Improving Fit Indices in Structural Equation Modeling with Categorical Data.

Area of Science:

• Quantitative Psychology
• Statistical Modeling
• Structural Equation Modeling (SEM)

Background:

• Current fit indices (e.g., RMSEA, CFI) in SEM often inflate model fit for categorical data.
• This inflation can lead researchers to incorrectly accept poorly fitting models.
• Existing computations do not accurately represent model fit as if data were continuous.

Purpose of the Study:

• To explain the computational issues leading to inflated fit indices with categorical data.
• To propose and evaluate alternative computations for categorical fit indices.
• To ensure fit indices approximate values obtained with continuous data.

Main Methods:

• Developed alternative computations for fit indices in SEM with categorical data.
• Focused on the diagonally weighted least squares (DWLS) estimator.
• Conducted a simulation study comparing existing and proposed categorical fit indices.

Main Results:

• Newly proposed fit indices more closely matched corresponding values from continuous data.
• The new indices demonstrated improved performance across various conditions.
• All categorical fit indices, including new ones, performed poorly with binary data at N=200.

Conclusions:

• The proposed fit index computations offer a more accurate assessment of model fit for categorical data in SEM.
• These revised indices mitigate the overestimation of model fit observed with current methods.
• Researchers should be cautious when interpreting fit indices for binary data with small sample sizes.