H-likelihood: problems and solutions
Statistics and Computing
Hierarchical-likelihood approach for nonlinear mixed-effects models
Computational Statistics & Data Analysis
Accuracy of Laplace approximation for discrete response mixed models
Computational Statistics & Data Analysis
Estimation in the probit normal model for binary outcomes using the SAEM algorithm
Computational Statistics & Data Analysis
Approximate conditional inference in mixed-effects models with binary data
Computational Statistics & Data Analysis
Alternating imputation posterior estimation of models with crossed random effects
Computational Statistics & Data Analysis
Restricted likelihood inference for generalized linear mixed models
Statistics and Computing
Conditional Akaike information criterion for generalized linear mixed models
Computational Statistics & Data Analysis
Modifications of REML algorithm for HGLMs
Statistics and Computing
Joint hierarchical generalized linear models with multivariate Gaussian random effects
Computational Statistics & Data Analysis
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The restricted maximum likelihood (REML) procedure is useful for inferences about variance components in mixed linear models. However, its extension to hierarchical generalized linear models (HGLMs) is often hampered by analytically intractable integrals. Numerical integration such as Gauss-Hermite quadrature (GHQ) is generally not recommended when the dimensionality of the integral is high. With binary data various extensions of the REML method have been suggested, but they have had unsatisfactory biases in estimation. In this paper we propose a statistically and computationally efficient REML procedure for the analysis of binary data, which is applicable over a wide class of models and design structures. We propose a bias-correction method for models such as binary matched pairs and discuss how the REML estimating equations for mixed linear models can be modified to implement more general models.