Testing parameters in structural equation modeling: Every "one" matters

A problem with standard errors estimated by many structural equation modeli ng programs is described. In such programs, a parameter's standard error is sensitive to how the model is identified (i.e., how scale is set). Alterna tive but equivalent ways to identify a model may yield different standard e rrors, and hence different Z tests for a parameter, even though the identif ications produce the same overall model fit. This lack of invariance due to model identification creates the possibility that different analysts may r each different conclusions about a parameter's significance level even thou gh they test equivalent models on the same data. The authors suggest that p arameters be tested for statistical significance through the likelihood rat io test, which is invariant to the identification choice.