Dear All:
Re: Second-Order Confirmatory Factor Analysis
I did fit a Confirmatory Factor Analysis with four factors, please see below.
But at least two factors are highly correlated. F1 and F4 (0.92), F2 and F4 (0.82), F1 and F2 (0.67).
One thought is to define a second-order factor that will account for the variability between the highly correlated factors. BUT I do not know how to conduct/build such a model.
So I need your help in this part.
Thank you very much in advance for your help
AbouEl-Makarim Aboueissa, PhD
Professor, Mathematics and Statistics
University of Southern Maine
Here is the code I used to conduct a CFA model with four factors and the data set.
data mydata;
input x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22;
datalines;
5 4 2 1 4 4 5 5 5 5 5 5 2 5 5 1 4
4 4 3 2 4 5 5 4 5 4 5 4 2 5 5 1 4
4 4 4 2 3 4 4 4 4 4 4 4 2 4 4 2 4
4 4 4 2 3 4 4 4 4 4 4 4 2 4 4 2 4
5 5 5 1 5 3 5 3 4 4 5 4 1 5 5 2 4
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
3 2 4 2 4 3 3 4 4 4 4 4 1 4 4 2 2
3 4 5 2 2 4 3 4 4 4 4 5 2 3 4 2 3
4 4 5 2 3 5 5 3 4 3 5 3 2 5 4 3 5
4 4 3 1 2 4 5 4 4 3 5 5 2 5 4 3 4
5 4 5 1 1 5 5 5 5 5 5 3 3 5 3 3 5
3 4 4 2 4 4 4 3 4 4 4 4 4 4 2 2 2
3 4 4 2 2 4 4 2 5 2 4 4 2 4 4 3 4
3 4 4 3 3 3 3 3 3 3 4 4 2 3 3 3 3
4 5 5 1 3 4 5 4 5 4 4 4 2 4 4 3 4
5 5 5 2 3 5 5 3 4 5 5 2 1 5 5 1 4
4 4 4 2 2 4 4 3 4 4 4 4 2 5 4 2 5
4 5 4 1 1 3 4 3 5 4 3 4 2 4 4 2 4
5 4 3 1 2 3 4 4 4 3 4 3 2 4 4 2 4
4 4 4 2 1 4 4 4 4 4 4 3 1 5 4 1 5
5 5 3 1 3 5 5 3 5 4 4 4 1 5 5 1 5
4 5 5 2 3 4 5 5 5 5 5 5 1 5 5 3 5
4 5 4 2 3 5 5 5 5 5 5 5 1 5 5 2 5
5 5 4 1 3 4 5 5 5 5 5 5 1 5 5 1 4
5 5 4 2 4 5 5 5 5 4 5 5 1 5 5 2 5
5 5 5 1 3 4 5 5 5 4 5 5 1 5 5 1 5
4 4 3 2 4 4 4 4 4 3 4 4 2 4 4 1 5
4 5 5 1 2 4 5 3 5 5 4 4 1 5 4 3 4
3 4 5 1 4 5 3 3 5 4 4 5 2 5 4 1 4
3 4 4 2 1 4 4 4 4 3 4 4 2 4 4 2 3
4 4 3 1 3 4 5 3 5 4 4 3 4 5 5 3 5
4 4 4 2 2 4 3 3 4 4 3 3 4 3 4 3 3
5 5 5 1 1 5 5 5 5 5 5 5 1 5 5 1 5
4 4 4 1 3 4 4 4 4 4 4 4 1 4 4 1 4
5 5 3 1 2 4 5 5 5 5 5 5 2 5 5 1 5
4 4 4 2 4 5 4 4 5 4 4 5 2 5 5 2 5
