Latent variable models for ordinal data by using the adaptive quadrature approximation

• Published in: Computational statistics Vol. 28; no. 2; pp. 597 - 619
• Main Authors: Cagnone, Silvia, Monari, Paola
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.04.2013; Springer Nature B.V
• Subjects: Ability tests; Algorithms; Approximation; Computation; Computational mathematics; Construction equipment; Economic Theory/Quantitative Economics/Mathematical Methods; Estimates; Generalized linear models; Mathematical analysis; Mathematical models; Mathematics and Statistics; Original Paper; Performance evaluation; Probability; Probability and Statistics in Computer Science; Probability Theory and Stochastic Processes; Quadratures; Simulation; Statistics; Studies; Variables; Generalized linear latent variable model; Adaptive Gauss Hermite quadrature; EM algorithm; Ordinal data
• ISSN: 0943-4062; 1613-9658
• DOI: 10.1007/s00180-012-0319-z

Latent variable models for ordinal data represent a useful tool in different fields of research in which the constructs of interest are not directly observable so that one or more latent variables are required to reduce the complexity of the data. In these cases problems related to the integration of the likelihood function of the model can arise. Indeed analytical solutions do not exist and in presence of several latent variables the most used classical numerical approximation, the Gauss Hermite quadrature, cannot be applied since it requires several quadrature points per dimension in order to obtain quite accurate estimates and hence the computational effort becomes not feasible. Alternative solutions have been proposed in the literature, like the Laplace approximation and the adaptive quadrature. Different studies demonstrated the superiority of the latter method particularly in presence of categorical data. In this work we present a simulation study for evaluating the performance of the adaptive quadrature approximation for a general class of latent variable models for ordinal data under different conditions of study. A real data example is also illustrated.