Title: The semnova Package for Latent Repeated Measures ANOVA

Authors: Benedikt Langenberg, Axel Mayer

Affiliation: RWTH Aachen University

Abstract:
Repeated measures analysis of variance (RM-ANOVA) is a broadly used
statistical method to analyze data from experimental designs. RM-ANOVA,
however, seeks to draw conclusions about main effects and interactions based
on manifest dependent variables. Different structural equation modelling based
approaches have been proposed to incorporate latent variables in repeated
measures designs. Latent growth curve models and the more general latent
growth components approach are two examples. Most of these approaches focus on
examining change across a single within-subjects factor (oftentimes, time) and
do not incorporate higher order interaction terms as is very common in
experimental designs with several within-subject factors. We present the
latent RM-ANOVA approach that is capable of handling complex factorial designs
of any size and introduce the R package semnova that makes latent RM-ANOVA
conveniently accessible for applied researchers. The software is based on the
R package lavaan for structural equation modelling. We use a simple three by
two experimental design with latent variables to illustrate the main
functionality of the software. We conclude the presentation with current and
future developments of the software. These developments include the use of
different test statistics, custom contrasts, and the examination of
interindividual differences in custom contrasts and standard main and
interaction effects.