Factor, structured factor and vine copula models for multivariate social science data

Kadhem, Sayed (2022) Factor, structured factor and vine copula models for multivariate social science data. Doctoral thesis, University of East Anglia.

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Abstract

The development of multivariate models with parsimonious dependence is of great interest in a wide range of applications. Two broad frameworks have been considered for parsimonious dependence modelling, namely the latent variable (factor) and copula frameworks. Within these two broad frameworks, we propose several factor models based on copulas for modelling parsimonious dependence structures in multivariate social science data.

We develop factor copula models for mixed continuous and discrete responses where the dependence among the observed variables is explained via a few factors. These are conditional independence models; the observed variables are conditionally independent given the factors.

We also propose the bi-factor and second-order copula models for item response data that can be split into non-overlapping groups, where each group of items has homogeneous dependence. These proposed models fall under the structured factor copula class. Our general models subsume the Gaussian bi-factor and second-order models as special cases and are suitable for capturing different dependencies between and within different groups of observed variables.

Using the vine copula framework, we extend the factor copula models in order to capture any residual dependence. We propose combined factor/truncated vine copula models for item response data. These are conditional dependence models given very few factors. The proposed models can be viewed as a truncated regular vine copula models that involve both observed and latent variables. They allow for flexible construction based on a sequence of bivariate copulas that can provide different tail, asymmetric and non-linear dependence properties.

All the proposed copula models are applied to real datasets and are compared with other relevant benchmark models showing substantial improvement and performance both conceptually and in fit to data.

Item Type:	Thesis (Doctoral)
Faculty \ School:	Faculty of Science > School of Computing Sciences
Depositing User:	Chris White
Date Deposited:	10 Aug 2022 14:09
Last Modified:	10 Aug 2022 14:09
URI:	https://ueaeprints.uea.ac.uk/id/eprint/87165
DOI:

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