rlaboiss / debian-gr-systemd-2019 Goto Github PK

IMHO, ties in ballots need to be taken care of more carefully. I suggest to add these lines to your preprocessing:

        choices = scipy.stats.rankdata(choices)
        # Add a small random, to avoid numerical collapse of "factanal" in R
        choices += numpy.random.rand(*choices.shape) * 1e-3
        choices = list(choices)

The first line will take care of normalizing different, yet equivalent, votes. For example, someone voting 12344444 likely has the same intention as someone voting 12388888; likely some will even be aware that it does not matter for the voting method. So these should be treated equally. With the standard tie-averaging approach, they will be transformed to 12366666.
Now because this removes one factor (value range) from the data, it introduces a correlation into the data that kills R factanal. To make the analysis still work, I add random noise of a magnitude substantially less than the rank differences, just enough to ensure the matrix is invertible.
I don't know which approach is better (I'd argue that your approach is more sensitive to measuring whether there are people with extreme opinions that vote, e.g., 18888888); but in lieu of a formal argument for one over the other, I'd argue that observations not supported by both more likely are artifacts than true observations. Some observations still persist (AG and DH are pairs); others look quite a bit different (no F+B+fd factor; E+G decompose into two factors). I'd argue that in this analysis, the factors mostly decompose into whether people liked (1) DH best, (2) E best, (3) G best, (4) A best. This is a very plausible outcome; given that F+B were overall popular it is plausible that they are also often ranked 2nd and 3rd.

===== Exploratory factorial analysis

Call:
factanal(x = ~F + B + A + D + H + E + G + fd, factors = 4, data = dat,
   scores = "regression", rotation = "promax")

Uniquenesses:
    F     B     A     D     H     E     G    fd 
0.140 0.300 0.005 0.290 0.158 0.005 0.005 0.629 

Loadings:
   Factor1 Factor2 Factor3 Factor4
F  -0.501  -0.305  -0.207  -0.214 
B  -0.247  -0.568  -0.197         
A  -0.194                   1.041 
D   0.980          -0.193  -0.108 
H   1.016                  -0.154 
E  -0.154   1.133  -0.157         
G  -0.166  -0.124   1.143         
fd -0.432   0.154  -0.115  -0.321 

               Factor1 Factor2 Factor3 Factor4
SS loadings      2.580   1.752   1.478   1.285
Proportion Var   0.323   0.219   0.185   0.161
Cumulative Var   0.323   0.542   0.726   0.887

Factor Correlations:
        Factor1 Factor2 Factor3 Factor4
Factor1   1.000   0.186   0.548  -0.480
Factor2   0.186   1.000   0.203  -0.285
Factor3   0.548   0.203   1.000  -0.523
Factor4  -0.480  -0.285  -0.523   1.000

Test of the hypothesis that 4 factors are sufficient.
The chi square statistic is 6331.72 on 2 degrees of freedom.
The p-value is 0 

===== Correlation between factors #1 and #2

	Pearson's product-moment correlation

data:  sc[, 1] and sc[, 2]
t = -5.3537, df = 423, p-value = 1.417e-07
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 -0.3389097 -0.1606376
sample estimates:
       cor 
-0.2519095 

But again - I'd not put too much trust on any observation not supported by both variants. Changing just a little bit to the preprocessing does produce quite different results.