The Comparative Fit Index (CFI) is a statistical measure used to assess the fit of a model in structural equation modeling and confirmatory factor analysis. It compares the fit of a target model to a baseline model, often a null model, helping researchers evaluate how well the specified model accounts for the data relative to a more basic one. A CFI value closer to 1 indicates a better fit, while values below 0.90 suggest a poor fit.
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The CFI ranges from 0 to 1, with values above 0.95 generally indicating an acceptable fit and values above 0.97 suggesting a good fit.
CFI is particularly useful in comparing models; it provides insight into whether adding parameters improves the fit significantly compared to a more constrained model.
One advantage of CFI is that it is less sensitive to sample size compared to some other fit indices, making it reliable even with smaller datasets.
The CFI can be influenced by the complexity of the model; overly complex models may artificially inflate CFI scores.
CFI is often reported alongside other fit indices like RMSEA and TLI to provide a comprehensive evaluation of model fit.
Review Questions
How does the Comparative Fit Index help in evaluating the quality of a model in confirmatory factor analysis?
The Comparative Fit Index helps evaluate the quality of a model by comparing its fit against a baseline model, usually a null model where all variables are uncorrelated. A high CFI value indicates that the specified model fits the data significantly better than the baseline model, making it easier for researchers to justify their model choice based on empirical evidence. Therefore, it serves as an essential tool in determining whether the proposed relationships among variables are plausible.
Discuss the implications of having a CFI value below 0.90 when analyzing a confirmatory factor analysis model.
A CFI value below 0.90 indicates poor fit, which raises concerns about the appropriateness of the specified model. When this occurs, researchers may need to reconsider their factor structure, potentially revising or simplifying their model. This may involve removing poorly fitting indicators or even hypothesizing new relationships between factors to enhance the overall model fit. Ignoring low CFI values could lead to misinterpretation of results and inaccurate conclusions.
Evaluate how the Comparative Fit Index can influence decision-making in research design and hypothesis testing.
The Comparative Fit Index plays a crucial role in research design and hypothesis testing by providing quantitative evidence on how well a proposed model fits observed data. If researchers find that their CFI values are inadequate, they may need to revisit their theoretical framework or data collection strategies. Furthermore, it can guide decisions about including additional variables or refining constructs, ultimately ensuring that conclusions drawn from their analyses are robust and valid. Thus, CFI not only aids in assessing current models but also shapes future research directions.
A measure that assesses how well a model fits the population covariance matrix, with lower values indicating a better fit.
Goodness-of-Fit Index (GFI): An index used to assess the fit of a model, measuring the proportion of variance explained by the estimated population covariance.
Structural Equation Modeling (SEM): A multivariate statistical analysis technique that is used to analyze structural relationships between measured variables and latent constructs.