ECM-based maximum likelihood inference for multivariate linear mixed models with autoregressive errors

• Published in: Computational statistics & data analysis Vol. 54; no. 5; pp. 1328 - 1341
• Main Authors: Wang, Wan-Lun, Fan, Tsai-Hung
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.05.2010; Elsevier
• Series: Computational Statistics & Data Analysis
• Subjects: Exact sciences and technology; General topics; Linear inference, regression; Mathematics; Multivariate analysis; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Probability and statistics; Sciences and techniques of general use; Statistics; Score test; Error estimation; Prediction theory; Autoregressive model; Multivariate analysis; Stochastic process; Statistical simulation; Linear model; Statistical test; Repeated measurement; Random effect; Score statistics; Data analysis; Test statistic; Prediction; AIDS; Statistical association; Statistical estimation; Infection; Statistical computation; Correlation analysis; Viral disease; Mixed model; Filtering theory; Maximum likelihood; Autocorrelation; Autoregressive processes
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/j.csda.2009.11.021

For the analysis of longitudinal data with multiple characteristics, we are devoted to providing additional tools for multivariate linear mixed models in which the errors are assumed to be serially correlated according to an autoregressive process. We present a computationally flexible ECM procedure for obtaining the maximum likelihood estimates of model parameters. A score test statistic for testing the existence of autocorrelation among within-subject errors of each characteristic is derived. The techniques for the estimation of random effects and the prediction of further responses given past repeated measures are also investigated. The methodology is illustrated through an application to a set of AIDS data and two small simulation studies.