## 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

**Task
**

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

- Compares the model fit for the one-factor and two-factor models,
- Evaluate model fit for the better-fitting model,
- Summarizes factor loadings and factor correlations,
- Provides a table of factor loadings.

**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.

Factor Loading for a one-factor model

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.

Factor Loading for a two-factor model

Examining the factor loadings for the two-factor model, we can observe a positive significant factors estimates were present in the model among factors loadings in both factors.

Factor correlations for a two-factor model

The factor correlations table for the two-factor model above shows that as high as 95.8% variation in factor 2 can be explained by paragraph variables. While 53.9% of the variation in factor 1 can be explained by Cubes. Lastly, all factors explained a good amount of variance in the two-factor model.