Overview

Linear mixed effect (LME) models [8] are very similar to the (M)ANOVA models described above, while there are some differences in scope and performance Instead of classifying model factors as “within-subject” or “between-subject”, they include a random variable to account for the variance component that is common to all regional values of the same individual. The spread of this interindividual variance is fitted iteratively together with a global mean (across all dependent variables), the mean effects of all model factors (regions, groups, etc) and specified interactions to minimize the residual error. Significance of each factor is determined by comparing the complete model with the next simpler model not including that factor. Because a random variable (with a normal distribution) accounts for most of the interindividual variance in this model, this also will absorb most of those covariate effects that affect all regions to the same degree. LME models may therefore be less suited than rm-ANOVA or MANOVA to analyse common effects of covariates, but they do not require balanced designs. In principle, they also tolerate a moderate amount of missing data, but in the current implementation statistical tests are not possible with missing data. Flexible and comprehensive post-hoc tests for main effects and interactions are available.

The available correction for multiple comparison used in LME are:

1. Holm correction, described by Holm et al [2] is a modified version of Bonferonni correction: relaxing requirements step-wise subsequently after reaching significance for the strongest signal according to the number of remaining tests. Still, it does not take into account possible correlations among regional values. The Holm correction controls the family wise errors (FWER) without assuming independence. The benefit is that tests are made more powerful (smaller adjusted p values) while maintaining control of FWER. It is more conservative. The FWER is the probability of getting at least one wrong significance (=one false positive test) <5%
2. Alternatively, the false discovery rate (FDR) can be controlled by procedures described by Benjamini and Hochberg [3]. The FDR correction controls the "false discovery rate" (FDR) and not the FWER.