carries out a test for the identity of covariance (or correlation) matrices proposed by [3] in a nonparametric framework. The null hypothesis to be tested is H0: RY, = lQ, versus Hy: RY = Iq, for each q = Q, ..., 2, where Ry is the correlation matrix of the q disjoint principal components. If the null hypothesis is rejected for all hier archical levels, M is settled on one and the equations in (1) model the whole hierarchy. If the null hypothesis is not rejected at the Mth level of the hierarchy, the correlation among the M disjoint principal components is not significant, and these components are supposed to form a general concept g, rather than reflect other “higher-order” disjoint principal com ponents. The model that formalizes the relationship between the M uncorrelated (or low correlated) disjoint principal components and the general concept g is the following multiple linear regression g = YMC + €, where c is the (M x 1) regression coefficient vector and € is the (n x 1) error vector. It is worth noting that in order to apply the multiple linear regression model, the response variable, that is, the hypothesized general concept g, needs to be quantified. When M > 1, g is assumed to be the first (standard) principal component of the J observed variables. Thus, the relationship between the general concept g and the principal components is inspected by estimating the regression coefficients.
The proposed methodology extends the formative part of HDPCA, namely the con struction of g once a non-significant correlation between M disjoint principal components (Yw) has been found. Instead of using a multiple linear regression that relies on the first principal component, the general composite indicator and the corresponding weights for its construction are directly estimated from YM, by best reconstructing the M disjoint SCIs, following the second level model proposed in [4]: ΥΜ = gc + EYM , where c is the (M x 1) vector of the weights and EYM is the error regarding the M disjoint princi pal components. This approach can be viewed as formative because it uses a PCA-based method that relies on a set of M uncorrelated first-order components. In this case, the first principal component of the M first-order components will be more heavily influenced by those components that have higher variances. Essentially, it represents a weighted “av erage” of these first-order components. The Least-Squares (LS) estimation of g and c is obtained minimizing ||YM - gc||2, thus, the optimal expressions for the general composite indicator and for the weights of the disjoint principal components to obtain it are given by g = YM(c" )* = Yyc (cc°)1, c° = ym(9")*. It has to be noted that, for C = 1M, the gCI reduces to g M = YM(1 M)* ^^(Yi + ... + ΥΜ), the arithmetic mean of the M disjoint components, i.e. a linear combination with equal weights M If g “ is multiplied by the con stant (c" c“)(c" 1M) 1, we have g WM = YMc (c 1 M) 1, the weighted arithmetic mean of the disjoint components.
Furthermore, a K-Means clustering is applied on the estimated g, thus obtaining a rank ing of units in equivalence classes where negligible differences in terms of g are not considered. This is done optimizing the norm llg-U g|12 with respect to the (n*K) membership matrix U and the (Κ x 1) centroids vector g, with the binary and row stochasticity constraints on U. The number of components Q to retain for variables’ dimensionality reduction is chosen
31
using Kaiser’s rule, while the number of clusters is chosen according to the Gap statistics.
By leveraging the above process, the CHDPCA methodology ensures reliable clustering
and the construction of a meaningful and interpretable Cl.
3.		Real data application
The data utilized in this study refers to the environmental impacts of food. It encompasses a wide range of food products and assesses their environmental impacts in terms of their greenhouse gas emissions, land use, freshwater withdrawals, and eutrophication. The aim of this study is to explore the relationships between these environmental variables to construct SCIs for common dimensions of environmental impact such as land or water consumption. Furthermore, SCIs are aggregated into a gCI, which measures each food’s overall environ mental impact. Finally, the clustering on the identified gCI helps uncovering which groups of food have the highest and the lowest environmental impact. The CHDPCA methodology has been applied considering Q=3 components for the variables and Κ = 7 clusters for the units. It returned a value of M equal to 2: this means that there exist three distinct latent concepts of food environmental impact that are then combined to return an Envi ronmental Impact Indicator (Ell). Figure 1 shows the estimated correlations, between the observed variables and the estimated disjoint components at the bottom level, and between the disjoint components and the Ell at the higher level.
Ell
0.91	0.23	0.80
L&E	Water	Eutr.
0.93	0.94	0.72	0,81	0.94 0.94
0:98 . 0.90 0.83 .\
Gas LI Lp Fk Fp Sii Sp Ex Ep
Figure 1: Correlations among observed variables and CHDPCA components.
The first component (L&E) in Figure 1 is defined by variables related to land use (land use per 1000kcal, Lk and land use per 100g protein, Lp) and greenhouse gases (GHGs) emissions (Gas), indicating that this component captures the environmental impact of food production concerning land occupation and emissions. The second component (Water) is strongly correlated with water usage metrics (Freshwater withdrawals per 1000kcal, Fk; Freshwater withdrawals per 100g protein, Fp; Scarcity-weighted water use per 1000kcal, Sk and Scarcity-weighted water use per 100g protein, Sp), underscoring its focus on water consumption intensity. Lastly, the third component is exclusively defined by eutrophying emissions (Eutr.). Eutrophying emissions (Eutrophying emissions per 1000kcal, Ek and Eu trophying emissions per 100g protein, Ep) refer to substances released into the environment that contribute to eutrophication, a process where water bodies, such as lakes, rivers, and oceans, experience an over-enrichment of nutrients. Each of the components is unidimen sional, ensuring that each identified SCI meaningfully represents a distinct aspect of the
32
Invited session IPS02 - SIS-ySIS - Advanced Methods for Assessing Environmental Impact and Green
Innovation
environmental impact of food. By looking at the CHDPCA higher-order part in Figure 1, we see that the Land use & Emission component is the one that mostly contributes to the construction of the EEl, while the water usage component shows the lowest correlation.
