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.