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A review of R-packages for random-intercept probit regression in small clusters

Haeike Josephy (UGent) , Tom Loeys (UGent) and Yves Rosseel (UGent)
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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 (PQL), 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.
Keywords
Structural Equation Modeling, Monte Carlo studies, Mixed models, Categorical Data Analysis, Multilevel Modeling

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Citation

Please use this url to cite or link to this publication:

Chicago
Josephy, Haeike, Tom Loeys, and Yves Rosseel. 2016. “A Review of R-packages for Random-intercept Probit Regression in Small Clusters.” Frontiers in Applied Mathematics and Statistics 2 (18): 1–13.
APA
Josephy, H., Loeys, T., & Rosseel, Y. (2016). A review of R-packages for random-intercept probit regression in small clusters. FRONTIERS IN APPLIED MATHEMATICS AND STATISTICS, 2(18), 1–13.
Vancouver
1.
Josephy H, Loeys T, Rosseel Y. A review of R-packages for random-intercept probit regression in small clusters. FRONTIERS IN APPLIED MATHEMATICS AND STATISTICS. 2016;2(18):1–13.
MLA
Josephy, Haeike, Tom Loeys, and Yves Rosseel. “A Review of R-packages for Random-intercept Probit Regression in Small Clusters.” FRONTIERS IN APPLIED MATHEMATICS AND STATISTICS 2.18 (2016): 1–13. Print.
@article{8197080,
  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 (PQL), 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.},
  author       = {Josephy, Haeike and Loeys, Tom and Rosseel, Yves},
  issn         = {2297-4687},
  journal      = {FRONTIERS IN APPLIED MATHEMATICS AND STATISTICS},
  language     = {eng},
  number       = {18},
  pages        = {1--13},
  title        = {A review of R-packages for random-intercept probit regression in small clusters},
  url          = {http://dx.doi.org/10.3389/fams.2016.00018},
  volume       = {2},
  year         = {2016},
}

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