Another output of the CHDPCA methodology is the clustering of foods based on the obtained EEl. Results are reported in the bullet list below, foods are ordered from the one with the highest EEl to the one with the lowest environmental impact.
-		: Beef (beef herd), Lamb & Mutton;
-		Cluster 2: Beef (dairy herd), Coffee, Dark Chocolate, Cheese, Fish; -	: Tomatoes, Berries & Grapes, Apples, Other Fruit, Soybean Oil, Milk, Pig Meat; - Cluster 4: Shrimps, Wine, Soymilk, Brassicas, Tofu, Barley (Beer), Rice, Other Vegetables; -
: Poultry Meat, Nuts, Olive Oil, Citrus Fruit, Bananas, Eggs, Wheat & Rye (Bread), Maize (Meal), Cane Sugar, Palm Oil;
-		Cluster 6: Beet Sugar, Sunflower Oil, Rapeseed Oil, Cassava, Groundnuts, Other Pulses, Oatmeal, Onions & Leeks, Potatoes;
-		Cluster 7: Root Vegetables, Peas.
By looking at the top and bottom position of the obtained foods ranking, we see that the item with highest environmental impact is Beef (beef herd). In fact, raising cattle requires large amounts of land for grazing and growing feed crops, often leading to deforestation, especially in sensitive ecosystems. Cattle farming is also extremely water-intensive, with significant quantities of water required for drinking, growing feed, and processing meat. Ad ditionally, beef production is a major source of GHGs, particularly methane, which cattle release during digestion. The energy-intensive nature of cattle farming, along with its sub stantial waste production, including manure, further contributes to soil degradation, water pollution, and biodiversity loss. On the other hand, Peas are identified as the food with the lowest environmental impact, due to their minimal resource requirements and their role in promoting soil health. In fact, as a nitrogen-fixing legume, peas naturally enrich the soil by converting atmospheric nitrogen into a form that plants can use, reducing the need for synthetic fertilizers and minimizing chemical inputs. They also require relatively little water compared to many other crops, making them a more sustainable option in areas with water scarcity. Furthermore, peas are a low-input crop that grows quickly, requiring less land and energy to produce than resource-intensive foods like meat. Their cultivation also contributes to biodiversity, as they can be grown in rotation with other crops, reducing the need for monocropping and supporting ecosystem balance.
Analysing more in detail the clustering result, we see that Cluster 1 comprises ruminant animal products with the highest environmental impact. These foods are resource-intensive, requiring large amounts of land and contributing heavily to GHGs emissions. Their high feed conversion ratios and methane emissions from digestion make them the most environmentally burdensome category. Cluster 2 groups diverse high-impact foods which have the common characteristic of requiring complex processing or resource-intensive production practices. Foods in this Cluster 3 (fruits, vegetables, oils, dairy, and pork) have moderate environmental impacts. It is worth noting that pork has a smaller environmental footprint than beef due to
33
the biology and efficiency of pigs. Pigs are monogastric animals, meaning they do not produce methane through enteric fermentation like ruminants and this results in significantly lower GHGs emissions. Cluster 4 groups plant-based and aquatic products which are characterized by very high water use (shrimp farming, wine, beer, rice and soybeans production). Some grains, oils, poultry, eggs, and fruits are in Cluster 5, which groups foods with a medium-low environmental footprint, while Cluster 6 is made of plant-based staples (pulses, oils, roots, and tubers), which have a very low impact. Finally, Root Vegetables (e.g., carrots, turnips) and Peas are in Cluster 7: they have have minimal resource requirements and contribute little to GHGs and eutrophying emissions.
4.		Concluding remarks
This study has provided a comprehensive evaluation of the environmental impacts associ ated with food production through the application of the proposed Clustering Hierarchical Disjoint Principal Component Analysis (CHDPCA). The methodology has effectively syn thesized complex environmental data into Specific Composite Indicators (SCIs), reflecting key dimensions such as land use, water consumption, and eutrophying emissions. The ag gregation of these SCIs into a General Composite Indicator (gCI) offers a robust framework for assessing foods’ overall environmental impact. Clustering has been applied to the gCI, further enhancing the analysis by identifying patterns within the general environmental im pact assessments. The future extension of this methodology consists in the simultaneous estimation and clustering of SCIs and gCI. Among the most significant findings, the analysis revealed stark differences in environmental burdens across food clusters. High-impact items, such as beef (beef herd) and lamb, demonstrated substantial environmental costs, driven by intensive land and water usage as well as high greenhouse gas emissions. In contrast, low-impact foods, including root vegetables and peas, highlighted the potential for more sustainable dietary choices due to their minimal resource requirements and ecological ben efits. The gained insights can inform policy-making, promoting shifts toward sustainable food production systems and consumer behavior.
