Factor Analysis

Lecture

Aim:

Seeks to uncover the underlying structure of a relatively large set of variables.
Data reducation tool:

• Removes redundancy or duplication from a set of correlated variables
• Represents correlated variables with a smaller set of 'derived' variables
• Factors are formed that are relatively independent of each other
• Reduces a large data set to a more manageable size while retaining as much of the original info as possible 

How many pps to do a factor analysis?

• At least N=100 (N>300 covers most criteria)
• No. of pps to no. of variables = 10:1
• No. of items to no. of factors = 4:1
• No of pps to no. of factors = 6:1 

Steps in exploratory factor analysis 

1. Initial considerations: check correlations 
Create correlation matrix 
Items should correlate with other items (r>.30, discord an item if all r<.30)
Avoid multicollinearity : items should not be too similar (r > .80)
Avoid singularity (r=1.00)
Check the determinant is > .00001
Discard if any of above items occur

Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy:
KMO < .50 not adequate
KMO > .50 and < .70 mediocre
KMO > .70 and < .80 good
KMO > .80 and < .90 very good 
KMO > .90 superb 

KMO below .5 means that finding distinct…