Instrumental Variables Two-Stage Least Squares (2SLS) vs. Maximum Likelihood Structural Equation Modeling of Causal Effects in Linear Regression Models

In the presence of omitted variables or similar validity threats, regression estimates are biased. Unbiased estimates (the causal effects) can be obtained in large samples by fitting instead the Instrumental Variables Regression (IVR) model. The IVR model can be estimated using structural equation modeling (SEM) software or using Econometric estimators such as two-stage least squares (2SLS). We describe 2SLS using SEM terminology, and report a simulation study in which we generated data according to a regression model in the presence of omitted variables and fitted (a) a regression model using ordinary least squares, (b) an IVR model using maximum likelihood (ML) as implemented in SEM software, and (c) an IVR model using 2SLS. Coverage rates of the causal effect using regression methods are always unacceptably low (often 0). When using the IVR model, accurate coverage is obtained across all conditions when N = 500. Even when the IVR model is misspecified, better coverage than regression is generally obtained. Differences between 2SLS and ML are small and favor 2SLS in small samples (N ≤ 100).     

Structural Models for Binary Repeated Measures: Linking Modern Longitudinal Structural Equation Models to Conventional Categorical Data Analysis for Matched Pairs

The current widespread availability of software packages with estimation features for testing structural equation models with binary indicators makes it possible to investigate many hypotheses about differences in proportions over time that are typically only tested with conventional categorical data analyses for matched pairs or repeated measures, such as McNemar’s chi-square. The connection between these conventional tests and simple longitudinal structural equation models is described. The equivalence of several conventional analyses and structural equation models reveals some foundational concepts underlying common longitudinal modeling strategies and brings to light a number of possible modeling extensions that will allow investigators to pursue more complex research questions involving multiple repeated proportion contrasts, mixed between-subjects × within-subjects interactions, and comparisons of estimated membership proportions using latent class factors with multiple indicators. Several models are illustrated, and the implications for using structural equation models for comparing binary repeated measures or matched pairs are discussed.     

Modeling Nonlinear Structural Equation Models: A Comparison of the Two-Stage Generalized Additive Models and the Finite Mixture Structural Equation Model

Researchers have devoted some time and effort to developing methods for fitting nonlinear relationships among latent variables. In particular, most of these have focused on correctly modeling interactions between 2 exogenous latent variables, and quadratic relationships between exogenous and endogenous variables. All of these approaches require prespecification of the nonlinearity by the researcher, and are limited to fairly simple nonlinear relationships. Other work has been done using mixture structural equation models (SEMM) in an attempt to fit more complex nonlinear relationships. This study expands on this earlier work by introducing the 2-stage generalized additive model (2SGAM) approach for fitting regression splines in the context of structural equation models. The model is first described and then investigated through the use of simulated data, in which it was compared with the SEMM approach. Results demonstrate that the 2SGAM is an effective tool for fitting a variety of nonlinear relationships between latent variables, and can be easily and accurately extended to models including multiple latent variables. Implications of these results are discussed.     

Trends and Issues in Distance Education: International Perspectives, 2nd Edition

Good books on broad topics are hard to find. The second edition of Trends and Issues in Distance Education does a great job of meeting this challenge by offering chapters on far‐reaching international trends that can have practical influence on the decisions that readers must make at the local level. From e‐learning in manufacturing companies in Malaysia to various models for supporting learners who are at a distance, the book is a valuable resource for when performance issues lead you beyond the boundaries of the traditional training classroom. Trends and Issues in Distance Education: International Perspectives, 2nd ed. (2012; ISBN: 978‐1‐61735‐828‐9) is published by Information Age Publishing (paperback).     

Development and Reliability of the Comprehensive Crisis Plan Checklist, 2nd Edition

As the research base for school crisis intervention and prevention expands, the need for well-developed tools to assess school readiness in the event of a crisis increases. This paper describes how the Comprehensive Crisis Plan Checklist (CCPC) was updated to reflect advances in crisis management and crisis planning. An extensive literature search and pilot study were used to refine existing items and create new items for the checklist. The Comprehensive Crisis Plan Checklist, 2^nd Edition (CCPC-2) has 102 items separated into three sections: prevention, intervention, and postvention. The CCPC-2 can be used by crisis teams to create new crisis plans or evaluate existing ones. Users are encouraged to carefully consider the inclusion of all items and articulate why individual items are not necessarily based on their specific needs. The CCPC-2 was given to 10 pairs of raters to evaluate school-based crisis plans; average interrater reliability was 89.04%. Discussion focuses on item analysis and how to use the checklist within a school setting.     

