The Detection and Correction of Specification Errors in Structural Equation Models

Abstract

Detection of specification errors in structural equation models normally requires two steps. The first step establishes whether (further) corrections of the model are necessary, and the second detects the restrictions that have to be corrected. The χ 2 test is frequently used in the first step, even though this test has been severely criticized. The modification index introduced by Joreskog and Sorbom in the LISREL program is commonly used in the second step. In this paper, we show that both procedures have serious problems and that the suggestions for corrections are not necessarily correct. Both procedures are affected not only by the size of the misspecification in the model but also by the kind and position of the misspecification and by other characteristics of the model. Thus, some small errors in the model may be detected and corrected while large errors go undetected. We propose a new procedure to overcome this problem.