Repeated Measures ANOVA with Latent Variables: A New Approach Based on Structural Equation Modeling
Creators: name: Langenberg, Benedikt
Publisher: name: Universität Bielefeld
Year: 2022
Subjects: subject: 150

description: This doctoral dissertation develops latent repeated measures analysis of variance (L-RM-ANOVA) as an alternative approach to traditional repeated measures ANOVA (RM-ANOVA). Traditional RM-ANOVA are commonplace for investigating phenomena in the social and behavioral sciences, and researchers often use RM-ANOVA as a statistical method for analyzing data from repeated measures designs. The popularity of RM-ANOVA is, to some extent, due to its generality (i.e., many hypotheses may be tested via main and/or interaction effects), ease of application (i.e., virtually all statistical packages conduct RM-ANOVA), and desirable statistical properties (since these are optimal when all assumptions are fulfilled). RM-ANOVA, however, has several shortcomings including that it (1) focuses on drawing conclusions about average (causal) effects and does not consider interindividual differences, (2) assumes both perfectly reliable measures and measurement invariance for latent constructs, (3) assumes homogeneity of variance and fixed group sizes when including between-subject factors, (4) cannot handle missing data, and (5) relies on the normality assumption. L-RM-ANOVA addresses the aforementioned issues. It is a structural equation modeling (SEM) based approach -- as opposed to RM-ANOVA which relies on the general linear model -- and extends the latent growth components model. (1) L-RM-ANOVA enables the researcher to not only consider mean differences between experimental conditions (i.e., main and interaction effects) but also to investigate variances of effect variables that represent interindividual differences. L-RM-ANOVA estimates variances of effect variables across individuals and also allows to predict effect variables by covariates which explain a share of the variances of the effect variables. (2) As L-RM-ANOVA is an SEM based approach, it can incorporate a measurement model for both the dependent variables and the predictors to explicitly model measurement error. It is also possible to test the oftentimes implicit assumption of measurement invariance across experimental conditions. (3) The approach can be further extended to include between-subject factors (i.e., groups) through dummy-coded variables or by using a multi-group SEM approach. The multi-group approach allows for the relaxation of the homogeneity of variance assumption across groups and to estimate the group sizes as a model parameter, thus accounting for uncertainty in the group sizes. (4+5) Lastly, L-RM-ANOVA profits from a variety of SEM benefits, namely fit indices, handling missing data through full information maximum likelihood, robust estimators, and robustness against violations of normality. Beyond these advantages over RM-ANOVA, L-RM-ANOVA provides further benefits. Through SEM, it is possible to place constraints on the covariance matrix of the effect variables, enabling the user to test patterned covariance matrices. This can be used to test assumptions such as sphericity (i.e., as an alternative test to Mauchly's test for sphericity), compound symmetry or auto-regressive effects. Although L-RM-ANOVA provides many advantages, it is not without its drawbacks for the user: L-RM-ANOVA uses maximum likelihood which relies on asymptotic theory and requires potentially large sample sizes. This dissertation will account for this shortcoming by showing how to use an alternative Bayesian estimation procedure which does not rely on sample size assumptions. In particular, this dissertation will show how to place informative priors on means, (co)variances and regression coefficients that constitute a particular main or interaction effect in the L-RM-ANOVA model. This dissertation will also show how different choices of priors affect statistical properties of the L-RM-ANOVA model.