Factor analysis Flashcards
Factor analysis
analyse patterns of correlations between variables (items) in order to reduce these variables to a smaller set of constructs (factors/components)
–> provide a new set of scores that can be applied to other multivariate tests
confirmatory factor analysis
confirming that the items in your scale have internal consistency
exploratory factor analysis
identify a smaller number of constructs - principle component analysis (PCA)
maximise proportion of variance accounted for by the factors
factor loadings
correlation between a variable and a factor - proportion of variance in a given variable
absolute loadings > .32 = salient
absolute loadings < .30 =dismissed
absolute loadings > .70 = account for over 50% of the variance = excellent
absolute loadings > .50 = account for over 30% of the variance = good
communalities
sum of the squared loadings - proportion of variance in an observed variable accounted for by the selected factors
< .30 = suggest that the factor is unreliable and should be removed (as the factors account for less that 30% of its variance)
eigenvalue
sum of the squared loadings of within factor for all items - amount of variance in a set of variables accounted for by the factor
range from 0 - total number of items
Kaiser’s criterion -eigenvalue > 1 = should be selected as a factor
Cattell’s scree test - factors above the debris should be selected (plotted in order of size)
plotting the loadings on factor axis
correlation between a factor and an item is measured by the distance on axis
simple structure - load on factors (or one factor)
bipolar - load on one factor at opposite ends of axis
complex structure - orthogonal rotation [varimax - high loadings higher and low loadings lower] - shift entire axis at right angle to place items on factors
- oblique rotation [direct oblimin] - if items are correlated over .32 (10% overlap) it justifies an oblique rotation
Report
exploratory factor analysis in the form of Principle Component analysis
correlations - where there many over .30? - suggests underlying facotr
what was extracted - eigenvalues (% of variance accounted for) for all factors
inspection of commonalities - >.30?
inspection of factor loadings (simple/complex?) - need for a rotation?
what items loaded on what factors
what do the items assess within factors - name
SPSS (descriptives)
check:
initial solution
coefficients
SPSS (extraction)
check:
correlation matrix
unrotated factor solution
scree plot
based on eigenvalues
SPSS (rotation)
check:
none
loading plots
orthogonal rotation
keeps the axis at right angles
VARIMAX
maximises the variance of the loadings within each factor, high loadings higher and low loadings lower
oblique rotation
correlated variables
if the correlation between the two factors is >.32 there is a 10% overlap.
DIRECT OBLIMIN
justifies an oblique rotation
