Estimation of latent variable models for ordinal data via fully exponential Laplace approximation

TL;DR

This paper introduces a fully exponential Laplace approximation method for estimating latent variable models with ordinal data, offering improved accuracy and computational feasibility over traditional methods like Gauss Hermite quadrature, especially with many latent variables.

Contribution

It develops an extended Laplace approximation method that enhances accuracy and scalability in estimating latent variable models for ordinal data.

Findings

The fully exponential Laplace approximation outperforms classical Laplace in accuracy.

The method remains computationally feasible with many latent variables.

It provides a practical alternative to Gauss Hermite quadrature for complex models.

Abstract

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. In such models, problems related to the integration of the likelihood function can arise since analytical solutions do not exist. Numerical approximations, like the widely used Gauss Hermite (GH) quadrature, are generally applied to solve these problems. However, GH becomes unfeasible as the number of latent variables increases. Thus, alternative solutions have to be found. In this paper, we propose an extended version of the Laplace method for approximating the integrals, known as fully exponential Laplace approximation. It is computational feasible also in presence of many latent variables, and it is more accurate than the classical Laplace method.