Analyzing Small Samples of Repeated Measures Data with the Mixed-Model Adjusted<i>F</i>Test

Arnau, Jaume; Bono, Roser; Vallejo, Guillermo

doi:10.1080/03610910902785746

Cited by 32 publications

(38 citation statements)

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“…Eight repeated measures were used in the studies by Keselman et al (2000), Kowalchuk and Keselman (2001), and Vallejo and Ato (2006). The intermediate value of K = 6 was also examined in the studies by Arnau et al (2009), Arnau et al (2012, Padilla and Algina (2007), and Wilcox (2006). Finally, we also analyzed an extreme number of repeated measures (K = 10), as was done in the simulation study by Ahmad, Werner, and Brunner (2008).…”

Section: Sphericity Valuesmentioning

confidence: 99%

“…The latter value was taken to be a good approximation to sphericity, whereas the former represented nonsphericity. Both values have been used in the majority of simulation studies of repeated measures designs Arnau et al, 2013aArnau et al, , b, 2014Arnau et al, 2012;Arnau et al, 2009;Berkovits et al, 2000;and Keselman & Keselman, 1990, among many others).…”

Section: Sphericity Valuesmentioning

confidence: 99%

“…Sample size The sample sizes chosen were the same as or similar to the cell sizes most widely used in the simulation studies of repeated measures designs published since 1990 (Arnau, Bendayan, Blanca, & Bono, 2013a, b, 2014Arnau et al, 2009;Keselman, Carriere, & Lix, 1993; 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5 UN, unstructured model Keselman, 1990;and Kowalchuk et al, 2004, among many others). On the basis of these studies, we chose to examine both very small (N = 5, 6, 7, and 10) and small (N = 12, 14, 15, 18, and 21) samples.…”

Section: Study Variablesmentioning

confidence: 99%

“…By means of simulation it is possible to generate not only normally distributed data but also data that reflect what is commonly found in real-world settings (Blanca, Arnau, López-Montiel, Bono, & Bendayan, 2013;Micceri, 1989). Thus, various Monte Carlo simulation studies have analyzed the fixed effects associated with time (repeated measures variable) using normally or nonnormally distributed data (Arnau, Bono, Blanca, & Bendayan, 2012;Arnau, Bono, & Vallejo, 2009;Kowalchuk, Keselman, Algina, & Wolfinger, 2004;Vallejo & Ato, 2006, among others). Most of these studies analyzed mixed models by generating data from an unstructured (UN) population covariance matrix with sphericity values of .57 and .75.…”

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Sphericity estimation bias for repeated measures designs in simulation studies

et al. 2015

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In this study, we explored the accuracy of sphericity estimation and analyzed how the sphericity of covariance matrices may be affected when the latter are derived from simulated data. We analyzed the consequences that normal and nonnormal data generated from an unstructured population covariance matrix-with low (ε = .57) and high (ε = .75) sphericity-can have on the sphericity of the matrix that is fitted to these data. To this end, data were generated for four types of distributions (normal, slightly skewed, moderately skewed, and severely skewed or log-normal), four sample sizes (very small, small, medium, and large), and four values of the within-subjects factor (K = 4, 6, 8, and 10). Normal data were generated using the Cholesky decomposition of the correlation matrix, whereas the Vale-Maurelli method was used to generate nonnormal data. The results indicate the extent to which sphericity is altered by recalculating the covariance matrix on the basis of simulated data. We concluded that bias is greater with spherical covariance matrices, nonnormal distributions, and small sample sizes, and that it increases in line with the value of K. An interaction was also observed between sample size and K: With very small samples, the observed bias was greater as the value of K increased.

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Section: Sphericity Valuesmentioning

confidence: 99%

Section: Sphericity Valuesmentioning

confidence: 99%

Section: Study Variablesmentioning

confidence: 99%

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confidence: 99%

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Sphericity estimation bias for repeated measures designs in simulation studies

et al. 2015

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“…3 The denominator degrees of freedom and p-values of F tests in this tutorial were computed using Satterthwaite's approximation (Fai & Cornelius, 1996;Satterthwaite, 1946), the preferred method when a constrained variance components model is used. An alternative method, Kenward-Roger Approximation (Kenward & Roger, 1997), is recommended when sample sizes are moderate to small and design is reasonably balanced (Schaalje, McBride, & Fellinghamm, 2001), although which method is better has not been fully resolved (Arnau, Bono, & Vallejo, 2009;Spilke, Piepho, & Hu, 2005). There are many ways to create contrast matrices to fit the mixed effects model, and different program may use different strategies to create the contrast matrices.…”

Section: Section 1: Technical Detailsmentioning

confidence: 99%

Generalizing across stimuli as well as subjects: A non-mathematical tutorial on mixed-effects models

Chang¹,

Lane²

2016

TQMP

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Although it has long been known that analyses that treat stimuli as a fixed effect do not permit generalization from the sample of stimuli to the population of stimuli, surprisingly little attention has been paid to this issue outside of the field of psycholinguistics. The purposes of the article are (a) to present a non-technical explanation of why it is critical to provide a statistical basis for generalizing to both the population subjects and the population of stimuli and (b) to provide instructions for doing analyses that allows this generalization using four common statistical analysis programs (JMP, R, SAS, and SPSS).

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On the analysis of very small samples of Gaussian repeated measurements: an alternative approach

Westgate

Burchett

2017

Statistics in Medicine

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SUMMARY The analysis of very small samples of Gaussian repeated measurements can be challenging. First, due to a very small number of independent subjects contributing outcomes over time, statistical power can be quite small. Second, nuisance covariance parameters must be appropriately accounted for in the analysis in order to maintain the nominal test size. However, available statistical strategies that ensure valid statistical inference may lack power, whereas more powerful methods may have the potential for inflated test sizes. Therefore, we explore an alternative approach to the analysis of very small samples of Gaussian repeated measurements, with the goal of maintaining valid inference while also improving statistical power relative to other valid methods. This approach uses generalized estimating equations with a bias-corrected empirical covariance matrix that accounts for all small-sample aspects of nuisance correlation parameter estimation in order to maintain valid inference. Furthermore, the approach utilizes correlation selection strategies with the goal of choosing the working structure that will result in the greatest power. In our study, we show that when accurate modeling of the nuisance correlation structure impacts the efficiency of regression parameter estimation, this method can improve power relative to existing methods that yield valid inference.

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Analyzing Small Samples of Repeated Measures Data with the Mixed-Model AdjustedFTest

Cited by 32 publications

References 27 publications

Sphericity estimation bias for repeated measures designs in simulation studies

Sphericity estimation bias for repeated measures designs in simulation studies

Generalizing across stimuli as well as subjects: A non-mathematical tutorial on mixed-effects models

On the analysis of very small samples of Gaussian repeated measurements: an alternative approach

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