Profiling or evaluation of health care providers involves the application of statistical models to compare each provider's performance with respect to a patient outcome, such as unplanned 30-day hospital readmission, adjusted for patient case-mix characteristics. The nationally adopted method is based on random effects (RE) hierarchical logistic regression models. Although RE models are sensible for modeling hierarchical data, novel high dimensional fixed effects (FE) models have been proposed which may be well-suited for the objective of identifying sub-standard performance. However, there are limited comparative studies. Thus, we examine their relative performance, including the impact of inadequate case-mix adjustment.