Structural Equation Modeling

Abstract Many constructs in psychology, such as intelligence, achievement motivation, and mental health status, cannot be measured directly. Such constructs are termed latent variables, or factors, and the data analytic technique designed to study the relationships among such variables is called structural equation modeling (SEM). SEM merges multivariate regression and factor analysis. In regression, a dependent variable y is predicted from p predictors as y = α + β 1 x 1 + β 2 x 2 + … + β p x p + e . SEM extends regression by allowing (1) latent variables, in which the x s are unobserved factors (a measurement model); (2) latent regressions, in which both x s and y s are latent variables; (3) multiple equations simultaneously with dependent variables y 1 , y 2 , … , y m , latent or observed; and (4) a dependent variable in one equation to be a predictor in another equation, and vice versa. A model with only observed x s and y s is called a path or simultaneous equation model.