A Review of R-packages for Random-Intercept Probit Regression in Small Clusters

Haeike Josephy,Yves Rosseel,Tom Loeys

doi:10.3389/fams.2016.00018

Haeike Josephy, Yves Rosseel + Show 1 more

Open Access

https://doi.org/10.3389/fams.2016.00018

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Abstract

Generalized Linear Mixed Models (GLMMs) are widely used to model clustered categorical outcomes. To tackle the intractable integration over the random effects distributions, several approximation approaches have been developed for likelihood-based inference. As these seldom yield satisfactory results when analyzing binary outcomes from small clusters, estimation within the Structural Equation Modeling (SEM) framework is proposed as an alternative. We compare the performance of R-packages for random-intercept probit regression relying on: the Laplace approximation, adaptive Gaussian quadrature (AGQ), penalized quasi-likelihood, an MCMC-implementation, and integrated nested Laplace approximation within the GLMM-framework, and a robust diagonally weighted least squares estimation within the SEM-framework. In terms of bias for the fixed and random effect estimators, SEM usually performs best for cluster size two, while AGQ prevails in terms of precision (mainly because of SEM's robust standard errors). As the cluster size increases, however, AGQ becomes the best choice for both bias and precision.

Highlights

In behavioral and social sciences, researchers are frequently confronted with clustered or correlated data structures
Generalized linear mixed models (GLMMs) are basically extensions of Generalized Linear Models (GLMs) [29], which allow for correlated observations through the inclusion of random effects
The Penalized Quasi-Likelihood method (PQL) [11, 33, 34] approximates the integrand; more intuitively put, PQL approximates the Generalized Linear Mixed Models (GLMMs) with a linear mixed model

Summary

Introduction

In behavioral and social sciences, researchers are frequently confronted with clustered or correlated data structures Such hierarchical data sets for example arise from educational studies, in which students are measured within classrooms, or from longitudinal studies, in which measurements are repeatedly taken within individuals. SEM supersects its GLMM counterpart, as the former is able to include latent measures (and measurement error) and assess mediation, in one big model. Discounting these two assets, recent literature proves that SEM is completely equivalent to its GLMM counterpart when considering balanced data (e.g., when considering equal cluster sizes in a random intercept model) [3,4,5]

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