A SIMPLE FUNCTIONAL FORM MISSPECIFICATION TEST FOR LINEAR MIXED MODELS

Linear mixed models are usually fitted to cluster correlated data. For prediction purposes, these models link the mean of the response variable to a set of covariates whose functional form should not be severely misspecified. In this article, an exact t -test for fixed linear covariate effect against unspecified polynomial alternatives is proposed. Using an orthogonal transformation of the response vector, a set of identically and independently distributed residuals is obtained. Based on the sum of those residuals, the test statistic systematically deviates from zero as we depart from the null hypothesis. Using a simulation study, the performance of the test is assessed. The testing procedures are illustrated using the German health care usage data set.