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TRANSCRIPT
Factor Analysis is Your Friend
AnnMaria De Mars, PhD. The Julia Group & 7 Genera>on Games
WHY?
Imagine this
What exactly were you planning on doing with that?
Let’s say you have a massive pile of data …
You Could:
“9% of adolescents reported blah blah blah” “23% of adults said blah blah blah”
The Problem:
1. Boring! No one is going to read each one.
2. Cannot conduct rela=onal analysis of each variable -‐-‐-‐ sta=s=cal sin
3. Individual items are notoriously unreliable.
SUBSCALES ?
• Do you own guinea pigs? • Do you have any stuffed animals?
Conceptually, it’s preJy simple
Don’t Be Scared of Factor Analysis!
Image Source: scoJyoungpsalm37.blogspot.com
Factor analysis is for …
• 1. Revealing paJerns of interrela=onships among variables
• 2. Detec=ng clusters of variables
• 3. Reducing a large number of variables to a smaller number of variables, the factors of factor analysis.
You can factor analyze anything
– test scores, – individual items on a test – measurements of various dimensions (i.e. height or weight)
– agricultural measures like yield of a rice field – Socioeconomic measres
Is this a fair test?
• You have studied for a final exam in Biology 101. There is one ques=on, “What is the rela=onship between respira=on and photosynthesis?”
• Your child is in fi[h grade. Her weekly spelling test consists of one word.
You already understand this
True Variance vs. Error Variance
Variability & Validity
Ques>ons … Image Source: www.edudemic.com
How do I …
• Decide on the number of factors • Interpret factors • With SAS Enterprise Guide
How to do Factor Analysis using SAS Enterprise Guide
A Brief Overview of the Process
1. Open a data set, run a factor analysis, and observe the data’s fit.
2. If necessary, run a correla=on analysis to create a dataset to analyze
3. If necessary , make modifica=ons and run your model once or twice more
A complete project
Our data
• From the 500 Family Study • Hundreds of ques=ons answered • Example uses 42 items asked adolescents regarding parent communica=on, rules, decision-‐making
FILE > OPEN > DATA
Hold down shi= key to select more than one at a Ame
Select the variables
TASKS > MULTIVARIATE > FACTOR ANALYSIS
Look at your log first!
• When you get your results, do NOT look at your results first. Be smarter than most people and look at your log. To do that you click on the tab that says LOG
What if you see this?
• WARNING: 123 OF 465 OBSERVATIONS IN DATA SET WORK.SORTTEMTABLESORTED OMITTED DUE TO MISSING VALUES.
• If we didn’t have a lot of people missing data, we could skip the next few steps, but hey, that’s life.
Tasks > Describe > Summary sta=s=cs
Drag and drop to select variables to analyze
• The default for SAS is to delete a record if it is missing ANY of the variables.
Why factor analyze the correla>on matrix?
My first analysis was missing 120 records but no single item was missing for more than 49 people
by clicking on them and pressing the blue arrows in between the panes
Select the variables you want
DATA SET > TASKS > MULTIVARIATE > CORRELATIONS.
Step Two: Create a Correla>on Matrix Dataset
Output matrix as SAS dataset of type=CORR:
OUTPUT DATA > SAVE OUTPUT > DATA > RUN
TASKS > MULTIVARIATE > FACTOR ANALYSIS
Hold down shi= key to select more than one at a Ame
Select the variables
So Now What does all of this Factor Analysis crap mean, anyway?
What exactly is a factor?
• Recall, a factor is some underlying trait that is measured indirectly by the items you measured directly.
• AKA ‘dimension reduc@on technique’
How many factors?
3 possibili=es
Eigenvalue
• The amount of variance in the individual measures explained by the factor.
Square the loadings in the factor paJern and add them up. The total is the eigenvalue. Predic=on: At least one person who reads this will do exactly that and be surprised that I am right. Contrary to appearances, I do not make this s*** up.
Eigenvalue
• Common criterion for deciding the number of factors is “Minimum eigenvalue greater than 1.”
• Makes intui@ve sense but …
Method 3
• Parallel analysis criterion (macros available – Google it)
Now do it again
What do the factors mean?
Important Point One
• The correla=on of a variable with a factor is called the loading. – loadings can be posi=ve or nega=ve.
Important point two
• To ease interpreta=on we’d really like to have “simple structure” – variables load close to 1.0 on one factor and close to zero on the others.
Next step: iterate
No, it is not party in the pool, sorry.
Secret to factor analysis
• Finding a solu=on that is defensible BOTH sta=s=cally and theore=cally
• Nice first step to structural equa=on modeling. In fact, it IS the first step.