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References
[1]		J. Poore and T. Nemecek. Reducing food’s environmental impacts through producers and consumers. Science, 360:987-992, 2018.
[2]		C. Cavicchia, M. Vichi, and G. Zaccaria. Hierarchical disjoint principal component analysis. ASM Advances in Statistical Analysis, 107:537-574, 2023.
[3]		S. X. Chen, L.X. Zhang, and P.S. Zhong. Tests for High-Dimensional Covariance Ma
trices. Journal of the American Statistical Association, 105:810-819, 2010.
[4]		C. Cavicchia and M. Vichi. Statistical Model-Based Composite Indicators for Tracking
Coherent Policy Conclusions. Social Indicators Research, 156:449-479, 2021.
Spatiotemporal clustering of GHGs emissions in Europe: exploring the role of spatial component
Caterina Morelli1, Paolo Maranzano1, Philipp Otto2 1Department of Economics, Management and Statistics, University of Milano-Bicocca
2School of Mathematics and Statistics, University of Glasgow 36
Invited session IPS02 - SIS-ySIS - Advanced Methods for Assessing Environmental Impact and Green
Innovation
Spatiotemporal clustering of GHGs emissions in Europe: exploring the role of spatial component
Caterina Morelli, Paolo Maranzano, Philipp Otto
Abstract In this study, we propose a novel application of spatiotemporal clustering to regionalised greenhouse gas (GHG) emissions data in Europe. Using a hierarchical clustering methodology, we analyse annual emissions time series by gases and sectors from 1990 to 2022 at the NUTS-2 level. The spatial component, incorporated via geographical distance, is assessed using a newly introduced indicator, the Joint Inertia, which quantifies spatial contribution to group formation. Empirical findings underscore the significance of spatial and temporal dimensions in revealing emission trends and dynamics, highlighting regional heterogeneity tied to economic and industrial factors. These insights provide a foundation for spatiotemporal modelling and support the development of regionally tailored environmental policies.
Keywords: Hierarchical spatiotemporal clustering, Spatial overlapping, Greenhouse gases emissions, European regions NUTS-2.
1.		Introduction
The rise of spatiotemporal data presents significant opportunities for environmental research, enabling detailed analyses through georeferenced datasets derived from remote sensing, GPS, and satellite imagery. While much focus has been placed on modeling pollutant concentra tions [1, 2, 3, 4, 5], the direct analysis of greenhouse gas (GHG) emissions remains underex plored. Understanding these emissions requires innovative approaches, and spatiotemporal clustering provides a powerful tool to uncover spatial and temporal patterns [6, 7].
Spatiotemporal clustering groups data based on shared spatial and temporal attributes, revealing trends and hotspots in emissions tied to industrial activity and economic changes. While popular density-based clustering methods like DBSCAN have been widely applied [8, 9], hierarchical approaches offer greater flexibility, particularly for datasets with multiple variables or complex structures [10, 11].
This paper adopts a spatiotemporal hierarchical clustering method, extending earlier work to include dissimilarity matrices for multiple variables [10, 11]. A novel measure, the Joint Inertia, is introduced to evaluate the spatial component’s contribution to clustering outcomes. Our contributions span both methodological and practical domains: a novel mea sure for evaluating spatial relevance in clustering and insights into GHG emissions dynamics across Europe. These results aid policymakers in crafting localized strategies and statisti cians in developing accurate spatiotemporal models, advancing environmental research and intervention strategies.
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2.		Methodology: spatiotemporal clustering
In our paper we exploit spatiotemporal hierarchical clustering methodology [11], which is an extension of spatial hierarchical clustering proposed by [10] based on Ward algorithm [12]. We denote Dp = [dpi, lp-1,.. ,P -1;ij=1,..,n the dissimilarity matrices for Ρ - 1 variables (non spatial features or time series) and let Dp = [dpj ]/y=1 „ refer to the spatial dissimilarity matrix, typically computed as geodetic distances. We assume that each matrix is normalized
with respect to its maximum value. The goal is to combine these matrices into a single dissimilarity matrix D(a) = PD=1 CpDp using a weighting vector g_= (01, a2,..., ap), such that PP-1 ap = 1, a2 > 0 V p. For each choice of K clusters and the weighting vector a, we apply the Ward hierarchical clustering algorithm to obtain the partition Ρ^·
For each partition PSx = {C1, C2,... , CK}, we can compute the inertia as measures of the within-cluster dissimilarity as follows:
Κ
Wp.(PK) = X	2 ieC W,d
K Cr	k 1 P’1
k=1
X	WjWj i’
where wis the weight of the /-th unit, typically set as W; = 1/n for simplicity. The dissimilarities dp,ij are the elements of the dissimilarity matrix D0, representing the squared distances between units i and j within cluster CK. The sum of these squared distances within each cluster provides the inertia for the clustering solution.
The proportion of explained inertia quantifies how well the partition explains the total dissimilarity within the data. For a given dissimilarity matrix Dp, the proportion of inertia explained by the partition P2K is defined as:
Qp(P4k) = 1 -Wpj(Pk)
Wos(P1y
where WDp(P1) represents the inertia of the dataset when treated as a single cluster, i.e., no partition is applied. The higher the value of QD (P-X ), the better the partition explains the dissimilarities in Dp. This proportion can be seen as a measure of the clustering quality, where a higher explained inertia indicates a more meaningful clustering result. To account for the relative contribution of each matrix, the proportion of explained inertia is normalized for each dissimilarity matrix. The normalized proportion of explained inertia is given by:
~ (DC, 0 (DC y
Q Dp K) = GDpP K)
QD(P K)
where QDp(P K) is the proportion of inertia explained when the clustering is based solely on the feature (or spatial) matrix. This normalization allows for a straightforward comparison of the contribution of each dissimilarity matrix to the clustering process.
