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Simplified Estimation and Testing in Unbalanced Repeated Measures Designs

Published online by Cambridge University Press:  01 January 2025

Martin Spiess ,
Pascal Jordan  and
Mike Wendt
Martin Spiess*
Affiliation:
University of Hamburg
Pascal Jordan
Affiliation:
University of Hamburg
Mike Wendt
Affiliation:
Medical School Hamburg
*
Correspondence should be made to Martin Spiess, Department of Psychology, University of Hamburg, Von-MellePark 5, 20146, Hamburg, Germany. Email: [email protected]
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Abstract

In this paper we propose a simple estimator for unbalanced repeated measures design models where each unit is observed at least once in each cell of the experimental design. The estimator does not require a model of the error covariance structure. Thus, circularity of the error covariance matrix and estimation of correlation parameters and variances are not necessary. Together with a weak assumption about the reason for the varying number of observations, the proposed estimator and its variance estimator are unbiased. As an alternative to confidence intervals based on the normality assumption, a bias-corrected and accelerated bootstrap technique is considered. We also propose the naive percentile bootstrap for Wald-type tests where the standard Wald test may break down when the number of observations is small relative to the number of parameters to be estimated. In a simulation study we illustrate the properties of the estimator and the bootstrap techniques to calculate confidence intervals and conduct hypothesis tests in small and large samples under normality and non-normality of the errors. The results imply that the simple estimator is only slightly less efficient than an estimator that correctly assumes a block structure of the error correlation matrix, a special case of which is an equi-correlation matrix. Application of the estimator and the bootstrap technique is illustrated using data from a task switch experiment based on an experimental within design with 32 cells and 33 participants.

Keywords

repeated measures designunbalanced designgeneralized estimating equationsbootstrapWald testtask switching paradigm
Type
Original Paper
Information
Psychometrika , Volume 84 , Issue 1 , 15 March 2019 , pp. 212 - 235
Copyright
Copyright © 2018 The Psychometric Society

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Footnotes

Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11336-018-9620-2) contains supplementary material, which is available to authorized users.

The authors thank Aquiles Luna-Rodriguez for programming the experimental software and Marvin Gensicke for collecting the data.

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