Factor Analysis

Question 1

Exploratory Factor Analysis

Answer 1

Used to explore the underlying structure within a set of variables. No correct solution because variables can be extracted and rotated differently.

Question 2

Steps in EFA

Answer 2

1. Check assumptions
2. Check factorizability
3. Select a method of identification
4. Determine how many factors to extract
5. Rotate factors
6. Interpret factors
7. Check fit

Question 3

Assumptions of EFA

Answer 3

theoretical and statistical relationship between variables (correlations above .32), large sample size, normality and no outliers, continuous data, equal intervals, independence and no multicollinearity (correlations below .85)

Question 4

Testing Factorizability

Answer 4

Assess whether the data is suitable for factor analysis.
Correlations between .32 and .85
KMO - assesses common variance (above .9 is best, .5 is bare minimum)
Bartlett’s - assesses whether matrices are different (should be significant)
Communality - proportions of variance in each variable that is explained by other variables

Question 5

Identifying Factors

Answer 5

SPSS provides multiple ways to identify factors.
PCA - assumes no error, default option, DON’T USE
Principal Axis Factoring - extracts for maximum variance
ULS - minimise differences between observed and expected data
GLS - same as ULS but communality given more weight
Maximum Likelihood - most generalisable

Question 6

Determining Extraction

Answer 6

How many factors should be included in the model? Typically use a combination of methods and test one above and one below.
Kaiser’s - retain all with eigenvalue above 1
Joliffe’s - retain all with eigenvalue about .7
Cattell’s - Use a scree plot and extract at point of inflection
Parallel Analysis - tell SPSS to generate a random data set and compare raw data to random data. When Random > Raw, extract

Question 7

Rotating Factors

Answer 7

Aids interpretation. SPSS can rotate each factor so that each item loads highly on one factor and low on all the others. Method of rotation depends on aim and theory.

Question 8

Orthogonal Rotation

Answer 8

Preserves the independence of all factors.
Quartimax (maximises spread)
Varimax (maximises loadings)
Equamax (does both)

Question 9

Oblique Rotation

Answer 9

Allows factors to correlate (more reflective of real world)
Oblimin (maximises loadings while allowing correlation between factors)
Promax (like oblimin but for large samples)

Question 10

Interpreting and Naming Factors

Answer 10

Examine pattern matrix. Meaning of factors can be inferred from examining high loading items (above .32). Naming is arbitrary, but be sensible.

Question 11

Checking EFA Fit

Answer 11

Check residuals (should be small)
Chi Square is usually significant which indicates poor fit between data and model, but it is highly influenced by sample size (which should be large)

Question 12

Common Issues in EFA

Answer 12

Factors are unclear - check extraction and rotation
Items load on multiple or no factors - poor items
Low factor loadings - to many factors, not enough data
Poor model fit - check assumptions and factorizability, over/under extraction.