# Confirmatory factor analysis assignment solution

The solution provided below covers confirmatory factors analysis on the sixth intelligence measures in a dataset.

## Intelligence scale using confirmatory factor analysis

The CFA was used to evaluate the factor structure of the intelligence Scale. The two-factor model had a significantly better fit than the one-factor model: Δ χ2 (2) = 51.386, p < .001, indicating a preference for the two-factor structure of the intelligence scale

Perform Confirmatory Factor Analysis (CFA) for the six intelligence measures in a grant.sav dataset. Write a summary that:

1. Compares the model fit for the one-factor and two-factor models,
2. Evaluate model fit for the better-fitting model,

Solution

Model fit Comparison

One factor Model; χ^2(14) = 119.122, p<0.001

Two factor Model; χ^2(12) = 67.736, p<0.001

Is the difference significant?

Δ χ2 (2) = 119.122-67.736 = 51.386 p < .001Significant

Model Fit of the better Model.

RMSEA of the best model is 0.18

CFI of the best model is 0.818

AIC of the better model is 97.736

Results: Confirmatory factor analysis was used to evaluate the factor structure of the intelligence Scale. The two-factor model had a significantly better fit than the one-factor model: Δ χ2 (2) = 51.386, p < .001, indicating preference for the two-factor structure of the intelligence scale Furthermore, the two-factor model shave a good model fit: χ2 (12) = 67.736, p < .001; CFI = .818, RMSEA = .18 and AIC=97.736.

Examining the factor loadings for the one-factor model, we can observe a positive significant factors estimates were present in the model at p<0.001.

Factor correlations for a one-factor model

The factor correlations table above shows that as high as 82.4% variation in intelligence scale can be explained by paragraph variables. Overall, factors explained a good amount of variance in all items.