The optimal clustering solution is obtained by maximizing the weighted average of the explained inertia across all dissimilarity matrices. For a given K, the weighted average of explained inertia is computed as:
_	P
4 P p=1 WDp(P1),
Q (P-K)- 1 -	/
p	38
P p=1 ^Dp^^
Invited session IPS02 - SIS-ySIS - Advanced Methods for Assessing Environmental Impact and Green Innovation
which represents the overall effectiveness of the partition P-K in explaining the dissimilarity in the combined data. This metric ranges between 0 and 1, with 1 indicating that the partition explains all the dissimilarity in the dataset.
The optimization process involves searching for the optimal weighting vector g that maximizes Q (P9K ) for each K. The best number of clusters K is selected based on the elbow rule with respect to the maximum value of Q (Pe
κ) across the range of possible Κ values, ensuring that the clustering solution best captures the dissimilarities in both spatial and non-spatial data.
The selection of the weighting vector a doesn’t require the spatial component unless it significantly explains the overall dissimilarity. The weight of the spatial component should not be seen as a direct measure of relevance. While increasing ap might seem to increase explained inertia, the relationship is unclear. Instead, a reflects a maximization task, where the spatial component is relevant when included, but redundant when spatial and feature
dissimilarities result in identical clustering.
To assess the spatial component’s role, we examine changes in explained inertia when combining matrices. The normalized proportion of explained inertia quantifies variability in the combined partition relative to a single matrix. The spatial component’s contribution is captured by the Joint Inertia (JI) difference between partitions incorporating spatial and feature dissimilarities. For two matrices, D0 (features) and D1 (spatial), JI is computed as:
JI(PBK) = QDi(P°K) " 1 - QDo(PK) =Qpx(P °g) (P 1. 0 a y K)+ K)
Qoo(P °κ)- 1
For multiple matrices, the multi-matrix Joint Inertia is:
, D-p(F K)

κ) 1
QD_P(P-\ap =0

JIp(P8k) = Q DE(P°K) 1 - Q d-p(p~k)
=QDE(PE) QDp(P°p=1
The Joint Inertia index, ranging from 0 to 1, shows how much the spatial dissimilarity matrix explains inertia in the clustering. A low JI value suggests minimal spatial contribu tion, while a high JI value indicates significant spatial influence in the clustering.
3.		Application
In this section, we present a spatiotemporal clustering application of greenhouse gas (GHG) emissions in different sectors at the regional level in Europe. The emissions are measured in tons per km2of CO2 equivalent, based on data from the EDGAR database and the European Commission’s ARDECO project. The dataset covers yearly emissions from 1990 to 2022 across 234 regions in the European Union. We employ the Dynamic Time Warping (DTW) distance metric for time series dissimilarities [13, 14] and we compute the spatial dissimilarity matrix using the geodetic distance between region centroids.
In the full paper we present empirical findings from emissions by gases and by sec tors, but in this short version we only report clustering results from emissions by sectors,
Map c* wstciinpiys clusters o' emissions by sector

Figure 1: Map of spatiotemporal clusters obtained combining the dissimilarity matrices of the time series of emissions of different sectors between 1990 and 2022, and the geodetic distances across centroids of nuts2 level regions.

including emissions from agriculture, buildings, energy, industry, transport, and waste. Us ing the above described algorithm, we select Κ= 5 according to the elbow rule and a 5,p = (0.20, 0.10, 0.10, 0.20, 0, 0.10, 0.30) as the weight of the dissimilarity matrices respec tively for DAgri DBuild, DEnergy Dind, DTran, Dwaste and Dap- The Joint Inertia of the spatial component in the resulting clustering was found to be 0.56.
In Figure 1, we show a map of the regions belonging to different clusters. Figure 2 presents the average annual emissions per km2for each cluster across the different sectors. The clusters reveal distinct patterns in the emissions dynamics of European regions.
Cluster 1, primarily located in Central Europe, shows stable emission levels that are neither the highest nor the lowest across sectors. Cluster 2, mainly from Eastern Europe, exhibits the lowest emission levels, with decreasing emissions in most sectors, except for transport. Cluster 3, consisting of regions in Belgium, the Netherlands, and some industrial ized areas, has the highest emissions across all sectors except agriculture, with a decreasing trend in the Buildings and Industry sectors. Cluster 4, covering areas like Belgium, the Netherlands, and parts of France and Germany, also shows high agricultural emissions, alongside moderate levels in other sectors. Finally, Cluster 5, which includes regions in Spain, Portugal, Ireland, and parts of France, is characterized by relatively low emissions, with slight increases in the Transport sector and modest reductions in the Energy sector.
