Assessing the fitting propensity of factor models.

Area of Science:

• Statistics
• Psychometrics
• Quantitative Psychology

Background:

• Model selection is crucial in structural equation modeling (SEM).
• Traditional parsimony metrics in SEM focus on parameter count.
• Fitting propensity, a model's ability to capture data patterns, also depends on functional form.

Purpose of the Study:

• To systematically assess the fitting propensity of common SEM models.
• To evaluate how fit indices and information criteria account for fitting propensity.
• To investigate the influence of functional form versus parameter count on model fit.

Main Methods:

• Compared exploratory and confirmatory factor analysis models (single-factor, correlated factors, higher-order, bifactor).
• Assessed the behavior of fit indices (CFI, SRMR, RMSEA, TLI) and information criteria (AIC, BIC).
• Analyzed the impact of parameter count and model functional form on fitting propensity.

Main Results:

• Models exhibited varying fitting propensities, mainly due to differences in the number of free parameters.
• Little evidence suggested that the functional form of the models significantly impacted fitting propensity.
• Fit indices like RMSEA and TLI effectively accounted for fitting propensity by adjusting for parameter count.

Conclusions:

• The number of free parameters is the primary driver of fitting propensity differences in SEM.
• Functional form differences between common SEM models have a minimal impact on fitting propensity.
• Adjusted fit indices adequately capture model fitting propensity, supporting their use in model selection.