REML estimation for binary data in GLMMs

By M. Noh, Youngjo Lee. 2007

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Multilevel Analysis with Few Clusters: Improving Likelihood-Based Methods to Provide Unbiased Estimates and Accurate Inference (2020, background): “…with n observations, k independent variables, a constant, and normally distributed errors, this test statistic (also referred to as the t-statistic) is known to 6See also Drum and McCullagh (1993); Liao and Lipsitz (2002); Noh and Lee (2007). have a t-distribution with n− k− 1 degrees of freedom.”
Testing environmental and genetic effects in the presence of spatial autocorrelation (2014, methodology): “Even the above Laplace approximation may fail for binary data, for which a second-order correction has been proposed (Noh and Lee 2007).”
Variational Inference for Generalized Linear Mixed Models Using Partially Noncentered Parametrizations (2012, methodology): “ 1;2 and used 0 = 1 = 2, ˙= 1:25 for the Poisson random intercept model and 0 = 1 = 1, ˙= 2 for the logistic random intercept model. These settings have been considered by Ormerod and Wand (2012) and Noh and Lee (2007). The NCVMP algorithm was initialized using the t obtained from PQL. However, ther”