Reporting Goodness of Fit with RMSEA-P Curve: Structural Equation Modeling in Environmental Sciences

Structural equation models are extensively used in environmental research. To assess Goodness of Fit in structural equation modeling, one can report the upper-bound of RMSEA confidence interval (e.g., .043) at a commonly used probability criterion (e.g., 90% confidence level). Alternatively one can report the p-value using a popular RMSEA close-fit criterion (e.g., .05). In essence both approaches summarize the RMSEA-p curves into some quantities, but with reference to different common standards (RMSEA≤ .05, p ≤ .05 respectively). SAS CNONCT/PROBCHI codes are provided online to search for boundary conditions in which the two approaches may provide different information and conclusion. We differentiate the implicit and explicit roles of substantial knowledge against statistical conclusion and recommend using RMSEA-p curves.