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Comparative Fit Index Calculator

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The Comparative Fit Index (CFI) Calculator is a tool used in structural equation modeling (SEM) to evaluate how well a proposed model fits the observed data compared to a null (baseline) model. CFI is a widely used goodness-of-fit statistic that provides a standardized measure of model quality, aiding researchers in validating theoretical frameworks and ensuring robust data analysis.

Formula of Comparative Fit Index Calculator

The formula for calculating the Comparative Fit Index (CFI) is:

CFI = 1 – [(χ²_model – df_model) / (χ²_null – df_null)]

Where:

  • χ²_model = Chi-square statistic for the tested model
  • df_model = Degrees of freedom for the tested model
  • χ²_null = Chi-square statistic for the null (baseline) model
  • df_null = Degrees of freedom for the null (baseline) model

Additional Notes:

  1. The CFI value ranges from 0 to 1:
    • A value closer to 1 indicates a better fit.
    • A value above 0.90 is considered acceptable, while a value above 0.95 is considered excellent.
  2. Special Adjustment:
    If χ²_null = df_null, adjust the calculation to avoid division by zero.

Key Interpretation:

  • A higher CFI value reflects a model that fits the observed data well relative to the null model.
  • Values below 0.90 suggest a poor fit and may require model revision or additional variables.

Useful Conversion Table

ParameterDescriptionExample Values/Notes
χ²_modelChi-square statistic for the tested modelDerived from SEM software
df_modelDegrees of freedom for the tested modelNumber of observations minus estimated parameters
χ²_nullChi-square statistic for the null modelIndicates the worst-case fit scenario
df_nullDegrees of freedom for the null modelMatches the null model’s parameter count
CFIComparative Fit Index value0.90–0.95 is acceptable; >0.95 is excellent

Example of Comparative Fit Index Calculator

Scenario:

A researcher evaluates a theoretical model and a baseline null model using SEM software. The results are:

  • χ²_model = 250
  • df_model = 20
  • χ²_null = 500
  • df_null = 30

Step 1: Apply the Formula

CFI = 1 – [(250 – 20) / (500 – 30)]
CFI = 1 – 0.489 = 0.511

Step 2: Interpret the Result

The CFI value of 0.511 indicates a poor fit. The researcher may need to revise the model or include additional variables to improve the fit.

Most Common FAQs

What is a good CFI value?

A CFI value above 0.90 is considered acceptable, while a value above 0.95 is considered excellent, indicating a strong model fit.

Can the CFI calculator handle multiple models?

Yes, the CFI can be calculated for different models to compare their fit relative to the baseline null model.

What should I do if my CFI value is low?

If the CFI value is low, consider revising the model by adding relevant variables, re-evaluating the data, or testing alternative theoretical frameworks.

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