These findings highlight that while a small number of regions are responsible for the highest emissions, there is a general trend of decreasing emissions across many sectors,
Invited session IPS02 - SIS-ySIS - Advanced Methods for Assessing Environmental Impact and Green Innovation

Figure 2: Annual average of emission per km2of sectors for spatiotemporal clusters obtained com bining the dissimilarity matrices of the time series of emissions of different sectors between 1990 and 2022, and the geodetic distances across centroids of nuts2 level regions.

signaling positive progress in emission reductions, albeit at varying rates. 41
References
[1]		Calculli C., Passò A., Finazzi F., Pollice A., and Turnone A. Maximum likelihood estimation of the multivariate hidden dynamic geostatistical model with application to air quality in Apulia, Italy. Environmetrics, 26:406-417, 2015.
[2]		Taghavi-Shahri S.M., Passò A., Mahaki B., and Amini H. Concurrent spatiotemporal daily land use regression modeling and missing data imputation of fine particulate mat ter using distributed space-time expectation maximization. Atmospheric Environment, 224:2020.
[3]		Maranzano Ρ., Passò A., Pelagatti M., and Mudelsee M. Statistical modeling of the early-stage impact of a new traffic policy in Milan, Italy. International Journal of Environmental Research and Public Health, 17:2020.
[4]		Maranzano Ρ., Otto Ρ., and Passò A. Adaptive LASSO estimation for functional hid den dynamic geostatistical models. Stochastic Environmental Research and Risk As sessment, 2023.
[5]		Otto P., Fusta Moro A, Rodeschini J., Shaboviq Q., Ignaccolo R., Golini N., Cameletti M., Maranzano P., Finazzi F., and Fassò A. Spatiotemporal modelling of PM 2.5 con centrations in Lombardy (Italy): a comparative study. Environmental and Ecological Statistics, 31:245-272, 2024.
[6]		Derya Birant and Alp Kut. ST-DBSCAN: An algorithm for clustering spatial-temporal data. Data and Knowledge Engineering, 60:208-221, 2007.
[7]		Ansari M. Y., Ahmad A., Khan S., Bhushan G., and Mainuddin. Spatiotemporal clus tering: a review. Artificial Intelligence Review, 53:2381-2423, 2020.
[8]		Ester M, Kriegel H.P., Sander J., and Xu X. A Density-Based Algorithm for Discov ering Clusters A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise. In 2nd International Conference on Knowledge Discovery and Data Mining, 226-231, 1996.
[9]		Tietbohl A., Bogorny V., Kuijpers Β., and Alvares L. 0. A clustering-based approach for discovering interesting places in trajectories. In Proceedings of the ACM Symposium on Applied Computing, 863-868, 2008.
[10]		Chavent M., Kuentz-Simonet V., Labenne A., and Saracco J. ClustGeo: an R package for hierarchical clustering with spatial constraints. Computational Statistics, 33:1-24, 2018.
[11]		Morelli C., Boccaletti B., Maranzano Ρ., and Otto P. Multidimensional spatiotem poral clustering - An application to environmental sustainability scores in Europe. Environmetrics, 36:2025.
[12]		Ward J. H. Hierarchical Grouping to Optimize an Objective Function. Journal of the American Statistical Association, 58:236-244, 1963.
Invited session IPS02 - SIS-ySIS - Advanced Methods for Assessing Environmental Impact and Green Innovation
[13]		Sakoe Η. and Chiba S. A Dynamic Programming Approach to Continuous Speech Recognition. Computer Science, Linguistics, 1971.
[14]		Sakoe H. and Chiba S. Dynamic Programming Algorithm Optimization for Spoken Word Recognition. IEEE Transactions on Acoustics, Speech, and Signal Processing, 26:43-49, 1978.
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Invited session IPSOS - Evaluation in transportation and mobility: different points of view
Organiser: Antonello D’Ambra
Chair: Ida Camminatiello
•		R. Santonastaso, R. Macchioni, and A. D’Ambra - Greenhouse gas emissions and audit fees in the transportation and logistic sector
•		L. Della Ragione, and G. Meccariello - The environmental assessment of sustainable vehicular transport through the Life Cycle Analysis (LCA) methodology applied to a vehicle
•		A. Vanacore, and A. Ciardiello - Towards a more accurate prediction of aircraft passen ger discomfort by integrating temporal analysis of seat-interface pressure with static passenger anthropometric features
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Greenhouse gas emissions and audit fees
in the transportation and logistic sector
Rosalinda Santonastaso1, Riccardo Macchioni1, Antonello DAmbra1
1University of Campania ‘Luigi Vanvitelli’ - Department of Economics
46
Invited session IPSOS - Evaluation in transportation and mobility: different points of view
Greenhouse gas emissions and audit fees in the transportation and logistic sector Rosalinda Santonastaso, Riccardo Macchioni, Antonello D’Ambra
Abstract This study aims to investigate the impact of greenhouse gas (GHG) emissions on audit fees. The moderating effect of board gender diversity on that relationship is also investigated. Using a sample of EU non-financial companies between 2012 and 2023, the study employs winsorization for data normalization and implements various regression tech niques to achieve a thorough evaluation. The authors find that firms in the transportation sector with higher GHG emissions are charged higher fees they are charged for auditing ser vices. This paper shows that auditors consider climate change-related risks in their audit fee decisions that could influence audit risk and effort. Findings also reveal that the presence of female directors on the board moderates the association between GHG emissions and audit fees. The findings reveal significant implications for firm management, regulators, investors, and auditors. This study provides empirical evidence that climate change, as an external risk factor, has a measurable impact on audit fees.
