A Necessary and Sufficient Condition for Identification of Confirmatory Factor Analysis Models of Factor Complexity One

After specification of a structural equation model and before estimation of parameters, the identification status of the model must be determined. For the measurement portion of the model, however, there are very few rules to help the researcher verify whether the model is identified or not. This article introduces a necessary and sufficient identification rule for models of factor complexity one. The rule is easy to understand, is easy to apply, and applies to portions as well as to the whole model. Moreover, it provides a diagnostic tool that helps with identification questions. Many examples are given.