Covariates in Nonparametric Mixed Models
                 by Arne Bathke
Dept. of Statistics, University of Kentucky, USA

The Analysis of Covariance (ANCOVA) is designed for the many practical situations in which factor effects are obscured by concomitant variables, or the main purpose of the investigation lies in assessing the effect of the concomitant variables. Not taking covariates into account may cause misleading results.

However, if the response variable or the covariable are only measured on an ordinal scale (like typically psychological and other scores), or if they show distinct nonnormal distributions, one would be reluctant to use ANCOVA methods.

In the last decade, important contributions have been made to the asymptotic theory of nonparametric, rank-based procedures. These procedures have become widely accepted due to the fact that they are not only a robust, but also a powerful alternative to the linear model in factorial design.

In this talk, we introduce a nonparametric mixed model with covariates. Thus, we try to combine the power gain through introduction of covariates into a factorial design with the robustness of nonparametric procedures. Asymptotic distributions are derived for tests on factor effects as well as for tests on the effect of a covariate.

The proposed procedures are computationally simple, and simulations show good small-sample performance. The tests can be used for data with ties, and even for completely ordinal data.