Overview
- Consider the following principal components solution with five variables using no rotation and then a varimax rotation. Only the first two components are given, because the eigenvalues corresponding to the remaining components were very small (< .3).
Unrotated Solution | Varimax Solution | |||
Variables | Comp 1 | Comp 2 | Comp 1 | Comp 2 |
1 | .581 | .806 | .016 | .994 |
2 | .767 | -.545 | .941 | -.009 |
3 | .672 | .726 | .137 | .980 |
4 | .932 | -.104 | .825 | .447 |
5 | .791 | -.558 | .968 | -.006 |
- Find the amount and percent of variance accounted for by each unrotated component.
- Find the amount and percent of variance accounted for by each varimax rotated component.
- Compare the variance accounted for by each unrotated component with the variance accounted for by each corresponding rotated component.
- Compare (to 2 decimal places) the total amount and percent of variance accounted for by the two unrotated components with the total amount and percent of variance accounted for by the two rotated components. Does rotation change the variance accounted for by the two components?
- Compute the communality (to two decimal places) for the first observed variable using the loadings from the (i) unrotated loadings and (ii) loadings following rotation. Do communalities change with rotation?
- Run an exploratory factor analysis using principal axis extraction using the correlations shown below using the first nine items (exclude the bodily symptom items). Run a two- and three-factor solution for the remaining nine items.
- Which solution(s) have empirical support?
- Which solution seems more conceptually meaningful?
Items Correlations for the Reactions-to-Tests Scales | ||||||||||||
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
Ten1 | 1.000 | |||||||||||
Ten2 | .657 | 1.000 | ||||||||||
Ten3 | .652 | .660 | 1.000 | |||||||||
Wor1 | .279 | .338 | .300 | 1.000 | ||||||||
Wor2 | .290 | .330 | .350 | .644 | 1.000 | |||||||
Wor3 | .358 | .462 | .440 | .659 | .566 | 1.000 | ||||||
Tirt1 | .076 | .093 | .120 | .317 | .313 | .367 | 1.000 | |||||
Tirt2 | .003 | .035 | .097 | .308 | .305 | .329 | .612 | 1.000 | ||||
Tirt3 | .026 | .100 | .097 | .305 | .339 | .313 | .674 | .695 | 1.000 | |||
Body1 | .287 | .312 | .459 | .271 | .307 | .351 | .122 | .137 | .185 | 1.000 | ||
Body2 | .355 | .377 | .489 | .261 | .277 | .369 | .196 | .191 | .197 | .367 | 1.000 | |
Body3 | .441 | .414 | .522 | .320 | .275 | .383 | .170 | .156 | .101 | .460 | .476 | 1.000 |