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;