Structural Equation Modeling

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 + β1x1 + β2x2 + … + βpxp + e. SEM extends regression by allowing (1) latent variables, in which the xs are unobserved factors (a measurement model); (2) latent regressions, in which both xs and ys are latent variables; (3) multiple equations simultaneously with dependent variables y1, y2,  … , ym, 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 xs and ys is called a path or simultaneous equation model. Keywords: latent variables; mean and covariance structure analysis; factor analysis; simultaneous equations