SAS factor analysis (proc factor process, factor rotation and regression method for factor score function)

The data given in the following table are obtained from the population survey conducted in the 12 standard metropolitan areas of Los Angeles . It has five socio-economic variables , They are the total population (pop) 、 The educational level of the residents or the number of years of secondary education (school )、 Total number of employees (employ )、 Number of people in various service industries (services ) And moderate prices (house ), Try factor analysis .

Five social factors survey data

n	pop	school	employ	services	house
1	5700	12.8	2500	270	25000
2	1000	10.9	600	10	10000
3	3400	8.8	1000	10	9000
4	3800	13.6	1700	140	25000
5	4000	12.8	1600	140	25000
6	8200	8.3	2600	60	12000
7	1200	11.4	400	10	16000
8	9100	11.5	3300	60	14000
9	9900	12.5	3400	180	18000
10	9600	13.7	3600	390	25000
11	9600	9.6	3300	80	12000
12	9400	11.4	4000	100	13000

Experimental code ：

proc import out=temp1                                                                                                                  
datafile="D:\1 Common desktop files \IT\SAS experiment \ experiment 8\1.xls"                                                                                
DBMS=EXCEL2000 replace;                                                                                                                 
run;
proc factor data=temp1 method=prin priors=one simple corr proportion=0.80 rotate=varimax score n=3 out=test;
var  pop school employ services house;
run;
proc print data=test;
var factor1 factor2 factor3;
run;
proc  plot  data=test;
plot   factor2*factor1  $  n=′*′/
href=0 vref=0;
run;

Code result interpretation ：

method by principal The principal component method is used for factor analysis
priors=one Specify the method for calculating the variance estimation of a priori common factor , Both are program default parameters
corr Find correlation matrix and partial correlation matrix ,simple Output simple conditional quantity
score The coefficient of factor score model is estimated by regression method
proportion To select the number of common factors m, send m To satisfy λ1+…+λm / p ≥ 0.80 The smallest positive integer of
The common factor solution obtained , The initial factor load matrix does not satisfy “ Simple structure criterion ”, That is, the typical representative variables of each common factor are not very prominent , Therefore, it is easy to make the meaning of common factors ambiguous , It is not conducive to the explanation of factors . Therefore, it is necessary to perform rotation transformation on the factor load matrix , So that the square of the load of each factor is in the column 0 and 1 Bipolar transformation , Achieve the purpose of simplifying its structure . This method of transforming factor load matrix is called factor rotation , The methods of rotation transformation mainly include orthogonal rotation , Skew rotation, etc .

Pop=0.58096F1+0.80642F2

School=0.76704F1-0.54476F2

Employ=0.67243F1+0.72605F2

Services=0.93239F1-0.10431F2

House=0.79116F1-0.55818F2

The variances that can be explained by common factors are 2.8733136 and 1.7966601, The sum of the final common factor variances is 4.669974=2.8733136+1.7966601=0.98782629+0.88510555+0.97930583+0.88023562+0.93750041. Common factor F1 stay 4 The factor loads on all variables are positive , Where it is related to the variable Services,house,school Is particularly relevant , Common factor F2 In variables Employ,Pop There is a large positive load on the 0.80642,0.72605. Combined with professional knowledge, I think F1 Economic development factor ,F2 Population factor . If it is necessary to conduct an analysis , It is necessary to obtain the factor score function after factor rotation for analysis . The author does not conduct the analysis after rotation , If necessary, the reader can conduct experiments and analysis with the above methods , The operation of factor rotation is only carried out after factor analysis because the factor load is average and it is difficult to explain , The purpose is to polarize the load , It is convenient for professional explanation .