Rotation, factor loadings & Interpretation

Question 1

What is rotation for?

Answer 1

It enhances the interpretability of the factor solution

aims to clarify the relationships between clusters of variables by rotating the axis

Look at where the factors load on the axes

Question 2

Orthogonal rotation

Answer 2

produces uncorrelated/ independent factors

(factors are kept at 90 degrees)

:) helps interpret variables

:( often difficult to assume that factors will be uncorrelated

Question 3

Oblique rotation

Answer 3

Factors are correlated

(factors are free to correlate, so they are not kept at 90 degrees)

:) more realistic

:( can hamper interpretation

Best to begin with oblique then decide from there

Question 4

where do you look at the factor loadings?

Answer 4

look in the FACTOR/ COMPONENT LOADING MATRIX

check the ROTATED COMPONENT MATRIX as is it often easier to interpret (but not always so look at both)

Question 5

What does the COMPONENT/ ROTATED COMPONENT MATRIX show?

Answer 5

The correlation of each factor with each variable

Factors are define by high loadings

Question 6

What counts as a significant factor loading?

Answer 6

Rule of thumb: >.32 (i.e. the factor explains around 10% of the variance in the variable)

Question 7

Verimax

Answer 7

Orthogonal rotation

Question 8

Direct oblimin

Answer 8

Oblique

Question 9

What does orthogonal rotation change in PCA?

Answer 9

It just changes the weightings, not the total variance accounted for by each factor

Question 10

why does the sum of squared loading give more than 100% in oblique rotation?

Answer 10

SSLs for all the factors added together can add to more than 100% variance because the factors are correlated, so shared variance exists and can be included in more than one factor.

Question 11

What matrix is produced when an orthogonal rotation is used?

Answer 11

FACTOR LOADING MATRIX- easy for interpretation

Question 12

What matrix is produced when an oblique rotation is used?

Answer 12

STRUCTURE MATRIX

PATTER MATRIX (factor loading but after partialling out overlap with other factors- best of interpretation)

FACTOR CORRELATION MATRIX (deree of relationship between the factors)

Question 13

Interpretation: how do you label and define the factors?

Answer 13

Use the pattern of factor loading to help with this

Look for marker variables i.e. very high loading variables on the factor

Question 14

Problems with interpretation

Answer 14

:( cross-loading variables (those that load highly on two or more factors)

:( variables that zero load across all factors- r-run with these variables removed

:( factor naming is subjective- you need to provide construct validity beyond FA

Question 15

Interpretation: what if there are a large number of variables?

Answer 15

Select SPSS to suppress loadings of a size e.g.

Question 16

How do you know how much variance is accounted for by the model?

Answer 16

look at SQUARED MATRIX FOR EIGENVALUES

Sum down each column (each factor)

Divide by the number of variables for variance accounted for by each factor (i.e. the number of variables that load on that factor)

Sum these values for variance
accounted for by
the model.

Question 17

Factor scores

Answer 17

estimates of scores for participants if factors had been measured directly

Simplest way: sum the score on high loading variables

Question 18

Negatives of FA

Answer 18

:( you only get out what you put in

:( FA isn’t always the only and correct solution