Seemingly Unrelated Regression (SUR) Models as a Solution to Path Analytic Models with Correlated Errors

Abstract

Multivariate regression requires the design matrix for each of p dependent variables to be the same in form. Zellner (1962) formulated Seemingly Unrelated Regression (SUR) models as p correlated regression equations. SUR models allow each of the p dependent variables to have a different design matrix with some of the predictor variables being the same. Of particular relevance to path analysis, SUR models allow for a variable to be both in the Y and X matrices. SUR models are a flexible analytic strategy and are underutilized in educational research.