Violation of the sphericity assumption and its effect on Type-I error rates in repeated measures ANOVA and multi-level linear models (MLM)

This study aims to investigate the effects of violations of the sphericity assumption on Type I error rates for different methodical approaches of repeated measures analysis using a simulation approach. In contrast to previous simulation studies on this topic, up to nine measurement occasions were considered. Therefore, two populations representing the conditions of a violation vs. a non-violation of the sphericity assumption without any between-group effect or within-subject effect were created and 5,000 random samples of each population were drawn. Finally, the mean Type I error rates for Multilevel linear models (MLM) with an unstructured covariance matrix (MLM-UN), MLM with compound-symmetry (MLM-CS) and for repeated measures analysis of variance (rANOVA) models (without correction, with Greenhouse-Geisser-correction, and Huynh-Feldt-correction) were computed. To examine the effect of both the sample size and the number of measurement occasions, sample sizes of n = 20, 40, 60, 80, and 100 were considered as well as measurement occasions of m = 3, 6 and 9. For MLM-UN, the results illustrate a massive progressive bias for small sample sizes (n =20) and m = 6 or more measurement occasions. This effect could not be found in previous simulation studies with a smaller number of measurement occasions. The mean Type I error rates for rANOVA with Greenhouse-Geisser-correction demonstrate a small conservative bias if sphericity was not violated, sample sizes were small (n = 20), and m = 6 or more measurement occasions were conducted. The results plead for a use of rANOVA with Huynh-Feldt-correction, especially when the sphericity assumption is violated, the sample size is rather small and the number of measurement occasions is large. MLM-UN may be used when the sphericity assumption is violated and when sample sizes are large.Comment: 14 pages, 6 figure

Unit-Weighted Scales Imply Models that Should Be Tested!

In several studies unit-weighted sum scales based on the unweighted sum of items are derived from the pattern of salient loadings in confirmatory factor analysis. The problem of this procedure is that the unit-weighted sum scales imply a model other than the initially tested confirmatory factor model. In consequence, it remains generally unknown how well the model implied by the unit-weighted sum scales fits the data. Nevertheless, the derived unit-weighted sum scales are often used in applied settings. The paper demonstrates how model parameters for the unit-weighted sum scales can be computed and tested by means of structural equation modeling. An empirical example based on a personality questionnaire and subsequent unit-weighted scale analyses are presented in order to demonstrate the procedure

Intra-Subject Variability, Intelligence, and ADHD Traits in a Community-Based Sample

Objective: The present study investigates the predictive validity of intra-subject variability (ISV) for ADHD traits in a community-based sample and the stability of the relationship between ISV and fluid intelligence (gf) across the continuum of ADHD traits. Method: Age-residualized data from 426 participants (8-18 years, 6% ADHD) was used to investigate whether ex-Gaussian and DDM parameters derived from simple choice-reaction-time tasks can predict continuously assessed ADHD traits. Multiple-Group-Analyses and Latent-Moderated-Structural-Equations were used to test whether ADHD traits moderate the relationship between ISV and gf. Results: sigma and mu of the ex-Gaussian model as well as DDM parameters drift rate (v) and boundary separation (a) significantly predicted general ADHD traits, while tau predicted attention difficulties specifically. Across the ADHD continuum, sigma and v were significant predictors of gf. Conclusion: The results confirm the link between ISV and ADHD. The relationship between ISV and gf appears stable across the ADHD continuum