Ex. 5.4 Everitt: Apply the factor analysis model separately to the life expectancies of men and women and compare the results

Here some code and output

life <- fread('http://people.stat.sc.edu/Hitchcock/lifeex.txt')
life_M <- life[,c(1,2,3,4,5)]
life_W <- life[,c(1,6,7,8,9)]
factanal(x=life[,-1],factors =3) for both groups

The data is about life expectancies for different countries by age and gender.

Output for men group

Call:
factanal(x = life_M[, -1], factors = 1)

Uniquenesses:
   m0   m25   m50   m75 
0.594 0.552 0.005 0.434 

Loadings:
    Factor1
m0  0.638  
m25 0.669  
m50 0.998  
m75 0.752  

               Factor1
SS loadings      2.415
Proportion Var   0.604

Test of the hypothesis that 1 factor is sufficient.
The chi square statistic is 14.45 on 2 degrees of freedom.
The p-value is 0.000728 

Output for women group

Call:
factanal(x = life_W[, -1], factors = 1)

Uniquenesses:
   w0   w25   w50   w75 
0.220 0.005 0.115 0.526 

Loadings:
    Factor1
w0  0.883  
w25 0.998  
w50 0.941  
w75 0.689  

               Factor1
SS loadings      3.134
Proportion Var   0.784

Test of the hypothesis that 1 factor is sufficient.
The chi square statistic is 52.15 on 2 degrees of freedom.
The p-value is 4.74e-12 

Some points that I noticed:

(1) I can't use more than 1 factor for 4 variables with factanal and don't know why.

(2) In both cases the chi-square test says that 1 factor is not enough, but I can't use more than 1 based in (1).

(3) For the men group one factor explains 60.4% of variance structure and in women group 78.4%. In this case what I think is that one factor is sufficient for women group but not so good for men.

(4) For both group together 3 factors explain 88.9% of variance, what makes me think: What is the advantage of split the groups?

(5) Should not the number of factors be chosen based on the ratio of explained variance and the interpretability of the factors?

Ex. 5.4 Everitt: Apply the factor analysis model separately to the life expectancies of men and women and compare the results

Here some code and output

library(data.table)
life <- fread('http://people.stat.sc.edu/Hitchcock/lifeex.txt')
life_M <- life[,c(1,2,3,4,5)]
life_W <- life[,c(1,6,7,8,9)]
factanal(x=life[,-1],factors =3) #for both groups

The data is about life expectancies for different countries by age and gender.

Output for men group

Call:
factanal(x = life_M[, -1], factors = 1)

Uniquenesses:
   m0   m25   m50   m75 
0.594 0.552 0.005 0.434 

Loadings:
    Factor1
m0  0.638  
m25 0.669  
m50 0.998  
m75 0.752  

               Factor1
SS loadings      2.415
Proportion Var   0.604

Test of the hypothesis that 1 factor is sufficient.
The chi square statistic is 14.45 on 2 degrees of freedom.
The p-value is 0.000728 

Output for women group

Call:
factanal(x = life_W[, -1], factors = 1)

Uniquenesses:
   w0   w25   w50   w75 
0.220 0.005 0.115 0.526 

Loadings:
    Factor1
w0  0.883  
w25 0.998  
w50 0.941  
w75 0.689  

               Factor1
SS loadings      3.134
Proportion Var   0.784

Test of the hypothesis that 1 factor is sufficient.
The chi square statistic is 52.15 on 2 degrees of freedom.
The p-value is 4.74e-12 

Some points that I noticed:

(1) I can't use more than 1 factor for 4 variables with factanal and don't know why.

(2) In both cases the chi-square test says that 1 factor is not enough, but I can't use more than 1 based in (1).

(3) For the men group one factor explains 60.4% of variance structure and in women group 78.4%. In this case what I think is that one factor is sufficient for women group but not so good for men.

(4) For both group together 3 factors explain 88.9% of variance, what makes me think: What is the advantage of split the groups?

(5) Should not the number of factors be chosen based on the ratio of explained variance and the interpretability of the factors?