Robust linear mixed models using the skew t distribution with application to schizophrenia data

• Published in: Biometrical journal 2010-08, Vol.52 (4), p.449-469
• Main Authors: Ho, Hsiu J., Lin, Tsung-I.
• Format: Article
• Language: English
• Subjects: AECM algorithm; Algorithms; Applications; Biology, psychology, social sciences; Biometrics; Data processing; Distribution theory; Exact sciences and technology; General topics; Humans; Intermittent missing values; Likelihood Functions; Linear Models; Mathematics; Mental disorders; Multivariate Analysis; Outliers; Probability and statistics; Random effects; Randomized Controlled Trials as Topic; Schizophrenia; Schizophrenia - drug therapy; Sciences and techniques of general use; Skew t linear mixed model; Statistics; Tails
• ISSN: 0323-3847; 1521-4036; 1521-4036
• DOI: 10.1002/bimj.200900184

We consider an extension of linear mixed models by assuming a multivariate skew t distribution for the random effects and a multivariate t distribution for the error terms. The proposed model provides flexibility in capturing the effects of skewness and heavy tails simultaneously among continuous longitudinal data. We present an efficient alternating expectation‐conditional maximization (AECM) algorithm for the computation of maximum likelihood estimates of parameters on the basis of two convenient hierarchical formulations. The techniques for the prediction of random effects and intermittent missing values under this model are also investigated. Our methodologies are illustrated through an application to schizophrenia data.