• Support from National Science Foundation grant SES-0617193 with funds from the Social Security Administration is gratefully acknowledged. I would like to thank Ken Bollen, Oksana Loginova, Cam McIntosh, and Kris Preacher for helpful comments, and Ni Li for research assistance on the project. I would also like to thank the editor and three referees for comments that helped improve the structure of the paper and prompted some of the examples and discussions. Direct correspondence to Stanislav Kolenikov at 146 Middlebush Hall, Department of Statistics, University of Missouri, Columbia, MO 65211; e-mail:


We deal with the problem of quantifying the degree to which parameter estimates in a structural equation model can be biased when structural relationships were not specified correctly by the researcher. We propose a framework to relate moment residuals to biases of parameter estimates and the overall noncentrality of the model. For each parameter in the model, an impact of either particular moment residual or the overall model noncentrality can be evaluated, although the latter tends to give error bounds that are rather conservative. We provide illustrative analytical and empirical examples to demonstrate the steps in application of the proposed procedures. The first example is a mildly misspecified model with causal indicators mistaken to be effect indicators. The resulting biases can be approximated very accurately by accounting for the effect of a single misfitted residual moment. The second example is a grossly misspecified model in which a mediating latent variable was erroneously omitted. In this case, the misspecification spreads to all entries of the covariance matrix, and measures based on overall noncentrality give a good indication of the magnitudes of plausible biases. The third example is an empirical study that uses Holzinger-Swineford factor analysis data that shows how the procedures can be used in practice.