Structural Equation Modeling

Statistical Modeling with SEM

The prototypical structural equation model includes several latent (unobserved) continuous variables, each measured by several manifest (observed) continuous variables. The latent variables typically serve as common factors for their manifest indicators. The factor loadings and the regression weights connecting the latent variables together account for the observed patterns of association between the manifest indicators. For example, several latent job competencies, each measured by several continuous items, might predict several job performance dimensions, each similarly measured. Structural equation modeling allows the expression of all of these relationships within one inclusive model rather than requiring the researcher to break up the relationships into a series of discrete hypotheses tested by separate analyses.

Like other latent variable models, SEM also allows researchers to estimate effect sizes controlling for measurement error. In the previous example, the regression weight connecting a latent job competency to a latent job performance dimension will generally exceed (in absolute value) the regression weight connecting two manifest measures of these constructs in a model without latent variables. This difference occurs because of measurement error in the manifest measures.

Multiple regression constitutes a special case of SEM with one manifest endogenous variable and several correlated manifest exogenous variables. Path analysis generalizes regression to multiple endogenous variables by combining a system of equations into one model. Confirmatory factor analysis limits itself to the effects of latent variables on manifest variables but allows the latent variables to covary. Multiple indicator, multiple cause models allow manifest exogenous variables to affect latent endogenous [Page 774]variables, measured by endogenous manifest variables. For example, a researcher might use such a model if he or she has multiple measures of job performance but not each job competency and wants to predict latent job performance from observed competency measures.

Latent growth curve models model individual variation in change over time in terms of latent slopes and intercepts. For example, employees may vary in how their job performance changes over time, some starting at different levels than others and some growing at different rates than others. Recursive models contain no loops, whereas nonrecursive models do. For example, if job motivation affects job knowledge, job knowledge affects job performance, and job performance affects job motivation, this forms a loop.

...