Choosing and modeling your mixed linear model

The literature has recently seen much debate as to what is the most appropriate way to specify the mixed linear model. Three different models are currently in wide use. Two of the models are formulated in terms of constants and random variables while the third specifies the mean and variance-covariance structure of the data as the model. This paper will relate the models for a general design. The mean and variance-covariance formulation will be used to unify the models, incorporate randomization restrictions, motivate when a factor should be called fixed or random, incorporate the inference space into the analysis of the problem and incorporate confounding factors into the design. The most common mixed model discussed in design texts will be shown to have some limitations in the model formulation stage of an analysis.