Generalized Linear Mixed Models with Gaussian Mixture Random Effects: Inference and Application.

We propose a new class of generalized linear mixed models with Gaussian mixture random effects for clustered data. To overcome the weak identifiability issues, we fit the model using a penalized Expectation Maximization (EM) algorithm, and develop sequential locally restricted likelihood ratio tests to determine the number of components in the Gaussian mixture. Our work is motivated by an application to nationwide kidney transplant center evaluation in the United States, where the patient-level post-surgery outcomes are repeated measures of the care quality of the transplant centers. By taking into account patient-level risk factors and modeling the center effects by a finite Gaussian mixture model, the proposed model provides a convenient framework to study the heterogeneity among the transplant centers and controls the false discovery rate when screening for transplant centers with non-standard performance.