Independent Variable: I have a survey of 50 states indicating the amount of control the state board of education has in 31 areas answered on a three point scale (1 = total control; 2 = partial control; 3 = no control). I have a solid theoretical underpinning for all 31, or to be more precise, the literature review found evidence for all 31 as being important (Study X found items 1, 4 and 7; Study Y found items 2, 9, and 11, etc.)
Dependent variable: % of students graduating HS within 4 years.
What I would like to do is the following:
- Use factor analysis (SPSS) to reduce the 31 down to no more than 4 to 6 variables.
- Using the results from 1), run a regression vs. the % of students graduating HS within 4 years.
Is there some sort of step by step guide somewhere on how to do this?
Ok, this is what I have done and I believe it is correct (any confirmation would be greatly appreciated) using SPSS 18:
- In SPSS Analyze -> Dimension Reduction -> Factor
- Descriptives: Initial Solution
- Extraction: Method = Principal components; Analyze = Correlation matrix; Display = Unrotated factor solution and Scree plot; Extract: Based on Eigenvalue greater than 1; Maximum Iterations for Convergence = 25
- Rotation: Method = Varimax; Display = Rotated Solution and Loading Plots; Maximum Iterations for Convergence = 25
- Scores: Save as variables; Method = Regression; Display factor score coefficient matrix
- Options: Exclude cases listwise; Suppress small coefficients [with] absolute value below. 10
The result are 9 saved columns (FAC1_1, FAC1_2, FAC1_3...FAC1_9) in the SPSS sheet.
The Total Variance Explained -> Rotation Sums of Squared Loadings indicates that the first 5 of these explain 51.51% of the variance.
So, should I then go back into SPSS run a linear regression (Analyze -> Regression -> Linear) with the Dependent Variable % of students graduating HS within 4 years and the Independent Variables being FAC1_1, FAC1_2, FAC1_3, FAC1_4, and FAC1_5?