Interpreting Confirmatory Factor Analysis (CFA) Output in AMOS

Interpreting the output from a confirmatory factor analysis (CFA) using AMOS involves a structured approach to understand the results accurately. This article provides a comprehensive guide to help you make sense of the various indices and measures that AMOS provides.

1. Model Fit Indices

Model fit indices are crucial for assessing the overall adequacy of a CFA model in AMOS. Here, we discuss some of the key indices:

1.1 Chi-Square χ2 Test

The Chi-square test is one of the most commonly used measures to evaluate model fit. A significant p-value (p

1.2 Goodness-of-Fit Index (GFI)

GFI values closer to 1 indicate a better fit. A GFI of .90 or above is generally considered acceptable. Higher values suggest a model that explains more of the variance in the observed data.

1.3 Adjusted Goodness-of-Fit Index (AGFI)

AGFI is similar to GFI but adjusted for the number of parameters. A value of .90 or above is preferred, as it accounts for the complexity of the model.

1.4 Comparative Fit Index (CFI)

CFI values above .90 or ideally .95 suggest a good fit. This index is particularly useful in comparing different models.

1.5 Tucker-Lewis Index (TLI)

TLI is similar to CFI and values above .90 indicate a good fit. This index is also commonly used to compare models.

1.6 Root Mean Square Error of Approximation (RMSEA)

RMSEA values below .06 indicate a good fit, while values up to .08 are acceptable. A confidence interval that does not include .08 is preferable, indicating a higher level of confidence in the fit of the model.

2. Factor Loadings

Factor loadings are essential for determining the relevance and direction of each item on its respective factor. Here are some key aspects to consider:

2.1 Item Relevance

Each item’s loading on its respective factor should ideally be above .40. Loadings below this threshold may indicate that the item does not contribute significantly to the factor.

2.2 Direction of Loadings

Examine the direction of the loadings to ensure they align with theoretical expectations. Consistency in the direction of loadings helps to validate the factor structure.

3. Reliability and Validity

Evaluating the reliability and validity of the factors is crucial for ensuring the quality of the CFA model:

3.1 Construct Reliability (CR)

Construct reliability (CR) is calculated from the factor loadings. Values above .70 indicate good internal consistency, suggesting that the factor is reliable.

3.2 Average Variance Extracted (AVE)

Average variance extracted (AVE) values above .50 suggest that the factor explains more than half of the variance of its items. Higher values indicate better discriminant validity, meaning that the factor is distinct from other factors.

4. Modification Indices

Modification indices suggest possible ways to improve model fit by allowing correlations between error terms or adding paths. However, use these indices cautiously and based on theoretical justification. Adding paths should not be done based solely on statistical significance but on practical and theoretical grounds.

5. Residuals

Examining the residuals helps identify any large discrepancies between observed and predicted covariances. Ideally, residuals should be small, indicating that the model fits the data well.

6. Cross-Validation

To ensure the robustness of the CFA model, it is important to validate the results with a different sample. This step confirms that the factor structure holds across different populations or datasets.

Summary

When interpreting CFA results in AMOS, focus on the model fit indices to assess overall model adequacy. Evaluate factor loadings for item relevance, check reliability and validity metrics, and consider modification indices for potential improvements. Always align findings with theoretical expectations and contextual understanding to ensure robust and meaningful results.

Key Takeaways:

Model fit indices help determine the overall adequacy of the CFA model. Factor loadings provide insight into the relevance and direction of items. Reliability and validity metrics ensure the quality of the factors. Modification indices suggest ways to improve the model, but use them cautiously. Residuals help identify discrepancies between observed and predicted covariances. Cross-validation ensures the robustness of the factor structure.