This paper studies the correlation of cognitive progression for subjects whose dementia has made a transition from a milder stage of severity to the next stage of impairment. We model the progression of cognitive decline at adjacent stages of dementia by using a general linear mixed model. We also propose a three-step procedure to detect the best configuration of the covariance matrices for the random components in the model. After the best configuration of covariance matrices for the random components in the model is determined, we then recommend another two-step process to test whether there exists a significant correlation between the rate of cognitive decline before the transition, the cognitive status at the transition time, and the rate of cognitive decline after the transition. In addition, we present asymptotic confidence interval estimates for the correlations associated with a transition. This method is applied to several composite psychometric factor scores in the longitudinal database from the Alzheimer's Disease Research Center (ADRC) at Washington University in St. Louis.