Latent Multilevel Structural Equation Models for Experimental Designs Using Maximum Likelihood and Bayesian Methods (MSEM-EX)

• Applicant: Professor Dr. Axel Mayer
• Subject Area: General, Cognitive and Mathematical Psychology ; Personality Psychology, Clinical and Medical Psychology, Methodology
• Term: since 2017
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 386867729

This renewal proposal continues the project „Repeated Measures ANOVA with Latent Variables: A New Approach Based on Structural Equation Modeling“. In the first project phase, we developed the latent repeated measures analysis of variance (L-RM-ANOVA), a structural equation modeling (SEM) based approach that is a more general alternative to traditional repeated measures analysis of variance that includes latent outcomes (e.g., latent traits, implicit motives, attention, and emotions). A key advantage of this approach is that it allows for examining and predicting interindividual differences in main effects, interactions and contrasts. We demonstrated several benefits of using the new L-RM-ANOVA approach, including the option to incorporate measurement models for latent variables, a power advantage compared to manifest models, the possibility to test different error structures, such as, sphericity and compound symmetry, and the option to investigate formerly hidden assumptions about measurement invariance and parallelism of indicators. The L-RM-ANOVA is a very flexible approach that has been developed for experimental designs with a single random factor (usually persons). However, many experiments involve at least two random factors (e.g., persons and the stimuli to which they respond, such as words or pictures). In the second project phase, we plan to extend this approach to experiments with more than one random factor using multilevel structural equation models. Currently, such data can be analyzed using linear mixed models (LMMs), but these models do not allow for latent dependent variables. It is very common in psychology and other fields to collect a number of replicates in each of the experimental conditions. Rather than averaging across replicates, LMMs allow to model random effects for participants and stimuli using repeated measures of a variable. L-RM-ANOVA is currently lacking this ability. This renewal proposal aims at closing exactly this gap. This new combination will bring together the strengths of multilevel SEM and the LMM framework and make this rich combination available to the analysis of repeated measures data. In this project, we will develop the general framework for latent multilevel SEMs for experimental designs with multiple random factors, including designs with nested and crossed random factors. We will consider different existing statistical frameworks that allow the specification of some (sub-)models, namely multilevel SEM, two-level SEM, cross-classified SEM, and ultra-wide SEM, and adapt them for experimental designs. We will implement frequentist and Bayesian estimation procedures for these models and thoroughly test the implementation in simulation studies and real world experiments. As in the first project phase, we will develop open source software that allows for convenient application of the new methods.

• DFG Programme: Research Grants