ST3900/4950 Factor Analysis Example
ST 3900 Lesson 36
ST 4950 Chapter 10
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Question 1
Terrill is interested in assessing how much women value their careers. He develops a 12-item scale, the Saxon Career Values Scale (SCVS). He has 100 college women taking the SCVS. All of the items reflect the value women place on having a career versus having a family. Students are asked to respond to each on a 4-point scale, with 0 indicating “disagree” and 3 indicating “agree.” Data are reported in qn1.txt.
(a) Conduct a factor analysis. How many factors underlie the SCVS based on the scree plot? Is rotation needed?
Answer: Only 1 factor as seen in the scree plot below; no rotation is needed because of one factor.
(b) How many factors underlie the SCVS based on the eigenvalue-greater-than-1 criterion? Is rotation needed?
Answer: One factor as seen in the output below:
(c) Now extract one factor/component as the measure of how much women value their careers. Explain the association of this measure to these question responses.
Answer:
As seen in the output, this factor retains about 50% of information in the data. See the output below for the extract component.
In addition, this is a meaningful measure of how much a woman value her career as the similar questions are all in the same direction, with either positive or negative coefficients. The smaller the component score is, the more a woman value her career compared to her family, because of the negative coefficients for q03, q04, q05,q07,q11,q12 and the positive coefficients for the other questions.
Appendix:
proc format;
value likert 0 ='disagree'
1 ='slightly disagree'
2 ='neutral'
3 = 'agree';
run;
data factor;
input Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 @@;
LABEL Q1='MARR>CAREER'
Q2='MARR=CAREER'
Q3='CAREER>MARR'
Q4='PREFER CAREER THAN FAMILY'
Q5='THINK OF JOB'
Q6='HAPPY WITHOUT CAREER'
Q7= 'UNFULFILLED WITHOUT CAREER'
Q8= 'CAREER IS NOT IMP'
Q9= 'WILL LEAVE CAREER FOR CHILDREN'
Q10='CAREER WILL INTERRUPT FAMILY'
Q11= 'CAREER SUCCESS IS PRIMARY GOAL'
Q12= 'VERY CAREER MINDED';
FORMAT Q1-Q12 LIKERT.;
DATALINES;
2 3 1 0 0 3 0 3 2 3 1 0
2 1 1 0 2 2 1 2 2 2 2 1
3 1 3 3 3 0 2 1 1 2 3 2
2 1 1 0 0 1 2 3 2 2 1 0
0 2 1 0 0 2 0 3 2 3 0 1
2 3 2 1 3 0 0 3 2 1 2 2
0 3 0 0 0 2 2 3 1 2 2 1
2 0 3 3 3 0 2 2 2 1 3 3
