In the "Structural Equation Modeling for Beginners" workshop, presenters were taught the basics of Structural Equation Modeling (SEM), under the assumption that participants possessed a limited understanding of multivariate procedures. Everything from identifying and assessing model fit, to interpreting and publishing results of an analysis were be covered.

Structural Equation Modeling (SEM), which appeared in the 1960's, is a relatively new methodology that is still evolving. SEM is generally regarded as a confirmatory rather than an exploratory technique. The function of SEM is to determine the validity of models that examine latent constructs such as intelligence, social adjustment or political attitudes. Consequently, SEM methodology is deemed suitable for a broad range of disciplines from the social and behavioral sciences to business to the spectrum of health professions. At least one journal is devoted exclusively to publishing SEM studies, while several other journals regularly publish SEM research. There are several websites that focus on SEM methodology and provide forums for researchers to gain information as well exchange views and opinions regarding new developments in SEM techniques.

In this section of the workshop, some very brief history and basic concepts of structural modeling are presented. This included the notions of measured and latent variables, the measurement model and the structural model. How to draw a model is covered as well as Wright's Rules. The concepts of under, just, and over specified are presented including examples with a brief explanation of model fitting. Finally, some available computer programs for structural modeling are listed.

During this portion of the workshop, I covered how to identify and test a structural equation model (SEM). Information on the notation used in identifying models and the criteria that must be satisfied for parameters to be estimated were discussed. In addition, I discussed how to assess whether an hypothesized model is consistent with observed data. Actual research examples were used and participants were introduced to various fit assessment strategies, such as examining parameter test statistics, residuals, and summary fit indices.

Structural Equation Modeling (SEM) is a complex procedure that yields many statistics and parameter estimates as well as convergence and computer-run information. The researcher choosing to employ SEM procedures has the difficult task of determining how best to clearly present the results of an analysis in such a way that readers can thoughtfully evaluate the results. Recommendations for how to interpret and write-up the results of a SEM investigation were presented. General guidelines around what can be excluded and what must be included in reporting results were provided. Actual examples were used to make concepts clear.

Society for Applied Multivariate Research:
Intermediate Level Structural Equation Modeling

In the "Intermediate Level Structural Equation Modeling" workshop, presenters were provided a moderately in-depth presentation of several important topics in Structural Equation Modeling (SEM). These topics included strategies for assessing model fit, the consequences of violating the assumptions of SEM, applications of SEM, and making causal inferences from SEM.

Researchers who apply Structural Equation Modeling (SEM) to answer research questions are typically confronted with a paradox in assessing model fit. The paradox is that the statistics associated with SEM are based on the assumption that a large sample is employed. However, the power associated with large sample based c ² goodness of fit statistic used to assess model fit is often so excessive that minor misspecifications result in rejecting a good model. In this talk, the presenter discussed the various alternatives to the c ² goodness of fit test and their relative strengths and weaknesses. Specific recommendations, based upon published research, were made regarding the various fit strategies available to researchers.

Much of the growth in popularity of Structural Equation Modeling (SEM) is no doubt due to its flexibility. Traditionally, SEM has been applied to data where observed measures are combined to represent latent constructs and various relationships among these latent constructs are identified. In recent years, however, researchers have explored many ingenious applications of SEM, such as to latent growth modeling processes and multi-trait multi-method studies. Some of these applications were described and examples from the literature were be presented.

My presentation deals with what to do when structural equation modeling assumptions are violated. My topics include: (a) sample size, (b) multivariate normality, c) continuity, and (d) effects of model respecification on nominal alpha levels. Specifically, many people look for "magical" ratios of subjects to variables. However, the latent variable structure is also important to consider. I will consider the issue of when to use weighted least squares rather than maximum likelihood estimation with nonnormal data. Lack of continuity is an often-overlooked problem—people often inappropriately factor items as if they were scales. I will pay particular attention to suggested solutions to this problem that use polychoric and polyserial correlations. Finally, I will remind users that nominal alpha levels are inadequate for testing modifications of previously unsatisfactory models.

One root historically of structural equation model is path analysis, which was developed to aid in causal reasoning. Although Structural Equation Models (SEMS) now have other uses, discovering causal connections or testing causal models is still an objective for many researchers. With the decline of behaviorism, philosophers and social scientists resumed their interest in causal explanation which, in the 70's and 80's, led to renewed study of probabilistic causation and related statistical theory. I reviewed some of these results and discussed some of the current models of causation, showing their connection with SEMS. Some of the most interesting work uses intelligent systems for analyzing data.