Simulation study of power and sample size for repeated measures with multinomial outcomes: an application to sound direction identification experiments (SDIE)

Abstract

This study focuses on sample size determination in repeated measures studies with multinomial outcomes from multiple factors. In settings where multiple factors have repeated measures, a single subject could have hundreds of observations. Sample size selection may then refer to the number of subjects, the number of levels within a factor, or the number of repetitions within the level. We simulate multinomial data through a generalized linear mixed model (GLMM) with and without overdispersion, compute the empirical power of detecting group difference for several analytical methods and contrast their performance in group comparison studies with repeated multinomial data. We use four spatial functions to model the spatial correlation structures among observations. We evaluate the factors affecting the power under various scenarios. We also present a dataset typical in hearing studies for sound localization, in which a spatially distributed array of audio loudspeakers plays multiple sounds in order to compare two programming schemes for a hearing aid device.

Non-normal Distributions Commonly Used in Health, Education, and Social Sciences: A Systematic Review

“…In relation to continuous distributions, numerous simulation studies have analyzed the lognormal distribution ( Algina and Keselman, 1998 ; Keselman et al, 2000 ; Kowalchuk et al, 2004 ; Arnau et al, 2012 ; Oberfeld and Franque, 2013 ; Bono et al, 2016 , among others), and also the exponential distribution ( Lix et al, 2003 ; Arnau et al, 2012 ). Among discrete distributions, simulation studies have been conducted with binomial ( Wu and Wu, 2007 ; Fang and Louchin, 2013 ) and multinomial distributions ( Kuo-Chin, 2010 ; Bauer and Sterba, 2011 ; Jiang and Oleson, 2011 ). If the results of simulation studies are to be truly useful they need to include the distributions most commonly used in empirical contexts.…”

Robustness of Generalized Linear Mixed Models for Split-Plot Designs with Binary Data

“…Finally, the robustness of the GLMM can also be studied in terms of power (Chen et al, 2016;Stroup, 2013). Despite the increasing use of GLMMs, there are few articles reporting a power analysis for these models (e.g., Dang et al, 2008;Jiang & Oleson, 2011;Johnson et al, 2015;Kain et al, 2015). A fur-ther study analyzing the robustness of the GLMM in terms of power and calculating the optimal sample, as proposed for the LMM (Vallejo et al, 2019), would therefore provide a useful complement to the present results.…”

“…More generally, the GLMM has most frequently been applied in longitudinal studies or repeated measures designs with binary response variables (Bakbergenuly & Kulinskaya, 2018;Cho & Goodwin, 2017;Gawarammana & Sooriyarachchi, 2017;Zhang et al, 2011), with count response variables (Coupé, 2018;Huang et al, 2016;Kruppa & Hothorn, 2021;Sun et al, 2019;Zhang et al, 2012), with multinomial outcomes (Jiang & Oleson, 2011) or, to a lesser extent, with continuous response variables (Lo & Andrews, 2015). It is worth noting that binary repeated measures are a common occurrence in biology, medicine, psychology, and sociology, as well as in many other practical fields (Gawarammana & Sooriyarachchi, 2017).…”