0 0 3 3 3 2 1 0 0 0 3 3
0 0 2 3 3 0 3 0 0 1 3 2
2 1 2 3 0 0 2 0 1 2 1 2
0 2 3 3 3 0 3 1 0 1 3 2
1 2 2 1 0 3 0 1 2 2 1 1
2 2 0 2 1 2 0 0 3 3 3 1
3 3 1 1 1 2 1 2 2 0 1 1
1 1 3 2 3 0 3 1 0 0 2 3
1 1 1 1 1 2 1 0 2 0 3 2
0 0 2 3 3 0 1 0 0 1 3 3
0 1 3 3 1 0 3 0 0 1 2 1
2 1 0 0 1 3 3 2 0 1 0 1
3 3 0 0 0 2 1 3 1 3 0 0
2 1 2 1 1 1 2 1 0 2 1 3
3 2 0 1 1 3 0 2 2 3 0 2
2 2 3 3 3 0 3 0 0 0 3 3
3 3 1 0 0 3 0 3 2 2 0 0
2 2 3 0 1 1 2 0 0 1 1 2
0 1 3 3 2 1 3 1 1 1 1 3
3 3 1 1 0 3 0 2 1 2 1 2
2 1 2 1 2 1 3 1 0 1 2 2
2 2 0 0 0 3 0 2 3 3 0 0
3 2 2 0 0 3 2 3 3 2 0 1
0 2 3 1 3 0 3 0 2 0 3 3
1 1 3 1 2 2 1 2 1 1 1 2
2 1 1 1 0 0 1 0 2 3 1 2
2 3 1 3 1 1 2 0 1 3 3 1
0 0 2 2 3 0 3 0 1 0 2 0
0 2 1 1 1 2 1 1 0 2 0 2
2 0 1 2 0 1 1 3 3 3 0 1
2 3 0 1 1 3 0 3 2 3 0 1
1 2 1 2 3 1 2 3 3 1 1 0
3 1 1 3 2 1 2 0 1 1 2 3
0 0 3 3 1 0 3 0 0 1 3 2
0 1 2 1 1 2 2 2 2 1 2 0
2 3 2 0 0 2 0 3 2 3 1 1
2 1 2 2 2 1 1 1 0 2 1 1
1 1 1 1 3 1 1 0 3 1 2 1
0 1 2 3 3 0 1 0 0 2 3 3
2 3 0 2 1 1 3 1 3 3 2 0
1 0 3 3 3 0 3 0 1 1 3 3
0 0 3 3 3 0 3 0 0 0 3 2
3 1 2 2 2 2 1 0 2 3 0 1
3 2 2 2 0 2 2 2 2 2 3 1
0 1 2 3 1 0 3 0 1 0 2 2
1 0 3 3 3 2 2 2 0 0 3 0
1 3 2 0 3 2 0 3 1 2 1 0
0 0 2 3 2 0 1 0 1 1 3 3
1 1 0 2 1 1 3 1 2 0 3 1
2 1 1 1 2 0 1 0 1 0 3 1
1 3 2 2 2 1 3 3 3 1 0 2
2 2 2 0 1 2 2 2 1 2 2 0
1 0 2 2 3 0 3 1 1 0 1 1
3 3 0 0 0 2 0 3 3 3 1 0
0 1 3 3 1 1 3 0 0 0 3 3
2 1 0 0 0 3 1 2 1 3 0 0
2 2 1 1 3 0 2 2 2 1 2 2
0 0 3 3 1 0 3 0 0 0 3 2
3 3 1 0 2 0 1 3 1 2 1 1
3 3 0 0 0 3 0 3 3 3 0 0
1 0 2 3 1 1 3 2 0 1 1 2
0 0 2 1 1 1 3 0 2 0 2 3
3 1 2 0 1 1 1 1 2 2 2 1
1 0 3 1 1 3 2 0 0 2 2 1
0 0 3 3 3 0 3 0 0 1 3 3
2 1 3 3 3 2 1 1 1 1 1 3
1 1 1 2 0 1 1 1 0 1 3 3
2 2 1 1 0 2 2 1 1 1 1 0
0 0 3 3 3 0 2 0 0 0 3 3
0 2 1 2 2 2 2 0 2 1 2 2
3 2 3 2 0 3 1 2 1 2 2 2
3 2 1 2 3 1 1 2 3 2 0 0
0 0 3 3 3 0 3 0 0 0 3 3
2 1 2 0 0 3 2 0 0 2 1 3
1 1 2 3 3 1 1 0 0 0 2 3
1 2 2 2 1 3 0 3 0 1 1 0
1 2 2 0 1 1 0 3 3 3 0 0
0 0 3 1 3 2 2 0 0 0 3 3
1 1 3 2 3 2 1 1 1 2 1 2
3 1 2 3 1 3 2 3 3 1 0 3
3 2 0 0 0 3 0 3 3 2 0 0
2 3 0 0 1 1 0 2 3 1 1 0
0 0 1 3 1 1 2 0 1 0 1 3
2 3 1 2 0 3 0 2 1 3 2 0
2 2 1 2 1 1 0 3 0 2 1 3
1 1 0 0 2 0 1 2 1 3 0 3
2 3 0 1 0 2 1 3 3 3 0 1
3 3 2 0 0 2 0 2 2 3 0 0
1 1 0 2 3 1 1 2 2 3 1 2
1 3 1 0 2 2 0 1 3 0 2 0
0 0 2 3 1 1 3 2 1 3 1 3
3 2 1 0 3 2 3 3 3 2 2 2
;
PROC FACTOR DATA=FACTOR PREPLOT PLOT ROTATE=VARIMAX NFACTORS=1 OUT=FACT SCREE;
TITLE "EXAMPLE OF FACTOR ANALYSIS";
VAR Q1-Q12;
RUN;