Bollen, Kenneth A. (1990). A Comment on Model Evaluation and Modification. Multivariate Behavioral Research, 25(2)
Rigorous statistical theory justifies the methods of structural equation models under the ideal conditions of a large sample and a correct model with variables that come from a known, typically multivariate normal, distribution. Less guidance is available in the more realistic situation of small to moderate sample sizes and an approximately true model with variables that come from an unknown distribution. Kaplan (1990) offers us a strategy with which to evaluate and modify models in the latter situation. In brief he recommends that we: (a) check the marginal skewness and kurtosis of the observed variables, (b) describe the missing data pattern and model it if necessary, and (c) use a combination of the Modification Index (MI) and the Expected Parameter Change (EPC)' to modify models. I agree with recommendation (b), have some qualms with (a), and would more seriously qualify the use of (c) than does Kaplan. I also find several important omissions from Kaplan recommendations. In the next two sections I elaborate these points.
Multivariate Behavioral Research
Bollen, Kenneth A.