Factor Analysis Lecture 4 Flashcards
What is Factor Rotation?
A statistical adjustment to where the factors are on axis and rotated lines.
Why do we rotate Factors?
We rotate items as it’s really hard to interpret items if they are placed arbitrarily in space. We rotate to fix this to try and get a better model.
By rotating, we get a clearer picture of what’s happening between factors.
What does Rotation change?
Just puts the factor closer to variation. Variation remains the same. Communality remains the same. The Eigenvalues do not stay the same and all that is happening is that a solution and variance is easier to interpret.
What is Simple Structure?
Simple Structure: Each factor should have some large loadings and some small ones -each factor should only have substantial loadings on only a few items known as simple structure.
Avoid large numbers of mediocre loadings.
What does Rotation depend upon?
Depends upon theory and interpretation:
Use depends on theory –If expect to be uncorrelated orthogonal
–If expect to be correlated oblique
• Orthogonal rotation look at the Rotated Component Matrix
• Oblique rotation: Pattern Matrix
What happens when you Rotate?
Communality of each variable remains the same
• Eigenvalues of factors do not. Factors positioned such that variance of the squared loadings is as large as possible.
Most stat packages use VARIMAX – MAXimisesVARIance of the (squared factor loadings) • Factors now explain more similar amount of variance.
What is Varimax?
MAXimisesVARIance of the (squared factor loadings) • Factors now explain more similar amount of variance.
How do you know if the loading is significant for the sample size used?
Loadings significant (alpha = .01, 2-tailed) when: – n=50: loading > 0.722 – n=100: loading > 0.512 – n=300 loading > 0.298 – n=600 loading > 0.21 – n=1,000 loading > 0.162
What is a Factor Score?
A single score from an individual entity representing their performance on some latent variable.
An individual’s single score on a factor can be calculated from their responses to items that load onto that factor.
It Takes into account the factor loading –item with greater loading has a higher weighting.
What are the benefits of Factor Scoring?
Benefits –Use factor scores for subsequent tests
• T-tests etc.
–Multicollinearity issues should be resolved post-FA.
Correlated variables now in one factor
How do you calculate Factor Score?
Regression. Several methods to calculate –Regression(accounts for initial correlations btw variables) • But factor scores can correlate even if factors are orthogonal
–Bartlett& Anderson-Rubin: Fix some of the issues with regression.
Regression is simplest.
How would you use an R-Matrix to identify potential problems? (2 problems)?
Correlations too low –Variables with lots of correlations .9 for two variables could be a problem
->.6 among many variables also possibly a problem
