Summary of Lecture 5 Part I Structural equation

Summary of Lecture 5 (Part I): Structural equation models (SEM): q Linear structural equation models. q Recovering the linear equations from the diagram of the model: Ø Ø A linear equation for each endogenous variable. The variables with an arrow emanating from it and ending at the endogenous variable make up the independent variables in the equation with the structural parameter associated with the arrow as coefficients. Reduction of the equations: Endogenous variables on the righthand side of the equations are replaced by the respective equation. The process of reducing may be repeated but ends after a number of steps.

Summary of Lecture 5 (Part II): Structural equation models (SEM): q Model predictions: Covariances and Means. Ø Ø On the basis of the reduced linear structural equations and the variances and covariances of the exogenous variables the covariance and mean structure of the endogenous variables can be predicted. The is best achieved using matrices: For latent variable models this results in a simple matrix expression (see below). q Using linear SEM to model the 3 classical test models: Ø Ø Ø congeneric -equivalent parallel

Summary of Lecture 5 (Part III): Using linear SEM to model the 3 classical test models: q Congeneric model: Central aspect: All tests measure the same latent construct

Summary of Lecture 5 (Part IV): Using linear SEM to model the 3 classical test models: q -equivalent model: Central aspect: All tests measure the same latent construct, and, in addition, with the same influence of the latent construct on the measures. Possibly with different errors.

Summary of Lecture 5 (Part V): Using linear SEM to model the 3 classical test models: q parallel model: Central aspect: All tests measure the same latent construct, with the same influence of the latent construct on the measures, and, in addition, with equal error. Measure are completely equivalent.