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Fast estimation of multiple group generalized linear latent variable models for categorical observed variables

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  • Andersson, Björn
  • Jin, Shaobo
  • Zhang, Maoxin

Abstract

A computationally efficient method for marginal maximum likelihood estimation of multiple group generalized linear latent variable models for categorical data is introduced. The approach utilizes second-order Laplace approximations of the integrals in the likelihood function. It is demonstrated how second-order Laplace approximations can be utilized highly efficiently for generalized linear latent variable models by considering symmetries that exist for many types of model structures. In a simulation with binary observed variables and four correlated latent variables in four groups, the method has similar bias and mean squared error compared to adaptive Gauss-Hermite quadrature with five quadrature points while substantially improving computational efficiency. An empirical example from a large-scale educational assessment illustrates the accuracy and computational efficiency of the method when compared against adaptive Gauss-Hermite quadrature with three, five, and 13 quadrature points.

Suggested Citation

  • Andersson, Björn & Jin, Shaobo & Zhang, Maoxin, 2023. "Fast estimation of multiple group generalized linear latent variable models for categorical observed variables," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).
    • Handle: RePEc:eee:csdana:v:182:y:2023:i:c:s016794732300021x
    DOI: 10.1016/j.csda.2023.107710
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    References listed on IDEAS

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