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Generalized latent variable models for location, scale, and shape parameters

Author

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  • Cardenas Hurtado, Camilo
  • Moustaki, Irini
  • Chen, Yunxiao
  • Marra, Giampiero

Abstract

We introduce a general framework for latent variable modeling, named Generalized Latent Variable Models for Location, Scale, and Shape parameters (GLVM-LSS). This framework extends the generalized linear latent variable model beyond the exponential family distributional assumption and enables the modeling of distributional parameters other than the mean (location parameter), such as scale and shape parameters, as functions of latent variables. Model parameters are estimated via maximum likelihood. We present two real-world applications on public opinion research and educational testing, and evaluate the model’s performance in terms of parameter recovery through extensive simulation studies. Our results suggest that the GLVM-LSS is a valuable tool in applications where modeling higher-order moments of the observed variables through latent variables is of substantive interest. The proposed model is implemented in the R package glvmlss, available online.

Suggested Citation

  • Cardenas Hurtado, Camilo & Moustaki, Irini & Chen, Yunxiao & Marra, Giampiero, 2025. "Generalized latent variable models for location, scale, and shape parameters," LSE Research Online Documents on Economics 127387, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:127387
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    File URL: http://eprints.lse.ac.uk/127387/
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    More about this item

    Keywords

    latent variable models; distributional regression; GAMLSS; EM algorithm; heteroscedasticity;
    All these keywords.

    JEL classification:

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

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