ABSTRACT
In grouped data sets, observations are assigned to groups, which constitute a sample from a population of groups. Linear mixed-effects models provide a justified analysis method in such cases through introduction of random group effects. Formulation of this model is conveniently done by exploring and modeling the variability among the individual groups of the data. The simplest mixed-effects model is the variance component model where no fixed predictors are included. Extension to general linear mixed-effect model arise by writing the fixed mean as a linear regression equation and associating random effects with other regressors than the intercept. Matrix formulation of the model is presented and demonstrated. The resulting model is a special case of the linear model with correlated errors, and the estimation methods presented in Chapter 4 are directly applicable. Also, Bayesian methods can be used. Prediction of the random group effects using the best linear unbiased predictor is formulated and demonstrated with several examples. Consequences of the random effects to graphical evaluation of model fit, hypothesis tests and coefficient of determination are discussed and demonstrated. A total of 26 examples illustrate the concepts and their use with real-life data.
