Comparative Fit Index

Definition

The Comparative Fit Index (CFI) is a statistical measure used to assess the fit of a model in structural equation modeling (SEM). It compares the fit of a target model to that of a baseline model, typically the independence model, which assumes no relationships among the variables. A CFI value closer to 1 indicates a better fit, making it an essential tool for evaluating how well the hypothesized model explains the observed data.

5 Must Know Facts For Your Next Test

1. CFI values range from 0 to 1, with values above 0.90 or 0.95 typically indicating acceptable or good fit, respectively.
2. It is less sensitive to sample size than some other fit indices, making it useful for smaller datasets.
3. CFI can be affected by the complexity of the model; overly complex models may result in lower CFI scores even if they are theoretically justified.
4. The CFI takes into account both the chi-square statistic and degrees of freedom, making it a more comprehensive measure than just looking at chi-square alone.
5. CFI should not be used in isolation; it's best interpreted alongside other fit indices to get a complete picture of model fit.

Review Questions

• How does the Comparative Fit Index help in determining the quality of a structural equation model?
  • The Comparative Fit Index helps by providing a value that indicates how well a proposed model fits compared to a baseline model, usually one that assumes no relationships among the variables. A higher CFI value suggests that the proposed model explains the data better than the baseline. This is essential for researchers to determine if their hypotheses are supported by the data.
• What are some limitations of using the Comparative Fit Index when evaluating model fit in structural equation modeling?
  • One limitation of using the Comparative Fit Index is that it can be affected by model complexity; more complex models may yield lower CFI values, which can be misleading if not interpreted correctly. Additionally, while CFI is less sensitive to sample size compared to other indices, it still requires caution in interpretation when sample sizes are extremely small or large. It is also important not to rely solely on CFI but to use it in conjunction with other fit indices for a more robust evaluation.
• Evaluate how the Comparative Fit Index interacts with other fit indices and why this interaction is crucial for comprehensive model evaluation.
  • The Comparative Fit Index interacts with other fit indices such as RMSEA and TLI to provide a holistic view of model fit. While CFI focuses on comparing models, RMSEA assesses approximation error, and TLI adjusts for model complexity. By examining these indices together, researchers can avoid misinterpretations that may arise from relying on a single measure. This comprehensive approach ensures that both theoretical assumptions and empirical evidence align effectively in structural equation modeling.

Related terms

Structural Equation Modeling: A comprehensive statistical technique that combines factor analysis and multiple regression, allowing researchers to examine complex relationships between observed and latent variables.

Goodness-of-Fit Index: A broad category of indices used to evaluate how well a statistical model fits the observed data, which includes various other measures besides CFI.

Root Mean Square Error of Approximation: An index that quantifies the difference between the predicted and observed covariance matrices, providing insight into how well the model approximates the actual data.