7: Factor Analysis Mechanics, Validity and Reliablity

Question 1

Which output matrices follow principal axis factoring and oblimin rotation?

Answer 1

Factor, pattern and structure matrices.

Question 2

Which output matrices follow principal components factoring and varimax rotation?

Answer 2

Component and rotation component matrices.

Question 3

Which output matrices follow principal axis factoring and varimax rotation?

Answer 3

Factor and rotated factor matrices.

Question 4

Describe simple indicators.

Answer 4

Highs indicate only one factor.

Question 5

What is acquiescence bias?

Answer 5

Where some (e.g. uninterested) participants response positively to all items, no matter how they are worded.

Question 6

Which factor extraction includes the full correlation matrix, with error?

Answer 6

Principal component analysis.

Question 7

Which factor extraction is only interested in the common variance between factors?

Answer 7

Principal axis factoring.

Question 8

What is the extraction communality?

Answer 8

The estimate of how much is shared by one variable and the extracted factors.

Question 9

What is the initial communality?

Answer 9

1.0 for PCA and estates for FA.

Question 10

How is the initial communality estimated for factor analysis?

Answer 10

Using the squared multiple correlation between as given variable and all other variables in a set, and updating it each time through the iteration process to find the optimal extraction.

Question 11

In FA, when is a large sample needed?

Answer 11

To analyses complex patterns, more items and less clear factors.

Question 12

What does it mean if a variable has low SMC/initial communality?

Answer 12

It is an outlier and another similar variable must be found, or this one must be dropped.

Question 13

What does it mean if a variable has low MSA?

Answer 13

It does not share enough variance to be a reliable factor, and more must be found, or this one must be dropped.

Question 14

What does it mean if a variable has low KMO?

Answer 14

The whole matrix has poor definition of factors and the solution will be poor and unstable.

Question 15

What do individual cells in the AIC represent?

Answer 15

The negative of the partial correlation of the respective row and column with all other variables partialled out.

Question 16

How many items should a factor be measured by?

Answer 16

At least 3.

Question 17

What does MSA summarise?

Answer 17

The AIC elements for each variable.

Question 18

Is MSA is near 1, what does that mean?

Answer 18

A variable does covary with at least 2 others, and so it belongs.

Question 19

What does KMO summarise?

Answer 19

The individual items MSAs.

Question 20

What should you do if KMO is middling to low?

Answer 20

Look at individual MSAs to see if the sample variable is wrong.

Question 21

What is in a reproduced correlations matrix?

Answer 21

The implied correlations in a factor model and the residuals.

Question 22

What do small residuals in reproduced correlations mean?

Answer 22

They are close to the original correlations and the factor model captures the constructs well.

Question 23

What do large residuals in reproduced correlations mean?

Answer 23

Some aspect of the data has not been captured by the factor model.

Question 24

What 3 things may cause large residuals?

Answer 24

Wrong interpretation, too many unreliable measures, or a methodological problem distorting the solution.

Question 25

When is PAF most appropriate?

Answer 25

When trying to understand an underlying construct that cannot be directly measured.

Question 26

When is PCA most appropriate?

Answer 26

When trying to reduce a data set to a smaller number of independent measures it when things of interest can be measured directly.

Question 27

What are factor scores?

Answer 27

Estimates of what the “score” might be on some latent variable.

Question 28

What analysts commonly used factor scores?

Answer 28

Principal components.

Question 29

What is content validity?

Answer 29

Does the variable measure what we think it does?

Question 30

How can we check content validity?

Answer 30

Face validity and manipulation checks.

Question 31

How is predictive validity usually measured?

Answer 31

Regression.

Question 32

How is convergent and discriminant validity usually measured?

Answer 32

Correlations.

Question 33

How do factor loadings act as a measure of reliability in a simple latent variable model?

Answer 33

When squared, they capture how much of the variance of the factors are predicted from the latent variable they measure.

Question 34

What can artificially inflate Cronbach’s alpha?

Answer 34

Using a large number of items and items that are only trivially different.