Biases of parameter estimates in misspecified structural equation models

We propose a framework to handle lack of fit problems in structural equation models by analyzing misspecified moments. This framework allows to relate misspecification of the moment equations to biases of parameter estimates and non-centrality of the model. Misspecification of a single moment is shown to lead to misfit of all moments as well as biases in most parameter estimates in full information estimation procedures such as FIML and WLS, unless such misspecification is absorbed by a corresponding error variance or error covariance parameter. We provide illustrative examples to quantify biases of parameter estimates and non-centralities of the model due to misfitting moments.