Fully Nonparametric Methods for Multivariate Data in Factorial Designs. Asymptotics, Finite Sample Approximations, and Implementation in R

Abstract

Abstract This article methodologically complements the R package nparMD, and it presents the follow-up to a previous article that had built the foundation for the procedure implemented initially within the package. We consider non-parametric rank-based inference methods for multivariate samples in completely randomized factorial designs. Assumption on the data are minimal: the variables need to be at least ordinal (including binary), and the multivariate observation vectors from different experimental units are assumed independent although there may be dependencies within the vectors. Different endpoints may be measured on different scales. That is, multivariate observation vectors with a count variable, a continuous metric response, and ordinal endpoints, are allowed for. Two different asymptotic settings are considered: (1) sample sizes are large while the number of factor levels is small and bounded, (2) small samples while the number of factor levels is large. Special attention is paid to deriving inference methods for the interaction effect, as here the variance-covariance matrix does not simplify under the null. In addition, we discuss some finite sample approximations and demonstrate application of the methods using real data from a psychological study on Seasonal Affective Disorder (SAD), also commonly referred to as Winter depression