This dissertation involves an application of mixture of regression models to 114 individuals who are cognitively intact (from the Alzheimer\u27s Disease and Neuroimaging Initiative-ADNI, data). The correct number of components in the model were estimated with the Singular BIC (SBIC), marking the first time it has been applied to such a problem. The smallest true model in conjunction with the approximation of SBIC was fixed at 1. The resulting posterior probabilities from the model were used to estimate the probability of a person transitioning and risk plots were obtained that could in principle be used by clinicians to identify patients at risk. This work also proposed a model selection criterion for mixture of regression models with application to the ADNI data. Finally simulation studies were conducted to compare the performance of the novel model selection and existing criteria
