A Comparative Gain in Areas under ROC Curve and Power of Tests Between Cumulative Logit GLMMs and Cumulative Probit GLMMs

Abstract

Generalized Linear Models (GLMs) extend ordinary general linear model with fixed effects in the linear predictor by allowing non-normal responses and a link function of the mean. The Generalized Linear Mixed Models (GLMMs) are further extensions of GLMs that permits both the fixed effect and the random effect in models and account for the dependency inherent in data. However, limitation of few applications was found due to the complexity of the models and their efficiency. In this article, a further comparative gain in area under ROC curves and power of tests between the cumulative logit GLMMs and the cumulative probit
GLMMs are investigated and discussed. The 1,000 empirical datasets for each condition of parameters and the number of clusters and cluster sizes are simulated using SAS rewritten macro program. The results reveal that the cumulative logit GLMM is superior (0.8%) to the cumulative probit GLMM. As the number of clusters and the cluster sizes are increased, the sensitivity and the precision through the AUC and power of the tests are better fitted. Overall, the maximum absolute percentage gain power between the two models is approximately 10% with satisfactorily high area under ROC curve values. It is clear that, for small and moderate intra-cluster correlation, the cumulative logit GLMMs are also preferred; otherwise, for more complicated cases; even if the two GLMMs are less efficiency than that before but still are closely adequate of fits significantly at 0.05. Hence the two GLMMs probably are used for further implementation in real data.