1. CONCEPTS TO BE INCLUDED
Items
Factor analysis
Data reduction / scale construction
Factors/dimensions
Factor loadings

2. Factor analysis and factor loadings

3. AIM
Reducing a set of (survey) items to a limited set of factors or dimensions, to create a few more abstract scales
= Factor analysis
Factor loadings

4. EXAMPLE: THE BIG FIVE
NEO-PI-R personality scales measure five domains of personality
Give an assessment of normal adult personality
Are used in personality assessment

5. EXAMPLE: THE BIG FIVE Five constructs/dimensions/factors:
Openness (closed minded – intellectual curiosity)
Conscientiousness (sloppy/unreliable – highly organized)
Extraversion (reflective – attention seeking)
Agreeableness (suspicious – compassionate)
Neuroticism (emotionally stable – emotionally unstable)

6. ITEMS MEASURING ONE CONSTRUCT: NEUROTICISM
Neuroticism (emotionally stable – emotionally unstable)
Items:
“Even minor annoyances can be frustrating to me”
“Sometimes I feel completely worthless”
Strongly Disagree
Disagree
Neutral
Agree
Strongly agree 1 2 3 4 ◻️

7. A DATA MATRIX Respondent Item 1 Item 2 Etc… 1 2 (= neutral) 2
4 (= strongly agree) 4 3
0 (= strongly disagree) 5 6 7 8 9

8. Item 1
Concept
correlation
NOT directly observed
Item 2

9. Neuroticism If the two items are indications of neuroticism,
the answers will be correlated.
Even minor annoyances can be frustrating to me
Neuroticism
correlation
Sometimes I feel completely worthless

10. WHAT IS ‘FACTOR ANALYSIS’?
A method to check whether a latent factor is able to account for the correlation between a set of items
Latent factor (a.k.a. ‘dimension’) is here neuroticism

11. Neuroticism Even minor annoyances can be frustrating to me
Then: correlation = 1
Neuroticism
Suppose: corr. = 1
perfect correlation
Sometimes I feel completely worthless
Then: correlation = 1

12. ONE FACTOR REPLACES TWO ITEMS
Item 1 = 1*Factor(N) Item 2 = 1*Factor(N)
Item 1
Concept
Factor loadings
Item 2

13. ONE FACTOR REPLACES TWO ITEMS, WITH ERROR
Item 1 = a * Factor(N) + Error Item 2 = b * Factor(N) + Error
Then: correlation is between 0.81 and 1
Item 1
error
Correlation = 0.81
Concept
error
Item 2
Then: correlation is between 1 and 0.81

14. FACTOR LOADING
The extent to which a factor is able “to explain” an item is called a factor loading Item 1 = a * Factor(N) + error Item 2 = b * Factor(N) + error In this example factor loadings are between 1 and 0,81

15. INTERPRETING FACTOR LOADINGS
A factor loading indicates how well a factor is able to explain an item
A low factor loading indicates that the item does ‘not belong’ to the factor (= dimension, scale, construct)
A high factor loading indicates the item belongs to the factor

16. FACTOR ANALYSIS Normally not just two, but many items
Often not just one, but two or even more factors
Factors ‘summarize’ a large set of ‘items’ into a smaller set of ‘variables’ (= dimensions, constructs)

17. FACTOR ANALYSIS
If there IS an underlying factor, we could add the answers to the items and use that as one single variable measuring the construct
Some items belong to a factor, whereas others do less

18. ONE FACTOR REPLACES TWO ITEMS, WITH ERROR
Item 1 = 0.8 * Factor(N) + Error Item 2 = 0.9 * Factor(N) + Error
Item 1
error
0.8
Factor loadings
Corr. = 0.72
Concept
error
Item 2
0.9

19. ( x ) + ( + ) = = A DATA MATRIX Resp Factor loading item 1 Item 1
Scale 1
0,8
0,9 2
2,7 4 3 6 5 7 8 9 ( x ) + ( + ) = =

20. THIS MICROLECTURE
A set of (survey) items can be reduced to a limited set of factors or dimensions, creating a few more abstract scales
This is done using factor analysis
Factor analysis gives you factor loadings, which can be used to create a summated scale