A Macro for Computing a Goodness of Fit Statistic for Linear Mixed Models

In the SAS System, PROC MIXED offers users the possibility to perform analysis of complex data where assumptions of traditional analysis of variance (ANOVA) methods such as homogeneity of variance or independence of error terms might be violated. Thus, this procedure can be used to analyze data where the observations are assumed to come from a normal distribution but are correlated such as in longitudinal studies or studies where the data are collected from clusters (center, school, city). Unfortunately, in the linear mixed models, there are few tools available for checking adequacy of the model. In this paper, we present a macro to compute a goodness-of-fit statistic denoted model concordance correlation that was proposed by Vonesh et al. (1996). One advantage of this statistic is that it is similar to the used in traditional ANOVA and can be used to assess the adequacy of the assumed mean and covariance structure. PROC IML is used to perform the computations. This paper should be accessible to anyone who is familiar with linear regression methods.