Fall 2002 Seminar Series - October 17, 2002
University of Minnesota
School of Statistics
College of Liberal Arts
Goodness-of-fit tests for normal mixed model
Christian Ritz
Department of Mathematics and Physics
The Royal Veterinary and Agricultural University
Copenhagen, Denmark
Thursday, October 17, 2002
4:00 PM, 115
Ford Hall
Minneapolis, East Bank Campus
Social at 3:30 PM, 300
Ford Hall
Abstract
To assess the normality assumption of the random effects
in a normal mixed linear model, the so-called estimated best linear unbiased
predictors (EBLUPs) could be used. One such approach, taken by Lange and
Ryan (Ann. Statist. 17 624--642, 1989), is to construct a weighted normal
plot based on a pointwise limit result for a weighted empirical distribution
function of the standardized EBLUPs. Using a weighted normal plot it is
possible to adjust for design imposed imbalances. Looking at the corresponding
(weighted) empirical process, it is possible to obtain goodness-of-fit statistics
for testing the null hypothesis that the random effects follow a normal
distribution in a mixed linear model. The test is performed by applying
a classical goodness-of-fit statistic, eg Kolmogorov-Smirnov, to the difference
between the empirical process based on standardized EBLUPs and some suitable
reference process. The limiting distributions of these statistics are governed
by the limiting distribution of the underlying processes, for which weak
convergence is established. The power of the tests against several alternatives
is explored in a small simulation study. An example illustrates the use
of the tests.