Nonparametric ANCOVA with two and three covariates

Fully nonparametric analysis of covariance with two and three covariates is considered. The approach is based on an extension of the model of Akritas et al. (Biometrika 87(3) (2000) 507). The model allows for possibly nonlinear covariate effect which can have different shape in different factor level combinations. All types of ordinal data are included in the formulation. In particular, the response distributions are not restricted to comply to any parametric or semiparametric model. In this nonparametric model, hypotheses of no main effect no interaction and no simple effect, which adjust for the covariate values, are defined through a decomposition of the conditional distribution functions of the response given to the factor level combination and covariate values. The test statistics are based on averages over the covariate values of certain Nadaraya-Watson regression quantities. Under their respective null hypotheses, such test statistics are shown to have a central χ² distribution. Small sample corrections are also provided. Simulation results and the analysis of two real datasets are also presented.