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Module 6: Research Lab 5 – Principal Component and Factor Analysis
Module 6: Research Lab 5 – Principal Component and Factor Analysis
Start Assignment
- Due Jul 24 by 11:59pm
- Points 75
- Submitting a file upload
Purpose
This assignment is intended to help you learn to do the following:
- Assess the assumptions of the principal component and factor analysis.
- Conduct the principal component and factor analysis.
- Report and interpret the results of the principal component and factor analysis.
Preparation
Before you work on this assignment, complete the assigned reading listed in the Module 6 Preparation page.
Overview
Factor analysis and principal component analysis identify patterns in the correlations between variables. These patterns are used to infer the existence of underlying latent variables in the data. These latent variables are often referred to as factors, components, and dimensions.
The most well-known application of these techniques is in identifying dimensions of personality in psychology. However, they have broad application across data analysis, from finance through to astronomy. At a technical level, factor analysis and principal component analysis are different techniques, but the difference is in the detail rather than the broad interpretation of the techniques.
Action Items
- 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 |
Rubric
Module 6: Research Lab 5 – Principal Component and Factor Analysis
| Criteria | Ratings | Pts | |
|---|---|---|---|
| This criterion is linked to a Learning OutcomeStatistical Analysis |
75 to >68.0 pts Proficient Answers, or responses, or computations (if required) for the learning activities are accurate and indicate a comprehensive understanding about what the analysis requires.
68 to >60.0 pts Acceptable Answers, or responses, or computations (if required) for the learning activities are mostly accurate and indicate a basic understanding about what the analysis requires.
60 to >0 pts Unacceptable Answers, or responses, or computations (if required) for the learning activities are inaccurate and indicate a lack of understanding about what the analysis requires.
|
75 pts |
|
| Total Points: 75 | |||
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