Factor Analysis

Question 1

Factor analysis

Answer 1

Ways of chunking data into theoretically reverent sub-scales or factors

SPSS lists it as ‘data reduction method’

Way of summarising large amount of info in terms of its underlying dimensions or factors

Like a quantitative thematic analysis- runs correlations between all items in large data set

Then generates themes (components/factors) based on the patterns (which items correlation more/less)

Question 2

When would you use factor analysis/principal component analysis

Answer 2

When developing new scale/questionnaire-identify sub-scales & superfluous/irrelevant items

When trying to reduce number of items on existing questionnaire

When testing underlying structure of dataset

To see if there might be common theoretical underpinning or set of separate measures

Individual differences literature

Not when you want to chunk groups of pp together- cluster analysis

Question 3

(Exploratory) factor analysis vs PCA

Answer 3

SPSS treats them like they’re the same

Most often give same results so terms used interchangeably

Confirmatory factor analysis is different & SPSS can’t do it

Question 4

Stages of exploratory factor analysis

Answer 4

1) Make correlation matrix (of all variables)
2) extract principal components
3) rotate principal components
4) interpret components/factors

Question 5

Is it quantitative?

Answer 5

Yes in as far as calculations, rotations & sorting factors- based on numerical data & statistical transformations

But no critical values so no significant/non-significant or effect sizes

Factors named & interpreted far more like qualitative analysis

Question 6

Types of factor analysis

Answer 6

Exploratory= looks for emergent structure in current dataset based on patterns of correlations between variables (bottom-up)

Confirmatory= tests whether factor structure in current dataset fits specified model (top-down)

Question 7

Stage 1: correlation matrix

Answer 7

Straightforward correlation matrix of variables but rather than correlating mean or sum scales, this is a correlation matrix of every item in dataset

Factor analysis tries to identify underlying patterns or dimensions that explain patterns of correlations

Question 8

Stage 2: extracting components

Answer 8

Extracting first component is like finding a line of best fit in regression

Trying to explain as much variance between variables as possible with single factor

This new component will be as highly correlated as possible with as many items as possible- explains most variance

Second component will try to explain as much variable as possible while controlling for the first component & so on- explains less variance

Question 9

Stage 3; rotation

Answer 9

After components/factors extracted, they are rotated in statistical space

Puts number of stats constraints on what final factors look like

These different rotations (patterns of constraints) may make more or less sense to use depending on data & questions asked

Question 10

Types of rotation

Answer 10

Orthogonal= factors resulting from analysis effectively cannot correlate with one another, each factor is theoretically distinct

Oblique= factors can correlate with each other, so different factors can account for some of same underlying variability

Question 11

Factor loadings

Answer 11

A component/factor is way of reducing set of related variables into simpler, single score

But each of these items will have different strengths of relationships with component factor

Relationship of each item to given component/factor is called factor loading

We care about factor loadings of 0.3 or higher

Question 12

Orthogonal analyses

Answer 12

VARIMAX= maximises variance explained

QUARTIMAX= variables will load highly on one factor but low on others

EQUAMAX= seeks more equal variance explained by each factor

Question 13

Oblique analyses

Answer 13

DIRECT OBLIMIN= gives higher Eigen values but can be difficult to interpret due to overlapping constructs

PROMAX= same

Question 14

Deciding number of factors: Kaiser Criterion

Answer 14

Kaiser Criterion= Eigenvalues>1

Eigenvalues represent total (squared) factor loadings onto single factor
So higher factor loadings mean factor explains more of variance in sample

Ratio of total variance explained to number of items
So if Eigenvalues=1 for a factor, it explains same amount of variance as individual variables do by themselves

Question 15

Deciding number of factors: Scree plot

Answer 15

Look for knee or elbow of plot

Sometimes may be ambiguous

Question 16

Deciding number of factors; common sense

Answer 16

Does interpretation make theoretical sense?

e.g. is 6th factor a confusing mix of unrelated items?

Will probably use combination of methods

Question 17

Stage 4: interpreting factors

Answer 17

Once factors extracted, you use items that load onto that factor to name it

Can use the strength of factor loadings to inform this

Question 18

Requirements & assumptions

Answer 18

• assume linear relationships between all variables
• items/measure are all continuous variables/data
• assumes any relationships between items are theoretically pertinent (doesn’t take into account spurious correlations)

Question 19

Limitations/requirements of factor analysis

Answer 19

Notorious for needing large sample sizes to make sense so can be hard to recruit for

Not a very reliable analysis
Very possible that you’ll get different factor structure with different samples or in same sample
Interpretation of factors can be very subjective
So normally needs multiple replications to be convincing

Question 20

Sample size

Answer 20

Common rule of thumb is N>100
Not necessarily needed but around do to start with

Kaiser-Meyer-Olkin test for sampling adequacy should be above .6 & ideally between .8-1

Communality should be high- >.6, mean commonalities should be >/=.7

Question 21

Communalities

Answer 21

By generating correlation matrix of all variables, able to calculate how much of the variance for single item is shared with variance of other items in dataset

Communality score for an item gives proportion of how much of its variance is common/shared with other items

High communality means PCA will with better as groups components based on shared variance among items so don’t need as many pp

Mean communality should be >/=.7 & all communality should be >.6