title: Analyzing average and conditional effects with multigroup multilevel structural equation models.
abstract: Conventionally, multilevel analysis of covariance (ML-ANCOVA) has been the recommended approach for analyzing treatment effects in quasi-experimental multilevel designs with treatment application at the cluster-level. In this paper, we introduce the generalized ML-ANCOVA with linear effect functions that identifies average and conditional treatment effects in the presence of treatment-covariate interactions. We show how the generalized ML-ANCOVA model can be estimated with multigroup multilevel structural equation models that offer considerable advantages compared to traditional ML-ANCOVA. The proposed model takes into account measurement error in the covariates, sampling error in contextual covariates, treatment-covariate interactions, and stochastic predictors. We illustrate the implementation of ML-ANCOVA with an example from educational effectiveness research where we estimate average and conditional effects of early transition to secondary schooling on reading comprehension.
authors.affiliation: Department of Methodology and Evaluation Research, Institute of Psychology, University of Jena Jena, Germany ; Department of Data Analysis, Ghent University Ghent, Belgium.
authors.forename: Axel
authors.initials: A
authors.lastname: Mayer
authors.affiliation: Center for Educational Science and Psychology, University of Tübingen Tübingen, Germany.
authors.forename: Benjamin
authors.initials: B
authors.lastname: Nagengast
authors.affiliation: Department of Education, University of Oxford Oxford, UK.
authors.forename: John
authors.initials: J
authors.lastname: Fletcher
authors.affiliation: Department of Methodology and Evaluation Research, Institute of Psychology, University of Jena Jena, Germany.
authors.forename: Rolf
authors.initials: R
authors.lastname: Steyer
keywords: average effects; conditional effects; multilevel analysis of covariance; multilevel structural equation modeling; quasi-experimental designs