Keywords: Greenhouse gas emissions, Audit fees, Board gender diversity, Statistical model
1.		Introduction
Managing climate change-related risks has become a key priority for global sustainable devel opment initiatives [1]. The World Economic Forum’s 2020 Global Risks Perception Survey identified them among the top 10 global risks (World Economic Forum, 2021). Climate risks can be divided into physical and transition risks. Physical risks stem from natural disasters and their consequences, whereas transition risks emerge during the shift to a low carbon economy, encompassing stricter environmental regulations, market and technological changes, reputational losses, and increased disclosure requirements (FSB, 2017). Transition risks, often referred to as carbon risks in the context of greenhouse gas (GHG) emissions, are directly linked to high levels of GHG emissions, which define carbon risk in our study.
From an environmental perspective, the transportation sector is a critical economic driver and a major contributor to GHG emissions. It remains one of the largest sources of GHG emissions in the European Union, with limited progress in reducing emissions over recent decades. Despite measures such as the adoption of electric vehicles, emissions in the sector have not significantly declined since 2005 (EEA, 2024). This environmental significance has led to a growing number of empirical studies focusing on the transportation sector in recent years.
Moreover, interest in climate risks and their implications has significantly increased in accounting and auditing research. As part of the auditing process and in adherence to auditing standards, auditors are tasked with assessing a client’s business risk-the probability that the client’s financial condition may deteriorate in the future. Business risk is influenced by several factors, including the broader economic environment, industry dynamics, business models, technological advancements, market volatility, and geographic location [2]. Elevated business risk amplifies the likelihood of earnings management, as clients may attempt to
47
obscure poor performance, thereby increasing both inherent and audit risks. This also exposes auditors to reputational and economic losses [3]. In response to these heightened risks, auditors typically increase their audit efforts (reducing detection risk) and/or charge a fee premium.
Building on recent studies, it is essential to examine whether auditors consider climate risks when determining audit fees [4]. Additionally, we investigate the moderating effect of board gender diversity (BGD) on this relationship. Using a sample of 853 firm-year observations in the EU, our results suggest that GHG emissions are relevant in auditors’ risk considerations and pricing decisions. In addition, the association between GHG emissions and audit fees is less pronounced in firms with the presence of female directors on the board. The rest of this paper is organized as follows. Section 2 describes the literature review and the development of the research hypotheses. Section 3 discusses the data, the measurement of the variables and the empirical models used in the study. Section 4 presents the results, and Section 5 provides conclusions, recommendations and suggestions for future research.
2.		Literature review
2.1		GHG emissions and Auditors’ Risk Evaluation Prior research identifies three key components that influence audit pricing: the audit effort required to protect the auditor’s reputation, the need to minimize lawsuit risks, and com pensation based on anticipated audit costs [5]. According to [6], audit fees tend to be higher for larger firms or those with greater operational complexity, as these factors necessitate ad ditional audit effort. Increased audit effort is essential for improving the quality of financial reporting and reducing both litigation and reputation risks for auditors. [3] also underscores that a client’s business risk can influence audit pricing, particularly in cases where auditors may issue an unqualified opinion on materially misstated financial statements. The risk associated with a firm’s business can extend beyond financial considerations. [7] suggest that audit fees are closely tied to the firm’s operational performance and business risks. Specifically, firms with higher operational risk or those facing adverse public perception may require more extensive auditing efforts to ensure the accuracy and credibility of their financial statements. This brings us to the role of GHG emissions in shaping audit dynam ics. We argue that high carbon emissions can create negative internal consequences, such as increased employee dissatisfaction, higher turnover rates, and reduced productivity [8]. These factors, in turn, elevate operating costs and increase the overall risk to the firm. In some cases, to mask poor financial performance, firms may engage in earnings management [9], further elevating audit risk. Given these dynamics, auditors are likely to increase their audit effort, which is reflected in higher audit fees. Thus, we hypothesize: H1:Firms in the transportation and logistics sector with higher levels of GHG emissions incur greater audit fees for audit services.
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Invited session IPSOS - Evaluation in transportation and mobility: different points of view
2.2		The moderating role of the board gender diversity
Prior research suggests that BGD not only enhances a firm’s overall sustainability perfor mance but also strengthens environmental policies, ultimately contributing to a reduction in GHG emissions [10]. Scholars have highlighted that women and men often hold distinct perspectives on sustainability issues, shaped by early social interactions and experiences. Women, in particular, are assumed to exhibit heightened awareness of the needs of diverse stakeholders and to demonstrate greater sensitivity to environmental and social concerns [11]. Within the context of boards of directors, female directors are thought to bring unique ethical values and perspectives to decision-making processes, resulting in stronger consider ation for stakeholder interests beyond those of shareholders. Empirical evidence supports the notion that female directors perceive environmental risks differently from their male counterparts [12]. As female directors are often more engaged in stakeholder relations and are more attuned to environmental issues, it is argued that BGD can drive the adoption of more robust climate change policies and, in turn, contribute to lower GHG emissions [13]. Specifically, studies have documented a significant positive influence of female directors on environmental disclosure and performance metrics, including total environmental disclo sures, biodiversity initiatives, reductions in GHG emissions and green product innovations [14]. In addition, female directors’ heightened sensitivity to ethical concerns and their lower tolerance for opportunistic behavior [15] could influence the dynamics between GHG emis sions and audit-related considerations. Specifically, auditors may perceive reduced risk or greater transparency in organizations with gender-diverse boards, potentially leading to a moderation of the relationship between GHG emissions and audit fees. Thus, we hypothe size: H2:Board gender diversity negatively moderates the association between levels of GHG emissions and audit fees in the transportation and logistics sector.
