Residual analysis of linear mixed models using a simulation approach

In the framework of the general linear model, residuals are routinely used to check model assumptions, such as homoscedasticity, normality, and linearity of effects. Residuals can also be employed to detect possible outliers. Various types of residuals may be defined for linear mixed models. It is shown how residual plots can be used to check model assumptions by comparing empirical residual distributions with appropriate null distributions based on a parametric bootstrap approach. This allows constructing simultaneous tolerance bounds, which helps in assessing the normality and homoscedasticity of residuals of linear mixed models, identifying possible outliers and interpreting residual plots. The usefulness of this method is demonstrated by applying it to several previously published datasets.