Incompletely observed nonparametric factorial designs with repeated measurements: A wild bootstrap approach

TL;DR

This paper develops a wild bootstrap method for nonparametric factorial designs with repeated measurements, effectively handling missing data, singular covariance matrices, and ordinal data, validated through simulations and real data examples.

Contribution

It introduces a novel wild bootstrap approach for nonparametric multivariate factorial designs with missing and ordinal data, overcoming limitations of existing methods.

Findings

Method is asymptotically correct

Performs well in small samples

Successfully applied to real data examples

Abstract

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.