Join us for a Quantitative Area Brownbag with Ling Zhu (The Ohio State University)!
Title: Data-Matrix-Based Local Diagnostics for Confirmatory Factor Analysis: In-Sample Prediction Error for Individual Observed Variables
Abstract: Global goodness-of-fit tests in confirmatory factor analysis (CFA) can detect model misspecification but do not identify where misfit is concentrated. Existing local diagnostics provide parameter- or covariance-level information, whereas conventional indicator-level R² describes model-implied variance decomposition rather than direct reproduction of observed data. This talk introduces the in-sample prediction error for an individual observed variable (ipej), a data-matrix-based local diagnostic that quantifies the proportion of an indicator's observed variability left unexplained by the fitted model. Its complement, 1 − ipej, provides an interpretable data-reproduction R², distinct from conventional variance-decomposition R². Derived within structured factor analysis (SFA) from the global in-sample prediction error for observed variables (IPEO), ipej enables a two-stage procedure that first tests global model fit and then localizes indicators associated with detected misfit. Monte Carlo simulations demonstrate increasing localization accuracy with sample size, conditional on global rejection. An empirical illustration further demonstrates how the proposed diagnostic can identify substantively meaningful indicators for further investigation.