3 5 3 1 1 1 5 5 3 3 4 3 3 4 3 1 3
5 5 4 1 3 4 5 4 5 4 5 4 1 5 5 1 4
5 5 5 2 2 4 5 3 4 4 5 4 2 4 4 3 3
4 4 1 1 4 3 4 3 4 3 4 5 1 3 3 2 2
5 4 3 1 5 4 5 3 3 3 4 4 1 4 5 1 4
5 5 2 1 2 4 5 5 2 4 5 4 2 4 4 2 2
4 4 5 2 4 5 4 5 5 4 5 4 4 5 4 3 5
4 4 4 1 1 5 5 5 4 4 5 4 2 5 5 1 3
5 5 2 1 4 2 5 2 4 4 4 5 1 4 4 1 4
5 5 4 2 2 2 5 2 5 5 5 5 2 5 4 4 4
5 4 3 1 4 4 5 3 4 4 5 5 1 5 5 1 4
4 5 5 4 2 4 4 4 4 4 4 4 2 4 4 2 4
3 5 4 2 3 4 5 5 5 5 5 5 1 5 5 2 1
3 4 4 2 2 3 4 4 5 4 5 4 2 5 5 3 4
5 5 4 1 3 4 5 3 4 2 4 4 1 5 4 1 4
4 4 4 1 5 4 4 4 4 4 3 3 2 4 4 2 4
3 5 3 4 3 3 4 3 4 3 5 4 3 5 5 3 4
2 4 4 2 4 4 4 4 4 4 4 4 2 4 4 2 4
1 3 1 1 2 4 4 2 4 5 3 5 2 3 4 1 5
1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
4 5 5 2 2 4 5 4 5 5 4 5 2 4 5 1 4
4 5 4 1 3 4 5 4 4 4 4 5 1 5 4 1 3
5 4 4 2 4 3 4 4 4 3 4 4 2 4 4 1 4
4 4 4 1 4 4 4 4 4 3 4 4 3 4 4 1 3
4 2 2 1 4 4 4 4 4 4 4 4 4 4 4 4 4
4 4 4 2 2 4 4 2 4 2 4 4 2 4 4 2 4
3 5 2 2 4 4 4 3 4 2 4 4 2 4 4 2 2
4 4 5 2 3 5 5 4 4 4 4 3 4 4 4 3 3
5 4 4 2 3 4 5 4 4 4 4 4 2 5 4 2 4
4 4 4 2 2 3 4 4 4 4 4 4 2 4 4 2 4
3 4 4 2 2 4 3 3 4 4 4 4 2 4 4 2 4
2 4 2 2 2 2 2 2 3 3 3 3 2 4 4 3 4
4 4 3 2 4 4 4 4 4 3 4 4 2 4 4 2 4
4 4 4 1 4 5 5 5 5 3 5 5 2 5 4 1 5
2 4 2 1 2 4 5 3 4 3 5 5 2 4 4 1 5
5 4 4 1 3 4 4 4 4 2 4 5 1 5 5 1 2
5 4 3 2 3 4 4 4 4 4 4 4 2 4 3 2 4
4 4 4 2 2 3 3 3 4 2 3 4 3 3 3 2 2
4 4 4 2 2 4 4 3 4 4 4 4 2 4 4 3 4
5 4 1 1 1 5 5 5 5 5 5 5 5 5 5 1 5
4 4 4 2 2 5 5 5 4 4 5 4 2 5 4 4 4
4 4 3 2 3 4 4 3 4 4 4 3 3 3 3 3 4
5 4 5 2 2 5 5 5 5 2 5 5 2 5 5 2 5
5 4 5 1 5 3 5 5 5 2 5 5 1 5 5 1 5
5 4 5 1 3 4 5 5 5 4 5 5 1 5 4 2 4
4 4 4 1 4 2 4 4 4 4 4 4 1 4 3 1 4
3 4 4 1 3 4 4 3 4 3 4 4 2 4 3 2 3
4 4 4 2 2 3 4 4 4 4 4 4 2 3 4 2 4
5 4 5 1 2 4 5 5 4 4 5 4 1 5 5 1 4
3 4 4 2 2 4 4 3 4 4 3 4 2 4 4 2 1
5 4 5 2 2 5 5 5 5 5 5 5 2 5 5 2 5
5 4 4 2 4 4 5 5 5 5 5 5 2 5 5 3 4
2 4 3 2 4 4 3 3 4 3 3 4 4 4 4 3 4
5 4 5 5 2 5 5 5 5 3 5 5 3 5 5 3 4
5 4 4 2 2 3 4 4 4 3 4 4 2 4 4 2 4
5 4 5 4 1 5 5 5 5 4 5 5 4 5 5 2 5
4 4 4 2 2 4 5 4 5 5 4 5 2 5 5 2 5
5 4 4 3 3 3 5 3 3 3 3 3 3 3 3 2 5
