Abstract
We define a model for the joint distribution of multiple continuous la- tent variables, which includes a model for how their correlations depend on explanatory variables. This is motivated by and applied to social scientific re- search questions in the analysis of intergenerational help and support within families, where the correlations describe reciprocity of help between genera- tions 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 jus- tify this approach and facilitate efficient implementation of it. The model is applied to data from the UK Household Longitudinal Study to analyse ex- changes of practical and financial support between adult individuals and their noncoresident parents.
Funding Statement
This research was supported by a UK Economic and Social Research Council (ESRC) grant “Methods for the Analysis of Longitudinal Dyadic Data with an Application to Inter-generational Exchanges of Family Support” (ref. ES/P000118/1).
For the purpose of open access, the authors have applied a Creative Commons attribution (CC BY) licence to any Author Accepted Manuscript version arising.
Additional funding for Siliang Zhang was provided by Shanghai Science and Technology Committee Rising-Star Program (22YF1411100) and National Natural Science Foundation of China (12301373).
Citation
Siliang Zhang. Jouni Kuha. Fiona Steele. "Modelling correlation matrices in multivariate data, with application to reciprocity and complementarity of child-parent exchanges of support." Ann. Appl. Stat. 18 (4) 3024 - 3049, December 2024. https://doi.org/10.1214/24-AOAS1921
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