# 25 Summary

This module presented two popular methods for conducting factor analysis, one that provides descriptive and relatively unstructured information about a test, and the other providing more structured results oriented around formal hypotheses. The main steps involved in fitting EFA and CFA and evaluating results were discussed and demonstrated using real data.

EFA and CFA can improve the test development process by allowing us to examine and confirm the presence of unobserved constructs that explain variability in our tests. In practice, tests without a confirmed factor structure may not be suitable for testing applications that require a total score calculated across items, in the case of unidimensional factor models, or scores across subscales, in the case of multidimensional models.

## 25.1 Optional Exercises

- Suppose an EFA is fit to data collected on a test containing 18 items. Ten factors are explored in the EFA. The eigenvalues for the first three factors are 4.5, 3.0, and 2.5. Describe what these values represent.
- Convert the eigenvalues from the previous question to percentages of variance explained. How much variability do the three factors account for together?
- Draw a scree plot for the EFA described in the previous two questions, using the eigenvalues given for the first three factors and eigenvalues of 0.8 for the remaining factors.
- Run three separate CFA models, with one factor each, on the memorization, elaboration, and control strategy scales. Evaluate the results based on model fit and factor loadings.