Implementation of the EM Algorithm for Maximum Likelihood Estimation of a Random Effects Model for One Longitudinal Ordinal Outcome

Abstract

Longitudinal data arise when we have repeated measures on subjects over time. The correlated probit model is frequently used for ordered longitudinal data since it allows to seamlessly incorporate different correlation structures. The estimation of the probit model parameters based on direct maximization of the limited information maximum likelihood is a numerically intensive procedure especially when we have repeated measures on subjects. We propose an extension of the EM algorithm for obtaining maximum likelihood estimates for one ordinal longitudinal outcome. The algorithm is implemented in the free software environment for statistical computing and graphics R. We use simulations to examine the performance of the developed algorithm and apply the model to data from the Health and Retirement Study (HRS). We apply a bootstrap approach for standard error approximation. Advantages of the presented algorithm include the potential of dealing with high-dimensional random effects and of extending the algorithm to combinations of ordinal and continuous longitudinal outcomes.