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

Frontiers in Applied Mathematics and Statistics

Josephy, Haeike¹  Loeys, Tom¹  Rosseel, Yves¹ 

[1] Department of Data Analysis, Faculty of Psychology and Educational Sciences, Ghent University, Ghent, Belgium

关键词: Categorical Data Analysis;    multilevel modeling;    mixed models;    Structural Equation Modeling;    Monte Carlo studies;   

DOI  :  10.3389/fams.2016.00018

学科分类：数学（综合）

来源: Frontiers

【 摘 要 】

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.

【 授权许可】

CC BY