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

Cardenas Hurtado, Camilo ORCID: 0009-0003-1073-0912, Moustaki, Irini ORCID: 0000-0001-8371-1251, Chen, Yunxiao ORCID: 0000-0002-7215-2324 and Marra, Giampiero (2025) Generalized latent variable models for location, scale, and shape parameters. Psychometrika. ISSN 0033-3123

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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.

Item Type:	Article
Additional Information:	© 2025 The Author(s)
Divisions:	Statistics
Subjects:	H Social Sciences > HA Statistics B Philosophy. Psychology. Religion > BF Psychology
Date Deposited:	24 Feb 2025 10:27
Last Modified:	02 Apr 2025 07:06
URI:	http://eprints.lse.ac.uk/id/eprint/127387

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