ABSTRACT
More advanced topics related to linear mixed-effects models are discussed. Extension of the linear mixed effect model to the multiple levels of grouping with both nested and crossed random effects is described in matrix form and demonstrated through real-data examples. A detailed discussion of between-group and within-group effects is included. With respect to an individual level predictor, the between-group effect can be described by adding the group mean to the model. Adding the deviation term into the model increases the between-group component of the error term. A new formulation in terms a bivariate random effects model is presented to deal with the problem that the true group mean is not known. Population averaged prediction is discussed by making a difference between the hierarchical population and the population of individuals. In the population of individuals, the standard prediction for the population mean is biased, if the model contains a random intercept which is correlated with the group size. The chapter discusses how an observed y-value can be predicted using a mixed-effects model when the observation is correlated with the residual errors in the data. Finally, the chapter derives the prediction variance when a previously estimated model is applied to predict y-variables in a new group without re- estimating the model.
