Search Results (4)

We propose and demonstrate a new two-stage maximum likelihood estimator for parameters of a social relations structural equation model (SR-SEM) using estimated summary statistics ($\widehat{\mathsf{\Sigma }}$) as data, as well as uncertainty about $\widehat{\mathsf{\Sigma }}$ to obtain robust inferential statistics. The SR-SEM is a generalization of a traditional SEM for round-robin data, which have a dyadic network structure (i.e., each group member responds to or interacts with each other member). Our two-stage estimator is developed using similar logic as previous two-stage estimators for SEM, developed for application to multilevel data and multiple imputations of missing data. We demonstrate out estimator on a publicly available data set from a 2018 publication about social mimicry. We employ Markov chain Monte Carlo estimation of $\widehat{\mathsf{\Sigma }}$ in Stage 1, implemented using the R package rstan. In Stage 2, the posterior mean estimates of $\widehat{\mathsf{\Sigma }}$ are used as input data to estimate SEM parameters with the R package lavaan. The posterior covariance matrix of estimated $\widehat{\mathsf{\Sigma }}$ is also calculated so that lavaan can use it to calculate robust standard errors and test statistics. Results are compared to full-information maximum likelihood (FIML) estimation of SR-SEM parameters using the R package srm. We discuss how differences between estimators highlight the need for future research to establish best practices under realistic conditions (e.g., how to specify empirical Bayes priors in Stage 1), as well as extensions that would make 2-stage estimation particularly advantageous over single-stage FIML. Full article

Examining interactions among predictors is an important part of a developing research program. Estimating interactions using latent variables provides additional power to detect effects over testing interactions in regression. However, when predictors are modeled as latent variables, estimating and testing interactions requires additional steps beyond the models used for regression. We review methods of estimating and testing latent variable interactions with a focus on product indicator methods. Product indicator methods of examining latent interactions provide an accurate method to estimate and test latent interactions and can be implemented in any latent variable modeling software package. Significant latent interactions require additional steps (plotting and probing) to interpret interaction effects. We demonstrate how these methods can be easily implemented using functions in the semTools package with models fit using the lavaan package in R, and we illustrate how these methods work using an applied example concerning teacher stress and testing. Full article

Background: Researchers frequently use the responses of individuals in clusters to measure cluster-level constructs. Examples are the use of student evaluations to measure teaching quality, or the use of employee ratings of organizational climate. In earlier research, Stapleton and Johnson (2019) provided advice for measuring cluster-level constructs based on a simulation study with inadvertently confounded design factors. We extended their simulation study using both Mplus and lavaan to reveal how their conclusions were dependent on their study conditions. Methods: We generated data sets from the so-called configural model and the simultaneous shared-and-configural model, both with and without nonzero residual variances at the cluster level. We fitted models to these data sets using different maximum likelihood estimation algorithms. Results: Stapleton and Johnson’s results were highly contingent on their confounded design factors. Convergence rates could be very different across algorithms, depending on whether between-level residual variances were zero in the population or in the fitted model. We discovered a worrying convergence issue with the default settings in Mplus, resulting in seemingly converged solutions that are actually not. Rejection rates of the normal-theory test statistic were as expected, while rejection rates of the scaled test statistic were seriously inflated in several conditions. Conclusions: The defaults in Mplus carry specific risks that are easily checked but not well advertised. Our results also shine a different light on earlier advice on the use of measurement models for shared factors. Full article

Structural equation modeling (SEM) has been proposed to estimate generalizability theory (GT) variance components, primarily focusing on estimating relative error to calculate generalizability coefficients. Proposals for estimating absolute-error components have given the impression that a separate SEM must be fitted to a transposed data matrix. This paper uses real and simulated data to demonstrate how a single SEM can be specified to estimate absolute error (and thus dependability) by placing appropriate constraints on the mean structure, as well as thresholds (when used for ordinal measures). Using the R packages lavaan and gtheory, different estimators are compared for normal and discrete measurements. Limitations of SEM for GT are demonstrated using multirater data from a planned missing-data design, and an important remaining area for future development is discussed. Full article