Using the linear mixed model to analyze non-normal data distributions in longitudinal designs

Abstract

Using a Monte Carlo simulation and the Kenward-Roger (KR) correction for degrees of freedom this paper analyzes the application of the linear mixed model (LMM) to a mixed repeated measures design. The LMM was first used to select the covariance structure with three types of data distribution: normal, exponential and log-normal. This showed that with ho mogeneous between-groups covariance, and when the distribution was normal, the covariance structure with the best fit was the unstructured population matrix. Wit h heterogeneous between-groups covariance and when the pairing between covariance matrices and group sizes was null the best fit was shown by the between-subjects heterogeneous unstructured population matrix, this being the case for all the distributions analyzed. By contrast, with posit ive or negative pairing the within-subject and between-subjects heterogeneous first-order autoregressive structure produced the best fit. In the second stage of the study, the robustness of the LMM was tested. This showed that the KR method provided adequate control of Type I error rates for the time effect with normally distributed data. However, as skewness increased, as occurs, for example, in the log-normal distribution, robustness was null, especially when the assumption of sphericity was violated. As regards the influence of kurtosis the analysis showed that the degree of robustness increased in line with the amount of kurtosis.