3.		Research methodology
3.1		Data and Sample
Our hypotheses are examined using a sample of European firms from 2012 to 2023, focus ing on the Transportation business sector, which includes three industry groups: Transport Infrastructure, Freight & Logistics Services, and Passenger Transportation Services, as clas sified in the Thomson Reuters Eikon database. Accounting information and GHG emissions data were sourced from the Thomson Reuters Eikon database, while audit-related data were obtained from the Global Audit Analytic database.
3.2		Dependent variable
The dependent variable, audit fees (AUD_FEE), is measured as the natural logarithm of the total audit fees paid by firms, consistent with prior auditing studies [16]. Audit fees are widely used as a proxy for audit effort and the auditor’s risk assessment [6]. Higher audit fees typically indicate greater audit effort, reflecting additional time spent on the audit and
49
the involvement of more experienced or specialized personnel within the audit team.
3.3		Independent variable
Following prior literature, we measure GHG emissions as the natural logarithm of the sum of reported Scope 1, 2, and 3 emissions [17]. Specifically, we distinguish between Scope 1 emissions and indirect emissions (Scopes 2 and 3). Scope 1 emissions represent a com pany’s direct GHG emissions resulting from its operations, such as electricity production through coal burning or emissions from manufacturing processes, like chemical production. In contrast, the sum of Scopes 2 and 3 emissions reflects a company’s indirect emissions. These stem from acquired sources, such as purchased electricity or other activities, including employee business travel and product-related emissions .
3.4		Moderating variable
To investigate the extent to which board gender diversity moderates the relationship between of greenhouse gas emissions and audit fees, we include the dummy variable Gender, which equals one if at least one female director seats on the board of directors and zero otherwise [18].
3.5		Control variables
Following prior literature [19], we include several control variables in the statistical model, and which are widely known as factors that affect the price setting of the audit procedure. We control for the following client-specific variables. Firm size (SIZE) is measured as the natural logarithm of total assets. A significant and positive relationship between firm size with audit fees is expected to be seen, as it is one of the most important factors affecting audit fees [16]. Firm leverage (LEV) is measured by total liabilities divided by total assets [20]. Return on assets (ROA) is calculated by net income divided by total asset. Growth in sales (GROW) is calculated as the percentage change in sales compared to prior year. GROW is expected to have a negative relationship with audit fees. Firm age (AGE) is measured as the natural log of the number of years since the firm was incorporated. Aside from client-specific attributes, we consider auditor characteristics. Thus, we include BIG is an indicator variable, which is equal to 1 if the firm auditor is one of the largest four auditing firms and 0 otherwise because [21] documents that auditor size plays a role in audit pricing, so we expect that a larger auditor size means more resources to conduct audits. Auditor tenure (TENURE) is measured by the natural logarithm of the number of years that the auditor is employed by the firm. Finally, we include year and country fixed effects to control for unobservable temporal, and country-specific variations within the sample.
3.6		Statistical model
To investigate the effect of greenhouse gas (GHG) emissions on audit fees (Η1), we draw upon established methodologies from prior audit literature [22]. In line with their approach, we
50
Invited session IPSOS - Evaluation in transportation and mobility: different points of view
employ a model to assess the relationship between GHG emissions and audit fees, controlling for other relevant factors that could influence audit pricing. Moreover, to test our second hypothesis (Η2), we include the interaction term GHG EmisXGENDER.
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References
[1]		Monika K. Rabarison, Ibrahim Siraj, and Bin Wang. Environmental policy and audit pricing. Journal of Business Finance & Accounting, 29:207-233, 2024.
[2]		Sven Hartlieb and Brigitte Eierle. Do auditors respond to clients’ climate change related external risks? Evidence from audit fees. European Accounting Review, 33:1075- 1103, 2024.
[3]		Jonathan D. Stanley. Is the audit fee disclosure a leading indicator of clients business risk? Auditing: A Journal of Practice & Theory, 30:157-179, 2011.
[4]		Brigitte Eierle, Sven Hartlieb, David Hay, David Hay, and David Hay. External factors and the pricing of audit services: A systematic review of the archival literature using a PESTLE analysis. Auditing: A Journal of Practice & Theory, 41:95-119, 2022.
[5]		Faisal Alshahrani, Baban Eulaiwi, Lien Duong, and Grantley Taylor. Climate change disclosure performance and audit fees: evidence from Australia. Sustainability Account ing, Management and Policy Journal, 2024.
[6]		Dan A. Simunic. The pricing of audit services: Theory and evidence. Journal of Ac counting Research, 18:161-190, 1980.
