Generalized Total Entropy Fit Index: A new fit index to compare bifactor and correlated factor structures in SEM and network psychometrics

The Generalized Total Entropy Fit Index (GenTEFI) is introduced as a new fit index for comparing the dimensionality of correlated traits and hierarchical/bifactor structures in Structural Equation Modeling (SEM) and Network Psychometrics. This study addresses limitations in recent simulation studies that focus solely on discrepancy due to estimation, by incorporating discrepancy due to approximation and population error. Three Monte Carlo simulations were conducted to assess the accuracy of GenTEFI and traditional fit indices (CFI, RMSEA, SRMR, BIC, AIC) in identifying correct model structures at both sample and population levels (correlated traits vs. bifactor, bifactor vs. correlated traits, bifactor vs. bifactor). Results show that GenTEFI is the only fit index that adequately differentiates between correlated traits and bifactor structures in both sample and population contexts, regardless of the true data generation mechanism. GenTEFI demonstrated high balanced accuracy (94-95%) across all conditions tested, outperforming traditional fit indices like BIC, AIC, RMSEA, and SRMR, when the data comes from a correlated traits model. When the data comes from a bifactor model, or when comparing different bifactor structures, GenTEFI performed comparably to traditional indices. Two empirical examples illustrate the practical application of GenTEFI in model selection for attachment styles and misinformation susceptibility. This study highlights the potential of GenTEFI to enhance the validity and reliability of measurement instruments in psychology, offering researchers a powerful new tool for understanding the structure of psychological constructs.