Exact Multivariate Permutation Tests for Fixed Effects in Mixed-Models

A test for the fixed effect in mixed-models is proposed. It is based on permutation strategy and is exact. The testing approach presented is very general and the class of model covered is very broad. Multivariate responses with different type of variables (e.g. continuous, categorical and ranks) are usually tested with separated models and the overall test are usually reached trough Bonferroni-like combinations, i.e. without taking in account the joint distribution of the tests statistics. On the contrary in this approach the joint distribution is immediately obtained and the dependence among tests is taken in account in the overall test.