A Diagnosis and Prognosis for Generalized Linear Mixed Models with Correlated Ordinal Responses: Power and Area under ROC Curve

The Generalized Linear Mixed Models (GLMMs) are designed to account for the dependency inherent in data and permit both the fixed effects in the linear predictors and the random effects in the models. However, the GLMMs’ implementations are still limited only in few applications due to the complexity of the model and its efficiency. In this article, we have investigated both the diagnosis and the prognosis of the ordinal-category logit GLMMs and the probit GLMMs for their power of the tests and the ability to predict the right categories in each condition of parameters and the sample size of the number of clusters and the cluster size. It is shown that the cumulative logit GLMM is superior to the probit GLMM. Furthermore, as the number of clusters and the cluster size are increased, the precision of parameter estimates through the power of the tests is much improved. However, the increasing of the intra-cluster correlation affects the AUC estimates, which probably mean that it gets difficulty to the prognosis of the right categories when there are many units in the same cluster, that is when the intra-cluster correlation occurs. But, such impact is only little for the power of the tests. Hence, in conclusion the GLMMs may well be recommended to use in applications since their power are very high and approaching to 1 for moderate and large number of clusters and the cluster size with the satisfactorily high AUC values.