Permuting longitudinal data despite all the dependencies

TL;DR

This paper introduces a permutation-based method to improve the small sample performance of the Wald-type statistic in repeated measures designs, maintaining large sample validity and controlling type-I error more accurately.

Contribution

It proposes a novel permutation procedure for the Wald-type statistic that enhances finite sample accuracy in repeated measures analysis.

Findings

Permutation WTS controls type-I error well in small samples

Method maintains asymptotic properties for large samples

Extensive simulations demonstrate improved finite sample performance

Abstract

For general repeated measures designs the Wald-type statistic (WTS) is an asymptotically valid procedure allowing for unequal covariance matrices and possibly non-normal multivariate observations. The drawback of this procedure is the poor performance for small to moderate samples, i.e. decisions based on the WTS may become quite liberal. It is the aim of the present paper to improve its small sample behavior by means of a novel permutation procedure. In particular, it is shown that a permutation version of the WTS inherits its good large sample properties while yielding a very accurate finite sample control of the type-I error as shown in extensive simulations. Moreover, the new permutation method is motivated by a practical data set of a split plot design with a factorial structure on the repeated measures.