MODELLING CORRELATION MATRICES IN MULTIVARIATE DATA, WITH APPLICATION TO RECIPROCITY AND COMPLEMENTARITY OF CHILD-PARENT EXCHANGES OF SUPPORT

Siliang Zhang; Jouni Kuha; Fiona Steele

doi:10.1214/24-AOAS1921

MODELLING CORRELATION MATRICES IN MULTIVARIATE DATA, WITH APPLICATION TO RECIPROCITY AND COMPLEMENTARITY OF CHILD-PARENT EXCHANGES OF SUPPORT

Siliang Zhang
, Jouni Kuha
, Fiona Steele

School of Statistics

The London School of Economics and Political Science

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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 noncoresident parents.

Original language	English
Pages (from-to)	3024-3049
Number of pages	26
Journal	Annals of Applied Statistics
Volume	18
Issue number	4
DOIs	https://doi.org/10.1214/24-AOAS1921
State	Published - Dec 2024

Keywords

Bayesian estimation
covariance matrix modelling
item response theory models
positive definite matrices
two-step estimation

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10.1214/24-AOAS1921

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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 noncoresident parents.",

keywords = "Bayesian estimation, covariance matrix modelling, item response theory models, positive definite matrices, two-step estimation",

author = "Siliang Zhang and Jouni Kuha and Fiona Steele",

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AU - Zhang, Siliang

AU - Kuha, Jouni

AU - Steele, Fiona

PY - 2024/12

Y1 - 2024/12

N2 - 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 noncoresident parents.

AB - 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 noncoresident parents.

KW - Bayesian estimation

KW - covariance matrix modelling

KW - item response theory models

KW - positive definite matrices

KW - two-step estimation

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DO - 10.1214/24-AOAS1921

M3 - 文章

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SN - 1932-6157

VL - 18

SP - 3024

EP - 3049

JO - Annals of Applied Statistics

JF - Annals of Applied Statistics

IS - 4

ER -

MODELLING CORRELATION MATRICES IN MULTIVARIATE DATA, WITH APPLICATION TO RECIPROCITY AND COMPLEMENTARITY OF CHILD-PARENT EXCHANGES OF SUPPORT

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Keywords

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