Structural Equation Models of Latent Interactions: Clarification of Orthogonalizing and Double-Mean-Centering Strategies

The purpose of this investigation is to compare a new (double-mean-centering) strategy to estimating latent interactions in structural equation models with the (single) mean-centering strategy (Marsh, Wen, & Hau, 2004 Marsh, H. W., Wen, Z. and Hau, K. T. 2004. Structural equation models of latent interactions: Evaluation of alternative estimation strategies and indicator construction.. Psychological Methods, 9: 275–300. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar], 2006 Marsh, H. W., Wen, Z. and Hau, K. T. 2006. “Structural equation models of latent interaction and quadratic effects”. In A second course in structural equation modeling Edited by: Hancock, G. and Mueller, R. 225–265. Greenwich, CT: Information Age.  [Google Scholar]) and the orthogonalizing strategy (Little, Bovaird, & Widaman, 2006 Little, T. D., Bovaird, J. A. and Widaman, K. F. 2006. On the merits of orthogonalizing powered and product term: Implications for modeling interactions among latent variables.. Structural Equation Modeling, 13: 497–519. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]; Marsh et al., 2007 Marsh, H. W., Wen, Z., Hau, K. T., Little, T. D., Bovaird, J. A. and Widaman, K. F. 2007. Unconstrained structural equation models of latent interactions: Contrasting residual- and mean-centered approaches.. Structural Equation Modeling, 14: 570–580. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). A key benefit of the orthogonalizing strategy is that it eliminated the need to estimate a mean structure as required by the mean-centering strategy, but required a potentially cumbersome 2-step estimation procedure. In contrast, the double-mean-centering strategy eliminates both the need for the mean structure and the cumbersome 2-stage estimation procedure. Furthermore, although the orthogonalizing and double-mean-centering strategies are equivalent when all indicators are normally distributed, the double-mean-centering strategy is superior when this normality assumption is violated. In summary, we recommend that applied researchers wanting to estimate latent interaction effects use the double-mean-centering strategy instead of either the single-mean-centering or orthogonalizing strategies, thus allowing them to ignore the cumbersome mean structure.     

Unconstrained Structural Equation Models of Latent Interactions: Contrasting Residual- and Mean-Centered Approaches

Little, Bovaird and Widaman (2006) proposed an unconstrained approach with residual centering for estimating latent interaction effects as an alternative to the mean-centered approach proposed by Marsh, Wen, and Hau (2004, 2006). Little et al. also differed from Marsh et al. in the number of indicators used to infer the latent interaction factor and how they were represented, but this issue is separate from the mean versus residual centering distinction that was their primary focus. However, their implementation of the Marsh et al. mean-centered approach failed to incorporate the mean structure that Marsh et al. argued was necessary to obtain unbiased estimates. One might suppose that their new approach would suffer this same problem, an issue not addressed by Little et al. However, we demonstrate here why the Little et al. approach obviates this requirement that heretofore was thought to be necessary for all constrained, partially constrained, and unconstrained approaches. Both the Marsh et al. and Little et al. unconstrained approaches typically result in similar results and are much easier to implement than traditional constrained approaches. They differ primarily in that the Little et al. approach is a 2-step approach involving a potentially large number of separate analyses prior to estimating the structural equation model that apparently does not require the estimation of a mean structure, whereas the Marsh et al. approach is a 1-step approach that includes a mean structure.     

Simplifying Causal Complexity: How Interactions Between Modes of Causal Induction and Information Availability Lead to Heuristic‐Driven Reasoning

This article considers a set of well‐researched default assumptions that people make in reasoning about complex causality and argues that, in part, they result from the forms of causal induction that we engage in and the type of information available in complex environments. It considers how information often falls outside our attentional frame such that covariation falls short, mechanisms can be nonobvious, and the testimony that others offer is typically subject to the same constraints as our own perceptions. It underscores the importance of multiple modes of causal induction used in support of one another when discerning and teaching about causal complexity. It considers the importance of higher order reflection on the nature of causality that recognizes the challenging features of complex causality and how it interacts with human causal cognition.     

New Ways to Evaluate Goodness of Fit: A Note on Using Equivalence Testing to Assess Structural Equation Models

Structural equation models are typically evaluated on the basis of goodness-of-fit indexes. Despite their popularity, agreeing what value these indexes should attain to confidently decide between the acceptance and rejection of a model has been greatly debated. A recently proposed approach by means of equivalence testing has been recommended as a superior way to evaluate the goodness of fit of models. The approach has also been proposed as providing a necessary vehicle that can be used to advance the inferential nature of structural equation modeling as a confirmatory tool. The purpose of this article is to introduce readers to key ideas in equivalence testing and illustrate its use for conducting model–data fit assessments. Two confirmatory factor analysis models in which a priori specified latent variable models with known structure and tested against data are used as examples. It is advocated that whenever the goodness of fit of a model is to be assessed researchers should always examine the resulting values obtained via the equivalence testing approach.     

Standardized Parameters in Misspecified Structural Equation Models: Empirical Performance in Point Estimates,Standard Errors,and Confidence Intervals

In practice, models always have misfit, and it is not well known in what situations methods that provide point estimates, standard errors (SEs), or confidence intervals (CIs) of standardized structural equation modeling (SEM) parameters are trustworthy. In this article we carried out simulations to evaluate the empirical performance of currently available methods. We studied maximum likelihood point estimates, as well as SE estimators based on the delta method, nonparametric bootstrap (NP-B), and semiparametric bootstrap (SP-B). For CIs we studied Wald CI based on delta, and percentile and BC_a intervals based on NP-B and SP-B. We conducted simulation studies using both confirmatory factor analysis and SEM models. Depending on (a) whether point estimate, SE, or CI is of interest; (b) amount of model misfit; (c) sample size; and (d) model complexity, different methods can be the one that renders best performance. Based on the simulation results, we discuss how to choose proper methods in practice.