# Factor copula models for mixed data

## TL;DR

This paper introduces factor copula models for analyzing complex dependence structures in mixed continuous and discrete data, offering improved flexibility over traditional models through the use of vine copulas with latent variables.

## Contribution

It develops a novel factor copula modeling framework that captures tail, asymmetric, and non-linear dependence, with methods for model selection and goodness-of-fit.

## Key findings

- Substantial improvement over standard factor models for mixed data.
- Demonstrated effectiveness through simulation studies.
- Applied to real datasets showing practical utility.

## Abstract

We develop factor copula models for analysing the dependence among mixed continuous and discrete responses. Factor copula models are canonical vine copulas that involve both observed and latent variables, hence they allow tail, asymmetric and non-linear dependence. They can be explained as conditional independence models with latent variables that don't necessarily have an additive latent structure. We focus on important issues that would interest the social data analyst, such as model selection and goodness-of-fit. Our general methodology is demonstrated with an extensive simulation study and illustrated by re-analysing three mixed response datasets. Our study suggests that there can be a substantial improvement over the standard factor model for mixed data and makes the argument for moving to factor copula models.