Factor Analysis

Question 1

What is the aim of factor analysis?

Answer 1

To analyse patterns of correlations between items in order to reduce these items to a smaller set of underlying constructs called “factors” or “components”
The factors are informative, but they also have a new set of scores which might be employed in another multivariate analysis such as multiple regression

Question 2

What are the different types of factor analysis?

Answer 2

Exploratory factor analysis - one we use

Confirmatory factor analysis

Question 3

What do the correlations need to show to consider underlying factors?

Answer 3

If several correlations are > .30, this suggests that there are a smaller number of underlying factors than __ constructs.

Question 4

When is exploratory factor analysis used?

Answer 4

To identify a smaller number of underlying components when analysing a large number of items within a scale

Question 5

What is a component?

Answer 5

A linear combination of the variables

Question 6

What is the aim of an EFA?

Answer 6

To construct a linear combination of each PPs scores on the items with the coefficients chosen so as to maximise the proportion of total variance accounted for by this component.

Question 7

Is more than one component possible?

Answer 7

Yes it is. The first component employs coefficients to account for the maximum amount of total variance
The second component has the same aim but is constrained to be uncorrelated with the first
For each component, the coefficients are chosen to account for the maximum amount of variance remaining.

Question 8

What does the total number of components = number of items mean?

Answer 8

The more all the original variables are correlated together, the more the total variance will be accounted for by the first component.

Question 9

What is a factor loading?

Answer 9

Each loading is the correlation between a variable and a factor

Question 10

What is Loading^2?

Answer 10

The proportion of variance in a given variable accounted for by a factor

Question 11

What determines whether absolute loadings should be interpreted?

Answer 11

Those > .30 are called salient and ARE interpreted

Those < .30 are dismissed and sometimes written as 0.

Question 12

What is an eigenvalue?

Answer 12

The sum of squared loadings within a factor down the whole set of variables.
The amount of variance in the set of variables accounted for by a particular factor

Question 13

What do different eigenvalues infer?

Answer 13

They range from 0 to the total number of items

An eigenvalue > 1.00 suggests that this factor should be selected - it is a “principal component”

Question 14

How is the % of total variance accounted for by one or more factors calculated?

Answer 14

P = sum of selected eigenvalues x 100 / number of items

Question 15

What is a communality?

Answer 15

Sum of squared loadings within a variable, across the selected factors
The proportion of variance in an observed variable accounted for by selected factors

Question 16

What do different communalities suggest?

Answer 16

A communality < .30 suggests that the variable is unreliable and should be removed (as the factors account for less than 30% of its variance)

Question 17

What can we use to decide how many components/factors should be extracted?

Answer 17

We can use:

• Kaiser’s criterion: Eigenvalues > 1.00
• Cattell’s scree test: look at the scree plot

Question 18

What does an orthogonal rotation of factors do?

Answer 18

It redistributes the variance amongst the factors, instead of the first factor accounting for as much of the variation as possible
Orthogonal rotation keeps the axes at right angles.

Question 19

What does the Varimax method do?

Answer 19

It maximised the variance of the loadings within each factor, making high loadings higher and low loadings lower

Question 20

What does an oblique rotation of factors do?

Answer 20

The rotation allows for correlations between factors.

Question 21

What are the sequence of operations in conducting an EFA?

Answer 21

1) Compute a matrix of correlations
2) Extract factors based on Kaiser’s criterion and/or Cattell’s scree test
3) Examine factor loadings
4) Is the factor structure simple or complex?
5) Do the factors need rotating?
6) Check the factor loadings again
7) Repeat steps are needed

Question 22

How would you report the results of a principal components factory analysis?

Answer 22

See paper.