Testing Fixed and Random Terms in Linear Mixed Models

Abstract

In linear mixed models the selection of fixed and random effects using a testing hypothesis approach brings up several problems. We deal with the boundary point problem emerging when no randomness is hypotesized and the confounding impact of randomness on the coefficients arising when fixed effects are tested. The test statistics are defined by a ratio of two quadratic forms derived from ordinary least squares, are simple, sufficiently general, easy to compute, with known finite sample properties. The test statistic on randomness has a known exact distribution, the density of the statistic on fixed effect is unknown and is approximated by a noncentral F−distribution. The goodness-of-approximation and the selection approach is examined in-depth by simulation. The method proposed in this paper must be seen as complementary to existing selection procedures widening and enriching all information necessary for taking a decision.