Enter the Normed Fit Index, degrees of freedom for the model, and degrees of freedom for the baseline model into the calculator to determine the Comparative Fit Index.

Comparative Fit Index Formula

The following formula is used to calculate the Comparative Fit Index (CFI). 

CFI = (NFI - dfm / dfb) / (1 - dfm / dfb)

Variables:

  • CFI is the Comparative Fit Index
  • NFI is the Normed Fit Index
  • dfm is the degrees of freedom for the model
  • dfb is the degrees of freedom for the baseline model

To calculate the Comparative Fit Index, subtract the degrees of freedom for the model from the Normed Fit Index and divide by the degrees of freedom for the baseline model. Subtract the degrees of freedom for the model from 1 and divide by the degrees of freedom for the baseline model. Divide the first result by the second result to get the Comparative Fit Index.

What is a Comparative Fit Index?

The Comparative Fit Index (CFI) is a statistical tool used in structural equation modeling to assess how well a proposed model fits the observed data. It compares the fit of the proposed model to a baseline model, which typically assumes no relationships among the variables. CFI values range from 0 to 1, with values closer to 1 indicating a better fit. A CFI value of 0.95 or higher is generally considered to indicate a good fit.

How to Calculate Comparative Fit Index?

The following steps outline how to calculate the Comparative Fit Index (CFI).

  1. First, determine the value of NFI (Normed Fit Index).
  2. Next, determine the value of dfm (degrees of freedom for the model).
  3. Next, determine the value of dfb (degrees of freedom for the baseline model).
  4. Next, calculate the numerator of the formula: NFI – dfm / dfb.
  5. Finally, calculate the Comparative Fit Index (CFI) using the formula: CFI = (NFI – dfm / dfb) / (1 – dfm / dfb).
  6. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem:

Use the following variables as an example problem to test your knowledge.

NFI (Normed Fit Index) = 0.85

dfm (degrees of freedom for the model) = 10

dfb (degrees of freedom for the baseline model) = 5