What School Psychologists Need to Know about Structural Equation Modeling

By von der Embse, Nathaniel P. | National Association of School Psychologists. Communique, March/April 2016 | Go to article overview

What School Psychologists Need to Know about Structural Equation Modeling


von der Embse, Nathaniel P., National Association of School Psychologists. Communique


School psychology research often examines the relationship between variables, some of which are not directly observable. Thus, many school psychology researchers rely on structural equation modeling (or SEM) to examine the theoretical links between multiple variables in order to test potential causal directions. SEM is not one technique, but instead a large class of analyses typically used to model relationships among observed and/orunobserved variables (Kline, 2011). Given the challenge of learning the vast range of SEM analyses (requiring manyyears of study) and the finer intricacies of performing the requisite analyses (requiring many cups of coffee), this article will focus on a brief overview of the basic principles and applications of SEM to assist school psychologists in consuming research.

WHAT IS SEM?

SEM (also referred to as covariance structure analysis, latent variable modeling, simultaneous equation modeling, etc.) can generally be viewed as an extension of regression and may include techniques such as exploratory/confirmatory factor analysis, multilevel and multiple group modeling, latent class or profile analysis, latent growth curve modeling, and many more. SEM allows for analyses of rela tionships that are not possible to examine otherwise or would involve a multistep combination of traditional statistical methods. In addition, the greater complexity allowed for within SEM can better approximate a "natural" depiction among variables through a simultaneous evaluation of relationship s, rather than a step-bystep approach typically utilized in regression.

While SEM in some form has been around for more than 60 years (Kline, 2011), it has gained wide popularity and prominence in the behavioral and social sciences throughout the last 25 years due to (a) the ability to develop and test theories of observed/unobserved variables and their relationships, (b) the accounting for measurement error in explanatory variables, and (c) the evaluation of complex multivariable (categorical and continuous variables) models that may include mediation, moderation, and total effects. As such, SEM offers advantages over traditional statistical methodologies such as validity, reliability imeasurement error, complex modeling, and a confirmatory approach (Werner & Schermelleh-Engel, 2009). Validity may be enhanced by allowing a researcher to use several measured variables as indicators of a theoretical or latent construct, leading to more valid conclusions at the construct level. Reliability is improved and potential biases are reduced by explicitly modeling measurement error. Complex modeling allows a re searcher to te st several hypothèse s (including group comparisons, mean structures, factor loadings) simultaneously, whereas other methods may require several steps that may compound statistical error. Finally, SEM employs a confirmatory approach enabling a researcher to examine the relationships at a global level (theoretical model fits the data or not), local level (model reproduces hypothesized relationships between specific variables or not), and an exploratory level (identifying areas where the model may be improved).

KEY TERMS

School psychologists shouldhave knowledge of several key components that are common to many SEM methods. The first step within SEM is model specification or the creation of a model based on a priori theory. A structural equation model is a complex composite of hypothetical relationships represented and simultaneously tested with equations. A "typical" SEM consists oftwo parts: a measurement model andapath model. The measurement model (see Figure 1) is a set of observable variables that represents a small number of latent (unobserved) variables. For example, a researcher might be interested in measuring intelligence (latent variable) through multiple observed variables such as performance on block design, picture concepts, and matrix reasoning. The path model (see Figure 2) depicts relations of dependency between latent variables. …

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