[7]		Caren Schelleman and Robert W. Knechel. Short-term accruals and the pricing and production of audit services. Auditing: A Journal of Practice and Theory, 29:221-250, 2010.
[8]		Jianhua Tan, Kam C. Chan, Samuel Chang, and Bin Wang. Effects of carbon emissions on audit fees. Managerial Auditing Journal, 38:1112-1140, 2023.
[9]		Xuehui Zhang and Kam C. Chan. Jianhua Tan. Does environmental law enforcement matter for financial reporting quality? The North American Journal of Economics and Finance, 57:101-445, 2021.
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Invited session IPSOS - Evaluation in transportation and mobility: different points of view
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53
The environmental assessment of
sustainable vehicular transport through the
Life Cycle Analysis (LCA) methodology
applied to a vehicle
Livia DellaRagionel, Giovanni Meccariello1
Institute of Sciences and Technologies for Sustainable Energy and
Mobility (STEMS) - CNR
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Invited session IPSOS - Evaluation in transportation and mobility: different points of view
The environmental assessment of sustainable vehicular transport through the Life Cycle Analysis (LCA) methodology applied to a vehicle
Livia Della Ragione, Giovanni Meccariello
Abstract This paper explores the environmental assessment of urban vehicular transport sustainability through a comparative Life Cycle Assessment (LCA) of electric and internal combustion vehicles within the same category. The study evaluates different vehicle seg ments to assess efficiency and environmental impact, considering current social and political contexts. The research, conducted within the EXTREME project, analyzes technological so lutions in scenarios of "accelerated technological evolution" and "sustainable mobility." The overall impact is divided into: Vehicle production: Well To Tank (WTT) - energy supply before vehicle use; Tank To Wheels (TTW) - emissions during vehicle operation. Addition ally, an Excel-based tool was developed to modify parameters and scenarios, enabling future impact projections based on a comprehensive database.
Keywords: Comparative LCA, Energy Scenario, BEV, CO2 emissions
1.		Introduction
The LCA process is a methodology for evaluating the environmental footprint of the Life Cycle product. Regarding to the assessment study of a vehicle, according to the "cradle to grave" approach, it requires the identification and collection of multiple information. Be cause of its aim strictly related to human health and the quality of ecosystem and resource depletion, it is carried out by quantifying the impacts deriving both from the use of resources (energy, raw materials, water) and from emissions into the environment (into the air, water and soil). Specifically, it examines the various components of a product that present critical issues throughout different phases of a vehicle’s life cycle. Figure 1 provides a schematic rep resentation of these stages. Based on this premise, an LCA (Life Cycle Assessment) analysis was conducted to evaluate innovative and disruptive technologies for Spark Ignition Internal Combustion Engine (ICE) based powertrains compared to fully electric vehicles. The as sessment focused on the Global Warming Potential (GWP) indicator within the framework of the "EXTREME" research project, funded by MUR.
The analysis is based both on data available from the scientific literature and on data from the Extreme results in relation to new improvement technologies. For the real-use phase of the MHEV vehicle LCA analysis, it is essential to follow scientific and regulatory developments on reference driving cycles for vehicle type approval. Additionally, impact factors must be quantified based on the vehicle’s expected lifespan in kilometers. This requires extensive data availability and, in some cases, assumptions that are not universally validated. Primary energy consumption can also vary depending on the boundary conditions of the calculation. Therefore, the overall impact can be divided, as discussed in [1, 2, 3], into the following contributions:
•		Vehicle production;
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Figure 1: Schematic representation of the different stages of vehicle life cycle.

•		Well To Tank (WTT - "from the well to the tank"), due to the supply of primary energy to the vehicle (e.g. extraction of fossil fuel, production of biofuels, production of electricity, distribution), before this is used by the vehicle itself);
•		Tank To Wheels (TTW - "from the tank to the wheels"), calculated according to the performance of the vehicle after it has been refueled.
2.		LCA analysis
A comparative analysis between BEVs, ICEv, MHEVs or Hybrid vehicles involves evaluating various aspects of each type of vehicle to understand their strengths and weaknesses. Key factors in LCA analysis include defining the objective and measuring impacts in kg of CO2 equivalent from a GWP perspective. The methodology follows ISO 14040 and ISO 14044 standards [4, 5], using functional units to ensure comparability and consistency. The study compared vehicle characteristics and subsystem inventory data. BEVs produce zero tailpipe emissions and are more eco-friendly, especially with renewable energy, but have limited range and charging infrastructure. MHEVs improve fuel efficiency with an electric system but still rely on gasoline. The comparative LCA considered multiple scenarios incorporating com bustion and electric mobility, fuel extraction (WTT), and battery production/replacement. Three vehicle segments-small city cars, mid-size cars, and SUVs-were analyzed. Key factors in CO2 equivalent assessment (g/km) include: vehicle production, battery manufacturing, fuel emissions (WLTP), energy mix evaluation, battery replacement, fuel extraction (WTT), and vehicle disposal or reuse. The LCA analysis evaluates CO2 equivalent production per kWh based on the Euro/WLTP scenario. Figure 2 illustrates energy mix trends for dif ferent countries using 2018 data. The study projects a 2.6% annual decrease in electricity emissions until 2030, following recent trends. The baseline electricity production, used as starting point, for comparison is 320 gCO2e/kWh.
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