Asymptotic properties of adaptive maximum likelihood estimators in latent variable models

Efficient Likelihood Estimation of Generalized Structural Equation Models with a Mix of Normal and Nonnormal Responses

A maximum likelihood estimation routine is presented for a generalized structural equation model that permits a combination of response variables from various distributions (e.g., normal, Poisson, binomial, etc.). The likelihood function does not have a closed-form solution and so must be numerically approximated, which can be computationally demanding for models with several latent variables. However, the dimension of numerical integration can be reduced if one or more of the latent variables do not directly affect any nonnormal endogenous variables. The method is demonstrated using an empirical example, and the full estimation details, including first-order derivatives of the likelihood function, are provided.

Dynamic latent variable models for the analysis of cognitive abilities in the elderly population

Cognitive functioning is a key indicator of overall individual health. Identifying factors related to cognitive status, especially in later life, is of major importance. We concentrate on the analysis of the temporal evolution of cognitive abilities in the elderly population. We propose to model the individual cognitive functioning as a multidimensional latent process that accounts also for the effects of individual-specific characteristics (gender, age, and years of education). The proposed model is specified within the generalized linear latent variable framework, and its efficient estimation is obtained using a recent approximation technique, called dimensionwise quadrature. It provides a fast and streamlined approximate inference for complex models, with better or no degradation in accuracy compared with standard techniques. The methodology is applied to the cognitive assessment data from the Health and Retirement Study combined with the Asset and Health Dynamic study in the years between 2006 and 2010. We evaluate the temporal relationship between two dimensions of cognitive functioning, that is, episodic memory and general mental status. We find a substantial influence of the former on the evolution of the latter, as well as evidence of severe consequences on both cognitive abilities among less-educated and older individuals.

A note on the accuracy of adaptive Gauss–Hermite quadrature

Numerical quadrature methods are needed for many models in order to approximate integrals in the likelihood function. In this note, we correct the error rate given by Liu & Pierce (1994) for integrals approximated with adaptive Gauss–Hermite quadrature and show that the approximation is less accurate than previously thought. We discuss the relationship between the error rates of adaptive Gauss–Hermite quadrature and Laplace approximation, and provide a theoretical explanation of simulation results obtained in previous studies regarding the accuracy of adaptive Gauss–Hermite quadrature.

Pairwise likelihood estimation of latent autoregressive count models

Latent autoregressive models are useful time series models for the analysis of infectious disease data. Evaluation of the likelihood function of latent autoregressive models is intractable and its approximation through simulation-based methods appears as a standard practice. Although simulation methods may make the inferential problem feasible, they are often computationally intensive and the quality of the numerical approximation may be difficult to assess. We consider instead a weighted pairwise likelihood approach and explore several computational and methodological aspects including estimation of robust standard errors and the role of numerical integration. The suggested approach is illustrated using monthly data on invasive meningococcal disease infection in Greece and Italy.