What does the option rotation = "varimax" in factanal in R do

r
factor_analysis

#1

Hello,

In using the function factanal for factor analysis through R i came across the option rotation = "varimax.
Below is the output without using the option:

Call:
factanal(x = na.omit(auto_copy), factors = 3)

Uniquenesses:
   price engine_s horsepow wheelbas    width   length curb_wgt fuel_cap      mpg 
    0.24     0.18     0.00     0.19     0.33     0.07     0.11     0.14     0.21 

Loadings:
         Factor1 Factor2 Factor3
price     0.83                  
engine_s  0.69    0.38    0.44  
horsepow  0.95                  
wheelbas          0.82    0.38  
width     0.33    0.62    0.42  
length            0.93          
curb_wgt  0.37    0.45    0.74  
fuel_cap          0.41    0.79  
mpg      -0.42           -0.74  

               Factor1 Factor2 Factor3
SS loadings       2.59    2.55    2.38
Proportion Var    0.29    0.28    0.26
Cumulative Var    0.29    0.57    0.84

Test of the hypothesis that 3 factors are sufficient.
The chi square statistic is 42.03 on 12 degrees of freedom.
The p-value is 3.29e-05

I get the same output when I use the option rotation too.So why is this option used if there is no change in the factor loadings or output.My guess is the factor axes are rotated so that they explain the maximum possible variance (rotation = "varimax) but then there is no change in the output.
Where am I going wrong in the interpretation,can anyone please guide me here!


#2

Hello,

you get the same output because option varimax is the default value for rotation (meaning: its used by default if you specify no other value). You can see which arguments have default values in the R help, type: ?factanal
All values with an equal sign have the respective specified default value.

Cannot help you with varimax option though.


#3

@data_hacks

@Thomase is correct with the default option. Adding to it, i would say the rotation option just enhances the interpretability of the factors obtained. Still they are going to explain the same variance. The only difference would be in the interpretability of these factors.

For example, the unrotated principal components are hard to interpret but when rotated are fairly interpretable while still explaining the same variance.

Hope this helps.