Repeated Measures ANOVA with Latent Variables to Analyze Interindividual Differences in Contrasts

• Published in: Multivariate behavioral research Vol. 57; no. 1; pp. 2 - 19
• Main Authors: Langenberg, Benedikt, Helm, Jonathan L., Mayer, Axel
• Format: Journal Article
• Language: English
• Published: United States Routledge 2022; Taylor & Francis Ltd
• Subjects: Analysis of Variance; Data analysis; interactions; latent variables; main effects; Multivariate statistical analysis; Repeated measures ANOVA; repeated measures designs; Research Design; Statistical analysis; Variance analysis; Within-subjects design; main effects; latent variables; repeated measures designs; Repeated measures ANOVA; interactions
• ISSN: 0027-3171; 1532-7906; 1532-7906
• DOI: 10.1080/00273171.2020.1803038

Repeated measures analysis of variance (RM-ANOVA) is a broadly used statistical method to analyze data from experimental designs. RM-ANOVA aims at investigating effects of experimental conditions (i.e., factors) and predictors that affect the outcome of interest. It mainly considers contrasts that test standard main and interaction effects, even though more complex contrasts can in principle be used. Analyses, however, only focus on drawing conclusions about average effects and do not take into consideration interindividual differences in these effects. We propose an alternative approach to RM-ANOVA for analyzing repeated measures data, termed latent repeated measures analysis of variance (L-RM-ANOVA). The new approach is based on structural equation modeling and extends the latent growth components approach. L-RM-ANOVA enables the researcher to not only consider mean differences between different experimental conditions (i.e., average effects), but also to investigate interindividual differences in effects. Such interindividual differences are considered with regard to standard main and interactions effects and also with regard to customized contrasts that allow for testing specific hypotheses of interest. Furthermore, L-RM-ANOVA can include a measurement model for latent variables and can be used for the analysis of complex multi-factorial repeated measures designs. We conclude the presentation by demonstrating L-RM-ANOVA using a minimal repeated measures example.