Factor Analysis

Question 1

What are you trying to do in a factor analysis?

Answer 1

Trying to build a table - solid, dependable, everyone uses them, easy to understand. But when you look closer, it is hard to construct a table - legs, what it is made up of etc

First one won’t be very good

Question 2

How do you make a questionnaire?

Answer 2

Items: the part people interact with - see if they are good quality

Factors: the structure which holds up the items, want a few but provide the main support

Question 3

What is the main idea?

Answer 3

Reduce a large number of variables to a smaller set of representative, meaningful variables while keeping as much information as possible - identify factors from a large set of correlated items

Question 4

What do you get out of a FA?

Answer 4

A set of statistically identified factors - clusters of items which all measure the same characteristics / data - use these as variables for future analyses

Question 5

What are factors?

Answer 5

Clusters of items which all measure the same characteristic

Question 6

What is the goal?

Answer 6

Identify how many factors you have and what characteristic those factors each represent

Question 7

What are the stages of FA?

Answer 7

1. Identify variables and design
2. Check data and assumptions
3. Rotation
4. Interpret the results

Question 8

Identify variables and design: what are the initial checks?

Answer 8

Check the data
is there any missing?
what scale is the data measured on? - what do each end mean?
how many items and participants are there?

remove ppts who are incomplete cases or make invalid answers

Question 9

Checking data and assumptions: what are the initial checks?

Answer 9

Normality and standard deviations
check the items are normally distributed (all of them)
check SD’s are between 0.5 and 1.5
identify the worst offenders - if all the data is skewed, can’t chuck them all out, identify the worst ones, may want to exclude them

Question 10

What should the SD’s be?

Answer 10

Between 0.5 and 1.5

Question 11

Checking data and assumptions: what are the second checks?

Answer 11

Correlations
Sphericity
Sampling adaquacy

Question 12

Checking the correlations

Answer 12

You get a massive correlation - you expect them to correlate in FA, we are looking for underlying factors that explain groups of items so want correlations

Question 13

What are the possible problems with correlations?

Answer 13

1. items that don’t correlate with anything else - might indicate that an item doesn’t measure the construct, so not valid
   look for items with r < .3 or p > .05 (not just one, has to be many)
2. items that correlate too highly - too much overlap, measuring the same thing, not valid
   singularity r > .9
   problems with multicollinearity

Check the determinant - should be greater than 0.00001 - no problems with multicollinearity

Question 14

What should you do with correlations?

Answer 14

Identify the worst offenders - can’t discard them all if lots of WO, pick the ones which don’t correlate with loads of items, if it is just one item, then it is fine, report with justification

At this point, run the analysis with the final set of items

Question 15

How do you check for suitability of the data?

Answer 15

Kaiser-Meyer-Olkin Measure of sampling adequacy KMO
Do you have a sufficient sample to extract the factors?
Values range between 0 (inappropriate) and 1 (go for it)
marvellous - bigger than .9
middling - bigger than .7
miserable - above 0.5
if below 0.5, you should stop and collect more data or do something else

Report it and cite the data

Question 16

How do you check for the sphericity of the data?

Answer 16

Using Bartlettes test - see whether the correlations are too small for FA
if everything is okay, this test will be significant
Reporting: X2 (df) = chi square value, p value

Question 17

Interpreting the results: what do we do here?

Answer 17

Extraction - how many do we have, which items below with each factor, what do the factors represent?

Question 18

What is extraction?

Answer 18

Deciding how many factors best capture our data - we want parsimony, explaining as much variance as we can with as few factors as possible - don’t want to lose much data

Question 19

What is Kaisers criteria for extraction?

Answer 19

Automatically extracts eigenvalues bigger than 1

Question 20

What is an eigenvalue?

Answer 20

The variance in all the variables accounted for by a particular factor
If it is low, it doesn’t explain much - can be disregarded
A measure of how useful it is - each factor has its own eigenvalue - measure how much weight of the table each leg holds up, if it isn’t holding much up, we can get rid of it and not lose much

Question 21

What are the initial eigenvalues?

Answer 21

Tells you how much factors you have - a factor for each given variable

Question 22

Is Kaisers criteria always okay to use to extract factors?

Answer 22

No, it is only reliable if it meets certain circumstances

Question 23

What are the circumstances in which you can use Kaisers criteria?

Answer 23

There are fewer than 30 variables and all commonalities are bigger than 0.7
or
There are more than 250 participants and the average communality is bigger or equal to 0.6

Question 24

What is a communality?

Answer 24

The percent of variance in a variable explain by all of the factors together - after extraction, some information is lost
Communality after extraction - variance in each variable explained by the remaining factors
Higher - factor structure better explains the variance in variables - bigger is better
e.g. if .67 = 67% of variance of item 3 is explained by all of the factors

Question 25

What do we do if Kaisers criterion is unreliable?

Answer 25

If you have more than 200 ppts, you can use a scree plot to decide the number of factors

Question 26

What are we looking for in a screeplot?

Answer 26

The inflexion point: where the slope changes
It is the point where the slope changes and goes up, count from the left of the point of inflexion - don’t keep the factor where it changes
Very prone to interpretation - as long as you explain it
Can rerun the analysis with fixed amounts of factors

Question 27

How can you tell how much variance our factors explain?

Answer 27

Look at: total variance explained table
Extraction sum of loadings - at the end of factor 6, there will be a cumulative percentage of what all the factors explain together

Question 28

What do you do after deciding the amount of factors?

Answer 28

Rotation

Question 29

What is rotation?

Answer 29

It optimises how the items load onto a factor - it should equalise the variance explained of each factor, so they all explain similar amounts

Aids and clarifies the interpretation - doesn’t change the number of factors or effect the method of extraction

Question 30

What are the two types of extraction?

Answer 30

Orthogonal - factors are uncorrelated, independent of each other
Oblique - when the factors correlate, theoretical grounds thinking they will correlate

Question 31

What do you use if you believe the factors are independent of each other?

Answer 31

Orthogonal rotation

Varimax

Question 32

What do you use if you believe the factors are correlated?

Answer 32

Oblique rotation

Direct oblimin

Question 33

How do you decide which rotation to use?

Answer 33

Look at previous research - see what other questionnaires have done
Think about your factors - do you think they will correlate

Make a choice based on your own research and judgement - and explain why you have made this decision

Question 34

What does rotation actually do?

Answer 34

Spreads the variance more evenly among the factors - it is the same total variance explained, but the eigenvalues have changed so that they are better distributed - each factor explains a similar amount of variance rather than 1 explaining loads

Question 35

How do you identify and name the factors?

Answer 35

Look at the items listed that load onto each factor - the number is the loading, the higher the loading, the stronger the association with that factor
Name them yourself
Negative loadings - because some of the questions were worded negatively
Sometimes cross-loadings - items which led onto more than one factor - allocate to either a higher factor or one that makes the most sense