Specification tests in mixed effects models

Two methods are proposed for testing the error distribution in mixed effects models, where J measurements are taken on each of I individuals. The test statistics involve empirical characteristic functions resulting from estimation of the mixed effects. One method is designed for J   large and is justified by asymptotic results when J→∞J→∞. The other is appropriate for moderately small J  , and appears to be a simpler alternative method achieving the near n‐consistency of the procedure of Hall and Yao (2003). This method is based on a novel use of piecewise linear approximations to characteristic functions along a grid, and its computation may be simplified using complex arithmetic. Theoretical and computational issues are addressed while Monte Carlo results show that the new procedures compare favorably with classical methods.