title: Structural Equation Modeling Approaches for Analyzing Partially Nested Data.
abstract: Study designs involving clustering in some study arms, but not all study arms, are common in clinical treatment-outcome and educational settings. For instance, in a treatment arm, persons may be nested in therapy groups, whereas in a control arm there are no groups. Methodological approaches for handling such partially nested designs have recently been developed in a multilevel modeling framework (MLM-PN) and have proved very useful. We introduce two alternative structural equation modeling (SEM) approaches for analyzing partially nested data: a multivariate single-level SEM (SSEM-PN) and a multiple-arm multilevel SEM (MSEM-PN). We show how SSEM-PN and MSEM-PN can produce results equivalent to existing MLM-PNs and can be extended to flexibly accommodate several modeling features that are difficult or impossible to handle in MLM-PNs. For instance, using an SSEM-PN or MSEM-PN, it is possible to specify complex structural models involving cluster-level outcomes, obtain absolute model fit, decompose person-level predictor effects in the treatment arm using latent cluster means, and include traditional factors as predictors/outcomes. Importantly, implementation of such features for partially nested designs differs from that for fully nested designs. An empirical example involving a partially nested depression intervention combines several of these features in an analysis of interest for treatment-outcome studies.
authors.affiliation: a Department of Psychology and Human Development, Vanderbilt University.
authors.forename: Sonya K
authors.initials: SK
authors.lastname: Sterba
authors.affiliation: a Department of Psychology and Human Development, Vanderbilt University.
authors.forename: Kristopher J
authors.initials: KJ
authors.lastname: Preacher
authors.affiliation: b Department of Psychological Science, University of Vermont.
authors.forename: Rex
authors.initials: R
authors.lastname: Forehand
authors.affiliation: a Department of Psychology and Human Development, Vanderbilt University.
authors.forename: Emily J
authors.initials: EJ
authors.lastname: Hardcastle
authors.affiliation: a Department of Psychology and Human Development, Vanderbilt University.
authors.forename: David A
authors.initials: DA
authors.lastname: Cole
authors.affiliation: a Department of Psychology and Human Development, Vanderbilt University.
authors.forename: Bruce E
authors.initials: BE
authors.lastname: Compas