Goodness-of-fit tests of generalized linear mixed models for repeated ordinal responses

Categorical longitudinal data are frequently applied in a variety of fields, and are commonly fitted by generalized linear mixed models (GLMMs) and generalized estimating equations models. The cumulative logit is one of the useful link functions to deal with the problem involving repeated ordinal responses. To check the adequacy of the GLMMs with cumulative logit link function, two goodness-of-fit tests constructed by the unweighted sum of squared model residuals using numerical integration and bootstrap resampling technique are proposed. The empirical type I error rates and powers of the proposed tests are examined by simulation studies. The ordinal longitudinal studies are utilized to illustrate the application of the two proposed tests.