To calculate the Comparative Fit Index, subtract the ratio of model degrees of freedom (dfm) to baseline degrees of freedom (dfb) from the NFI. Then divide this result by 1 minus the same ratio (dfm/dfb).
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.
Formula:
| Variable | Meaning |
|---|---|
| CFI | Comparative Fit Index |
| NFI | Normed Fit Index |
| dfm | Degrees of Freedom for the model |
| dfb | Degrees of Freedom for the baseline model |
Solved Calculations :
Example 1:
Given Values:
- NFI = 0.90
- dfm = 20
- dfb = 30
| Calculation | Instructions |
|---|---|
| CFI = (0.90 – 20/30) / (1 – 20/30) | Divide dfm by dfb, subtract from NFI, and from 1. |
| CFI = (0.90 – 0.67) / (1 – 0.67) | Perform the subtractions. |
| CFI = 0.23 / 0.33 | Divide the results. |
| CFI = 0.70 | The result gives the Comparative Fit Index. |
Answer: CFI = 0.70
Example 2:
Given Values:
- NFI = 0.85
- dfm = 15
- dfb = 25
| Calculation | Instructions |
|---|---|
| CFI = (0.85 – 15/25) / (1 – 15/25) | Divide dfm by dfb, subtract from NFI, and from 1. |
| CFI = (0.85 – 0.60) / (1 – 0.60) | Perform the subtractions. |
| CFI = 0.25 / 0.40 | Divide the results. |
| CFI = 0.625 | The result gives the Comparative Fit Index. |
Answer: CFI = 0.625
What is Comparative Fit Index Calculator ?
A Comparative Fit Index (CFI) Calculator helps measure the goodness-of-fit of a statistical model in confirmatory factor analysis (CFA) or structural equation modeling (SEM). The CFI compares the fit of a user-specified model to a null model, indicating how well the proposed model fits the data relative to the null model. A CFI score closer to 1 indicates a good fit, with values above 0.90 or 0.95 considered acceptable in most cases.
The Normed Fit Index (NFI), another common fit index, can also be calculated to measure model fitness. An NFI value closer to 1.0 is desired, with values above 0.90 generally acceptable. The Tucker-Lewis Index (TLI) and Goodness of Fit Index (GFI) are other related measures that assess how well a model fits data, with values above 0.90 typically indicating good fit.
These fit indices are essential in determining the reliability and accuracy of statistical models used in various research fields like psychology, economics, and education.
