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Modelling correlation matrices in multivariate data, with application to reciprocity and complementarity of child-parent exchanges of support

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  • Zhang, Siliang
  • Kuha, Jouni
  • Steele, Fiona

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.

Suggested Citation

  • Zhang, Siliang & Kuha, Jouni & Steele, Fiona, 2024. "Modelling correlation matrices in multivariate data, with application to reciprocity and complementarity of child-parent exchanges of support," LSE Research Online Documents on Economics 123698, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:123698
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    References listed on IDEAS

    as
    1. W. R. Gilks & N. G. Best & K. K. C. Tan, 1995. "Adaptive Rejection Metropolis Sampling Within Gibbs Sampling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 44(4), pages 455-472, December.
    2. Frederick Wong, 2003. "Efficient estimation of covariance selection models," Biometrika, Biometrika Trust, vol. 90(4), pages 809-830, December.
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    More about this item

    Keywords

    Bayesian estimation; covariance matrix modelling; item response theory models; positive definite matrices; two-step estimation;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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