Abstract
We propose a new method to perform approximate likelihood inference in latent variable models. Our approach provides an approximation of the integrals involved in the likelihood function through a reduction of their dimension that makes the computation feasible in situations in which classical and adaptive quadrature based methods are not applicable. We derive new theoretical results on the accuracy of the obtained estimators. We show that the proposed approximation outperforms several existing methods in simulations, and it can be successfully applied in presence of multidimensional longitudinal data when standard techniques are not applicable or feasible.
Highlights
Latent variable models are used in many research fields where it is of interest to study constructs that are unobservable but can be indirectly measured by indicators related to them
We evaluate the performance of the proposed approach by applying the generalized linear latent variable models for multidimensional longitudinal data proposed by [6] and [3] to p binary variables observed at T different time points, such that the response vector y = (y11, . . . , ypT )T is pT - dimensional
One of the main problems in the estimation of the generalized linear latent variable models is that the integrals involved in the likelihood do not always have an analytical solution
Summary
Latent variable models are used in many research fields where it is of interest to study constructs that are unobservable but can be indirectly measured by indicators related to them. Numerical quadrature based methods represent a widespread solution to this problem and, among them, the adaptive Gauss Hermite quadrature is considered the gold standard [21, 25] It is computationally unfeasible with a large number of latent variables. We propose a new approach to approximate the integrals involved in the likelihood of latent variable models, that we refer to as dimensionwise quadrature method. It consists of representing the integrand as a sum of not overlapping components that are the terms of the Taylor series expansion of the function.
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