The Comparative Fit Index (CFI) is a statistical measure used in structural equation modeling (SEM) to evaluate how well a hypothesized model fits the observed data. It compares the model’s fit to a baseline model, helping researchers assess its validity.
Formula
The formula to calculate the Comparative Fit Index (CFI) is:
CFI = (NFI − dfm / dfb) / (1 − dfm / dfb)
Where:
- NFI = Normed Fit Index
- dfm = Degrees of freedom for the model
- dfb = Degrees of freedom for the baseline model
How to Use
- Enter the Normed Fit Index (NFI) value.
- Enter the degrees of freedom for the model (dfm).
- Enter the degrees of freedom for the baseline model (dfb).
- Click Calculate to get the CFI value.
Example
If a model has an NFI of 0.95, a dfm of 20, and a dfb of 50, the calculation would be:
CFI = (0.95 – 20/50) / (1 – 20/50) = (0.95 – 0.4) / (1 – 0.4) = 0.55 / 0.6 = 0.9167
FAQs
1. What is the Comparative Fit Index (CFI)?
The CFI is a statistical measure used to evaluate how well a structural equation model fits the observed data.
2. Why is CFI important?
It helps researchers determine whether their hypothesized model accurately represents real-world data.
3. What is a good CFI value?
A CFI value above 0.90 is generally considered acceptable, while above 0.95 is excellent.
4. Can CFI be negative?
No, CFI values typically range from 0 to 1, where higher values indicate a better fit.
5. What happens if dfb is zero?
The calculation will be undefined since division by zero is not possible.
6. How does CFI differ from other fit indices?
CFI compares model fit to a baseline model, whereas other indices like RMSEA and TLI measure absolute fit.
7. Can CFI be greater than 1?
In rare cases, if a model is overfitted, CFI might exceed 1, but this is uncommon.
8. What if my CFI is below 0.90?
A CFI below 0.90 suggests that the model may not fit well, and adjustments might be needed.
9. Does CFI work for all types of models?
CFI is primarily used in structural equation modeling (SEM) but can be applied in other model evaluations.
10. Is a high CFI always good?
A very high CFI might indicate overfitting, meaning the model fits the sample data too closely but may not generalize well.
11. How does NFI affect CFI?
A higher NFI generally leads to a higher CFI, indicating a better fit.
12. Can CFI be used alone to determine model fit?
No, it should be used alongside other fit indices like RMSEA, TLI, and SRMR for a comprehensive assessment.
13. What is the relationship between dfm and dfb?
The degrees of freedom for the model (dfm) should always be smaller than those of the baseline model (dfb).
14. How is CFI different from RMSEA?
CFI compares the model to a baseline, while RMSEA assesses how well the model fits the population covariance matrix.
15. Does sample size affect CFI?
Yes, CFI can be influenced by sample size, with small samples sometimes producing misleading results.
16. What if my CFI is very close to 1?
This usually means your model fits very well, but it is essential to check for overfitting.
17. Can I improve my CFI?
Yes, by adjusting model parameters, adding constraints, or refining the hypothesized model.
18. Is CFI used in machine learning?
Not directly, but it is commonly used in statistical modeling and confirmatory factor analysis.
19. How do I interpret a low CFI value?
A low CFI suggests poor model fit, meaning the hypothesized model does not align well with the data.
20. Does CFI account for model complexity?
Yes, it considers both the fit of the model and its complexity relative to a baseline model.
Conclusion
The Comparative Fit Index (CFI) is a valuable tool for assessing model fit in structural equation modeling. By comparing a model’s performance against a baseline, it provides a clear measure of how well the model represents real-world data. A well-calculated CFI can help researchers refine their models for better accuracy and reliability.