Structural equation models comprise a large class of popular statistical models, including factor analysis models, certain mixed models, and extensions thereof. Model estimation is complicated by the fact that we typically have multiple interdependent response variables and multiple latent variables (which may also be called random effects or…

Bayesian algorithms have been used successfully in the social and behavioral sciences to analyze dichotomous data particularly with complex structural equation models. In this study, we investigate the use of the Polya-Gamma data augmentation method with Gibbs sampling to improve estimation of structural equation models with dichotomous variables.…

The importance of sample size, although widely discussed in the literature on structural equation modeling (SEM), has not been widely recognized among applied SEM researchers. To narrow this gap, we focus on second language testing and learning studies and examine the following: (a) Is the sample size sufficient in terms of precision and power of…

This report summarizes the complex research literature on quantitative methods for assessing how impacts of educational interventions on instructional practices and student learning differ across students, educators, and schools. It also provides technical guidance about the use and interpretation of these methods. The research topics addressed…

A structural equation modeling approach to scale reliability evaluation can be employed to estimate generalizability theory indexes in settings where sampling of subjects and conditions is carried out. In one- and two-facet crossed designs, it is demonstrated how this method can be used to obtain estimates of relative generalizability…

Both structural equation models and hierarchical linear models (HLMs) have been commonly used in multilevel analysis. This study utilized simulated data to investigate the power difference among 3 multilevel models: HLM, deviation structural equation models, and a hybrid approach of HLM and structural equation models. Two factors were examined:…

Over the past 3 decades we have witnessed an increase in the complexity of theoretical models that attempt to explain development in a number of behavioral domains. The conceptual movement to examine behavior from both developmental and contextual perspectives parallels recent methodological advances in the analysis of change. These new analysis…

This paper is about the structural equation modelling of quantitative measures that are obtained from a multiple facet design. A facet is simply a set consisting of a finite number of elements. It is assumed that measures are obtained by combining each element of each facet. Methods and traits are two such facets, and a multitrait-multimethod…