The LMIXED Procedure

The LMIXED procedure fits a variety of linear mixed models to data and enables you to use these fitted models to make statistical inferences about the data. A linear mixed model is a generalization of the standard linear model that is used in the GLM procedure in SAS/STAT software; the generalization is that the data are permitted to exhibit correlation and nonconstant variability. Therefore, the linear mixed model provides you with the flexibility of modeling not only the means of your data (as in the standard linear model) but also their variances and covariances.

The primary assumptions underlying the analyses that the LMIXED procedure performs are as follows:

Because Gaussian data can be modeled entirely in terms of their means, variances and covariances, the two sets of parameters in a linear mixed model specify the complete probability distribution of the data. The parameters of the mean model are called fixed-effects parameters, and the parameters of the variance-covariance model are called covariance parameters.

The fixed-effects parameters are associated with known explanatory variables, as in the standard linear model. These variables can be either qualitative (as in the traditional analysis of variance) or quantitative (as in standard linear regression).

The covariance parameters are what distinguishes the linear mixed model from the standard linear model. The need for covariance parameters arises quite frequently in applications. A typical application follows a scenario in which the experimental units that the data are measured on can be grouped into clusters and the data from a common cluster are correlated. This scenario can be generalized to include one set of clusters nested within another. For example, if students are the experimental unit, they can be clustered into classes, which in turn can be clustered into schools. Each level of this hierarchy can introduce an additional source of variability and correlation.

The LMIXED procedure provides a variety of covariance structures. The most common covariance structures arise from the use of random effects, which are additional unknown random variables that are assumed to affect the variability of the data. The variances of the random effects, commonly known as variance components, become the covariance parameters for this particular structure. Traditional linear mixed models contain both fixed and random effects; in fact, it is the combination of these two types of effects that led to the name mixed model. The LMIXED procedure fits not only these traditional variance component models but also numerous other covariance structures.

The LMIXED procedure fits the structure you select by using the method of restricted maximum likelihood (REML), also known as residual maximum likelihood. The method of maximum likelihood (ML), is also available.