Data-Matrix-Based Overall Goodness-of-Fit Testing for Confirmatory Factor Analysis: In-Sample Prediction Error for Observed Variables

This preprint evaluates data-matrix-based goodness-of-fit tests for confirmatory factor analysis within structured factor analysis. The proposed IPEO test assesses a single model, and the ΔIPEO test compares nested models. IPEO measures the share of observed-data variation that a model fails to reproduce; a bootstrap p value evaluates statistical evidence of misfit. Simulations examined Type I error and power and found that the proposed tests remained usable in conditions where conventional chi-square procedures often failed. An empirical example illustrates how the fit index and its p value convey complementary information about the size and statistical significance of misfit. The authors present these procedures as complements to covariance-based CFA fit assessment.