The New England Journal of Statistics in Data Science

The purpose of this paper is to develop a practical framework for the analysis of the linear mixed-effects models for censored or missing data with serial correlation errors, using the multivariate Student’s t-distribution, being a flexible alternative to the use of the corresponding normal distribution. We propose an efficient ECM algorithm for computing the maximum likelihood estimates for these models with standard errors of the fixed effects and likelihood function as a by-product. This algorithm uses closed-form expressions at the E-step, which relies on formulas for the mean and variance of a truncated multivariate Student’s t-distribution. In order to illustrate the usefulness of the proposed new methodology, artificial and a real dataset are analyzed. The proposed algorithm and methods are implemented in the R package ARpLMEC.