Scale mixture of skew‐normal linear mixed models with within‐subject serial dependence

• Published in: Statistics in medicine Vol. 40; no. 7; pp. 1790 - 1810
• Main Authors: Schumacher, Fernanda L., Lachos, Victor H., Matos, Larissa A.
• Format: Journal Article
• Language: English
• Published: England Wiley Subscription Services, Inc 30-03-2021
• Subjects: autoregressive AR(p); damped exponential correlation; EM‐algorithm; irregularly observed longitudinal data; linear mixed models; Medical statistics; scale mixtures of skew‐normal distributions; autoregressive AR(p); linear mixed models; damped exponential correlation; scale mixtures of skew-normal distributions; EM-algorithm; irregularly observed longitudinal data
• ISSN: 0277-6715; 1097-0258
• DOI: 10.1002/sim.8870

In longitudinal studies, repeated measures are collected over time and hence they tend to be serially correlated. These studies are commonly analyzed using linear mixed models (LMMs), and in this article we consider an extension of the skew‐normal/independent LMM, where the error term has a dependence structure, such as damped exponential correlation or autoregressive correlation of order p. The proposed model provides flexibility in capturing the effects of skewness and heavy tails simultaneously when continuous repeated measures are serially correlated. For this robust model, we present an efficient EM‐type algorithm for parameters estimation via maximum likelihood and the observed information matrix is derived analytically to account for standard errors. The methodology is illustrated through an application to schizophrenia data and some simulation studies. The proposed algorithm and methods are implemented in the new R package skewlmm.