How do you compute MAX prior communality?
Take the largest absolute row correlation for each variable.
How do you compute SMC prior communality?
R-squared from regressing one variable on all others
—> needs full correlation matrix
How do MAX and SMC differ?
MAX is an upper bound; SMC is a lower bound.
What is the maximum number of factors?
Equal to the number of variables (p).
How many factors do you keep using PC?
Eigenvalues > 1.
How many factors do you keep using PF/SMC?
Eigenvalues greater than the average eigenvalue.
How do you interpret a scree plot?
Keep factors before the elbow.
What is the rule for parallel analysis?
Keep factors where actual eigenvalue > simulated eigenvalue
What if PC and PF give different results?
What if PC and PF give different results?
What is a loading?
Correlation between a variable and a factor.
How do you interpret loadings?
Absolute value = strength; sign = direction.
How do you compute communality (2 factors)?
L1-Squared + L2-Squared
How do you compute specificity?
1 − communality.
What does low communality mean?
Variable is poorly explained.
What changes after rotation?
Loadings.
How do you compute predicted correlation?
Loading variable 1 Factor 1 * Loading variable 2 Factor 1+….
How do you compute residual correlation?
Observed − predicted correlation.
What does a small residual mean?
Good model fit.
How do you compute total variance explained?
Sum of communalities divided by number of variables.
What is a shortcut for total variance explained?
Average of communalities.
What is the main difference between PC and PF?
PC uses total variance; PF uses common variance
PC has higher loadings; PF has lower loadings
PC better fit usually ; PF conceptually correct
What is the priority when selecting models?
- RMS (Lowes)
- Fit (highest)
- Conceptual correctness
- Total variance
How do you compute RMS for one variable?
Square residuals in the row, average, then take square root.
How do you compute global RMS?
Square all residuals, average, then take square root.
