The Comparative Fit Index (CFI) is a statistical measure used in structural equation modeling to assess the fit of a proposed model compared to a baseline model. It quantifies how well the proposed model fits the observed data relative to a more restricted baseline model.
Comparative Fit Index Calculator Formula and Variables:
The formula for the Comparative Fit Index (CFI) is:
$\mathrm{CFI}=\frac{\mathrm{NFI}\frac{\mathrm{df}{}_{m}}{\mathrm{df}{}_{b}}}{1\frac{\mathrm{df}{}_{m}}{\mathrm{df}{}_{b}}}$
 CFI: The Comparative Fit Index, indicating how well the proposed model fits the data compared to the baseline model.
 NFI: The Normed Fit Index, representing the fit of the proposed model.
 dfm: Degrees of freedom for the proposed model.
 dfb: Degrees of freedom for the baseline model.
Importance and Application:

Model Assessment: CFI provides a standardized measure to evaluate the goodness of fit of structural equation models. A higher CFI value indicates a better fit between the proposed model and the observed data.

Comparison: By comparing the CFI of the proposed model with that of a baseline model, researchers can determine if the proposed model offers a significant improvement in fit.

Decision Making: CFI assists researchers and practitioners in making decisions about model refinement, modification, or rejection based on how well the model fits the data.
How to Calculate:

Calculate NFI: First, compute the Normed Fit Index (NFI) for the proposed model using standard procedures in structural equation modeling.

Determine Degrees of Freedom: Calculate the degrees of freedom (df) for both the proposed model (dfm) and the baseline model (dfb).

Apply Formula: Plug the values of NFI, dfm, and dfb into the CFI formula and perform the calculations to obtain the Comparative Fit Index.
Conclusion:
The Comparative Fit Index (CFI) is a valuable tool in structural equation modeling for assessing model fit and making informed decisions about model adequacy. By comparing the fit of the proposed model with a baseline model, researchers can evaluate the validity of their theoretical frameworks and refine their models accordingly.
FAQs:
What is considered a good CFI value?
A CFI value close to 1 indicates a good fit, typically considered acceptable if above 0.90 or 0.95, although specific thresholds may vary depending on the context and field of study.
How does CFI differ from other fit indices like RMSEA and SRMR?
CFI focuses on overall fit by comparing the proposed model to a baseline model, while indices like RMSEA (Root Mean Square Error of Approximation) and SRMR (Standardized Root Mean Square Residual) assess specific aspects of model fit such as approximation error and residual variability.
Can CFI be used in all types of structural equation models?
Yes, CFI is widely applicable to various types of structural equation models, including confirmatory factor analysis (CFA), path analysis, and latent variable models, among others. However, it’s essential to consider the assumptions and limitations of each model type when interpreting CFI values.
Leave a Reply