3 4 3 3 4 3 4 3 4 3 4 4 3 4 4 3 4
4 4 4 2 3 4 4 4 4 4 4 4 2 4 4 2 4
5 4 5 1 1 5 5 5 4 5 5 5 2 5 4 5 5
5 4 5 4 3 5 5 4 5 5 5 5 2 5 4 3 5
5 4 4 2 4 4 5 4 4 3 4 4 5 5 5 3 5
5 4 2 1 3 2 4 4 2 2 5 2 2 5 2 2 2
4 4 4 2 2 4 4 4 4 4 5 5 1 4 4 1 4
4 4 4 3 4 4 4 3 4 4 4 4 4 3 3 4 4
5 4 4 3 2 4 4 4 4 2 4 4 2 4 4 2 4
5 4 5 2 2 4 4 2 4 4 4 4 2 4 4 3 4
5 4 5 1 1 2 5 4 2 2 5 5 1 5 4 1 4
5 4 3 1 4 4 5 4 4 3 4 5 1 5 4 2 5
5 4 5 1 1 3 5 5 4 5 5 4 3 5 3 3 4
3 4 4 1 3 5 5 5 5 5 5 5 1 5 5 2 2
5 4 5 1 1 4 4 4 5 4 4 4 2 5 4 2 4
5 4 5 1 1 4 4 4 5 4 4 4 2 5 4 2 4
4 4 4 1 2 4 4 2 4 4 4 4 4 4 4 3 4
5 4 3 1 4 4 5 5 4 4 4 5 1 4 4 1 5
4 4 1 1 1 1 4 2 3 2 4 4 3 3 3 2 4
5 5 2 1 2 4 5 4 5 1 5 5 1 5 5 1 5
5 5 4 1 4 4 5 5 4 4 5 4 1 5 4 1 4
4 5 3 1 1 2 5 5 5 5 5 4 1 5 5 1 5
4 4 3 4 4 4 4 3 4 3 4 3 2 4 4 2 4
4 5 5 2 5 4 4 4 5 4 5 5 2 5 4 2 5
1 1 3 2 2 4 3 3 4 4 4 4 3 2 4 3 4
4 4 4 1 2 4 4 4 4 4 4 4 4 4 2 4 4
4 4 4 2 2 4 4 2 4 4 4 4 2 4 4 2 2
3 4 4 2 4 4 5 4 4 4 4 4 2 4 4 2 4
5 5 4 2 2 4 4 3 5 3 5 4 2 5 4 2 4
3 3 3 3 3 3 3 2 4 3 2 3 3 3 3 3 3
4 5 4 1 2 2 5 4 5 5 5 5 2 5 4 2 5
5 5 5 1 2 4 5 4 5 5 5 5 1 5 5 1 4
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
4 3 2 2 2 4 2 3 4 4 4 4 2 4 3 4 4
3 4 3 3 2 4 4 4 4 4 4 4 2 4 4 2 3
1 1 1 2 2 4 4 4 4 4 4 4 4 4 4 4 4
3 4 3 2 4 4 4 3 3 4 3 3 2 4 4 3 3
3 3 3 4 4 4 3 4 4 3 4 4 3 3 3 3 4
4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
3 4 4 2 3 4 4 4 4 4 4 4 2 4 4 2 4
5 5 5 2 3 4 4 4 4 4 4 4 1 4 4 1 3
;
run;
proc print data = mydata;
run;
/* Confirmatory Factor Model */
proc calis data=mydata;
factor
Factor1 ===> x11 x13 x14 x15 Q17,
Factor2 ===> x6 x7 x12 x16 x19,
Factor3 ===> x9 x18 x21,
Factor4 ===> x19 x20 x22;
pvar
Factor1 Factor2 Factor3 Factor4 = 4 * 1.;
cov
Factor1 Factor2 Factor3 Factor4 /* = 4 * 0. */;
run;
ods graphics on;
proc calis data=mydata plots=pathdiagram;
factor
Factor1 ===> x11 x18 x14 x15 x17 = 1. ,
Factor2 ===> x6 x7 x12 x16 x19 = 1. ,
Factor3 ===> x9 Q18 Q21 = 1. ,
Factor4 ===> x19 x20 x22 = 1. ;
run;
ods graphics off;
