  In many life science experiments or medical studies, subjects are repeatedly
observed and measurements are collected in factorial designs with multivariate
data. The analysis of such multivariate data is typically based on multivariate
analysis of variance (MANOVA) or mixed models, requiring complete data, and
certain assumption on the underlying parametric distribution such as continuity
or a specific covariance structure, e.g., compound symmetry. However, these
methods are usually not applicable when discrete data or even ordered
categorical data are present. In such cases, nonparametric rank-based methods
that do not require stringent distributional assumptions are the preferred
choice. However, in the multivariate case, most rank-based approaches have only
been developed for complete observations. It is the aim of this work is to
develop asymptotic correct procedures that are capable of handling missing
values, allowing for singular covariance matrices and are applicable for
ordinal or ordered categorical data. This is achieved by applying a wild
bootstrap procedure in combination with quadratic form-type test statistics.
Beyond proving their asymptotic correctness, extensive simulation studies
validate their applicability for small samples. Finally, two real data examples
are analyzed.
