Advantages of Using Unweighted Approximation Error Measures for Model Fit Assessment

Area of Science:

• Psychometrics
• Statistical Modeling

Background:

• Fit indices like RMSEA and CFI are crucial for evaluating latent variable models.
• Current indices rely on noncentrality parameter estimates, which can be complex to interpret and vary with measurement levels (e.g., categorical vs. metric).

Purpose of the Study:

• To develop and investigate new fit indices for latent variable models that are independent of specific weighting functions.
• To address the interpretability and measurement-level dependency issues of existing fit indices.

Main Methods:

• Considered approaches for obtaining unweighted approximation discrepancy estimates.
• Calculated new fit indices analogous to RMSEA and CFI using these unweighted estimates.
• Investigated the finite sample properties of the new indices via simulation studies.

Main Results:

• The newly developed fit indices consistently estimate their true values.
• Unlike traditional indices, the new indices yield the same values for both metric and categorical variables.
• Demonstrated advantages in interpretability and consistency across measurement types.

Conclusions:

• The proposed unweighted fit indices offer a more robust and interpretable alternative for assessing latent variable model fit.
• These indices provide a unified assessment regardless of whether variables are metric or categorical.
• Further research into cutoff criteria for these new indices is warranted.