Assessing Generalized Linear Mixed Models Using Residual Analysis

A nonparametric smoothing method for assessing the adequacy of generalized linear mixed models (GLMMs) is developed. The proposed method is based on smoothing the residuals over continuous covariates to avoid the partition of continuous covariates on model checking. The global test statistic has a quadratic form and its formulae of expectation as well as variance are derived. The sampling distribution of the quadratic form test statistic is approximated by a scaled chi-squared distribution. For bandwidth selection, the leave-one-out cross-validation approach is recommendable for use. A longitudinal binary data set is utilized to demonstrate the proposed approach.