## Estimating structural equation models using James-Stein type shrinkage estimators (vol 86, pg 96, 2021) Ghent University

A Correction to this paper has been published

A Correction to this paper has been published

This Teacher's Corner paper introduces Bayesian evaluation of informative hypotheses for structural equation models, using the free open-source R packages bain, for Bayesian informative hypothesis testing, and lavaan, a widely used SEM package. The introduction provides a brief non-technical explanation of informative hypotheses, the statistical underpinnings of Bayesian hypothesis evaluation, and the bain algorithm. Three tutorial examples ...

We propose a two-step procedure to estimate structural equation models (SEMs). In a first step, the latent variable is replaced by its conditional expectation given the observed data. This conditional expectation is estimated using a James-Stein type shrinkage estimator. The second step consists of regressing the dependent variables on this shrinkage estimator. In addition to linear SEMs, we also derive shrinkage estimators to estimate ...

Multilevel SEM is an increasingly popular technique to analyze data that are both hierarchical and contain latent variables. The parameters are usually jointly estimated using a maximum likelihood estimator (MLE). This has the disadvantage that a large sample size is needed and misspecifications in one part of the model may influence the whole model. We propose an alternative stepwise estimation method, which is an extension of the Croon method ...

This study introduces the statistical theory of using the Standardized Root Mean Squared Error (SRMR) to test close fit in ordinal factor analysis. We also compare the accuracy of confidence intervals (CIs) and tests of close fit based on the SRMR with those obtained based on the Root Mean Squared Error of Approximation (RMSEA). The current (biased) implementation for the RMSEA never rejects that a model fits closely when data are binary and ...

Many researchers have specific expectations about the relation between the means of different groups or between (standardized) regression coefficients. For example, in an experimental setting, the comparison of two or more treatment groups may be subject to order constraints (e.g., H 1: µ1 < µ2 < µ3 = µ4). In practice, hypothesis H 1 is usually tested using a classical one-way ANOVA with additional pairwise comparisons if the corresponding ...

Using a simulation study, we investigated U+2013 under varying sample sizes U+2013 the performance of two-step modeling, factor score regression, maximum likelihood estimation and Bayesian estimation with default and informative priors. We conclude that with small samples, all frequentist methods showed signs of breaking down (in terms of non-convergence, negative variances, extreme parameter estimates), as did the Bayesian condition with ...

Structural equation modeling (SEM) is a widely used statistical technique for studying relationships in multivariate data. Unfortunately, when the sample size is small, several problems may arise. Some problems relate to point estimation, whereas other problems relate to small sample inference. This chapter contains several potential solutions for point estimation, including penalized likelihood estimation, a method based on model-implied ...

In multilevel data, units at level 1 are nested in clusters at level 2, which in turn may be nested in even larger clusters at level 3, and so on. For continuous data, several authors have shown how to model multilevel data in a 'wide' or 'multivariate' format approach. We provide a general framework to analyze random intercept multilevel SEM in the 'wide format' (WF) and extend this approach for discrete data. In a simulation study, we vary ...

Factor score regression (FSR) is a popular alternative for structural equation modeling. Naively applying FSR induces bias for the estimators of the regression coefficients. Croon proposed a method to correct for this bias. Next to estimating effects without bias, interest often lies in inference of regression coefficients or in the fit of the model. In this article, we propose fit indices for FSR that can be used to inspect the model fit. We ...