Modelling Correlation Matrices in Multivariate Dyadic Data: Latent Variable Models for Intergenerational Exchanges of Family Support

TL;DR

This paper introduces a latent variable model for analyzing intergenerational family support, capturing how correlations between types of help depend on explanatory factors, with an efficient estimation method validated on UK data.

Contribution

It develops a novel latent variable model for correlation matrices in dyadic data, including a new MCMC estimation procedure ensuring positive definiteness.

Findings

Model effectively captures reciprocity and complementarity in family support.

Application to UK data reveals significant intergenerational support patterns.

Estimation method is computationally efficient and theoretically justified.

Abstract

We define a model for the joint distribution of multiple continuous latent variables which includes a model for how their correlations depend on explanatory variables. This is motivated by and applied to social scientific research questions in the analysis of intergenerational help and support within families, where the correlations describe reciprocity of help between generations and complementarity of different kinds of help. We propose an MCMC procedure for estimating the model which maintains the positive definiteness of the implied correlation matrices, and describe theoretical results which justify this approach and facilitate efficient implementation of it. The model is applied to data from the UK Household Longitudinal Study to analyse exchanges of practical and financial support between adult individuals and their non-coresident parents.