Journal
COMPUTATIONAL STATISTICS & DATA ANALYSIS
Volume 182, Issue -, Pages -Publisher
ELSEVIER
DOI: 10.1016/j.csda.2023.107710
Keywords
Latent variable models; Item response theory; Integral approximation; Gauss-Hermite quadrature; Laplace approximation
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A computationally efficient method for marginal maximum likelihood estimation of multiple group generalized linear latent variable models for categorical data is introduced. The method utilizes second-order Laplace approximations and considers symmetries to improve computational efficiency. Simulation and empirical examples show that it performs similarly to adaptive Gauss-Hermite quadrature while being more efficient.
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.(c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons .org /licenses /by-nc -nd /4 .0/).
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