A NECESSARY AND SUFFICIENT CONDITION FOR IDENTIFICATION OF CONFIRMATORY FACTOR ANALYSIS MODELS OF FACTOR COMPLEXITY ONE (to appear in Sociological Methods and Research)

Abstract: 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 f ew rules to help the researcher verify whether the model is identified or not. This paper introduces a necessary and sufficient identification rule for models of factor complexity one. The rule is easy to understand, easy to apply, and applies to porti ons as well as to the whole model. Moreover, it provides a diagnostic tool that helps with identification questions. Many examples are given.

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THE INFLUENCE OF HOW THE METRIC IS SET ON THE FIT AND IDENTIFICATION OF MEASUREMENT MODELS (to appear in Structural Equation Models, Volume 2, #1, 1995 pp 1-12)

Abstract: Researchers using structural equation models with latent variables know that they must set the metric of each latent variable in the model. Whether the metric is set by fixing the variance of the latent variable or one of the loadings of one of its indicators to a non-zero constant is viewed by most researchers as a necessary but unimportant decision. The purpose of this article is to show researchers that how the metric is set can affect the fit of the model, the relative sizes of parameter estimates within the model, and even the identification status of the model. We demonstrate these problems with a multifactor measurement model with an equality constraint on $\lambda$s that load on different factors. These problems can occur in a wide variety of measurement models.

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