Interpreting MCA results

[eloiz]

Hello,

I am trying to run my first MCA and I am at loss looking at the
results below -- which seem to be very odd (particularly: $`Dim 1`
$quali and $`Dim 2`$quali). So I am wondering if someone could provide
general guidelines as to how to interpret MCA results or,
alternatively, direct me towards relevant literature that would cover
the type of results below.

Thanks for helping!

Eloiz.





############################################################
> res$eig
eigenvalue percentage of variance cumulative percentage of
variance
dim 1 0.5901904 29.50952
29.50952
dim 2 0.5000000 25.00000
54.50952
dim 3 0.5000000 25.00000
79.50952
dim 4 0.4098096 20.49048
100.00000

> res$var
$coord
Dim 1 Dim 2 Dim 3 Dim 4
Dim 5
adjective -0.1770910 4.864296e-15 2.062879e+00 -0.1475677
1.081908e-32
adverb 1.2091947 1.840723e+00 -3.088753e-01 1.0076071
1.081908e-32
lexical verb 0.4922449 -1.160488e+00 -4.131597e-01 0.4101816
1.081908e-32
modal -0.9449401 4.040962e-01 -6.222064e-01 -0.7874070
1.081908e-32
CHENG -0.7391583 -1.911714e-15 4.684826e-16 0.6159315
-7.262801e-33
FRENG 0.7984628 1.181716e-15 -5.060856e-16 -0.6653493
-7.262801e-33

$contrib
Dim 1 Dim 2 Dim 3 Dim 4 Dim
5
adjective 0.500484 4.457173e-28 8.016169e+01 0.500484
1.196507e-31
adverb 17.794800 4.867430e+01 1.370532e+00 17.794800
9.124696e-32
lexical verb 7.010858 4.599515e+01 5.829976e+00 7.010858
2.169334e-31
modal 24.693857 5.330551e+00 1.263780e+01 24.693857
2.073472e-31
CHENG 24.035774 1.897803e-28 1.139705e-29 24.035774
1.486377e-31
FRENG 25.964226 6.712959e-29 1.231221e-29 25.964226
1.375978e-31

$cos2
Dim 1 Dim 2 Dim 3 Dim 4
Dim 5
adjective 0.007278738 5.491654e-30 9.876671e-01 0.005054126
2.716712e-65
adverb 0.245282663 5.683964e-01 1.600445e-02 0.170316529
1.963608e-65
lexical verb 0.125677749 6.985172e-01 8.853844e-02 0.087266657
6.071224e-65
modal 0.432747313 7.913989e-02 1.876267e-01 0.300486057
5.672913e-65
CHENG 0.590190423 3.947871e-30 2.370851e-31 0.409809577
5.698040e-65
FRENG 0.590190423 1.292732e-30 2.370996e-31 0.409809577
4.883048e-65

$v.test
Dim 1 Dim 2 Dim 3 Dim 4
Dim 5
adjective -3.607545 9.909126e-14 4.202319e+01 -3.006123
2.203969e-31
adverb 20.941953 3.187935e+01 -5.349388e+00 17.450672
1.873748e-31
lexical verb 14.990391 -3.534047e+01 -1.258200e+01 12.491308
3.294746e-31
modal -27.816402 1.189547e+01 -1.831602e+01 -23.179065
3.184834e-31
CHENG -32.484773 -8.401663e-14 2.058903e-14 27.069162
-3.191880e-31
FRENG 32.484773 4.807708e-14 -2.058966e-14 -27.069162
-2.954808e-31

$eta2
Dim 1 Dim 2 Dim 3 Dim 4 Dim 5
TYPE.OF.MARKER 0.5901904 1.000000e+00 1.000000e+00 0.4098096 NA
ENGL.VARIETY 0.5901904 2.569099e-30 2.370926e-31 0.4098096 NA


> dimdesc(res, axes=c(1, 2))
$`Dim 1`
$`Dim 1`$quali
R2 p.value
TYPE.OF.MARKER 0.5901904 0
ENGL.VARIETY 0.5901904 0

$`Dim 1`$category
Estimate p.value
FRENG 0.5906299 0.000000e+00
adverb 0.8176690 5.967736e-184
lexical verb 0.2668805 1.830668e-43
adjective -0.2473291 7.430246e-27
modal -0.8372204 2.789563e-261
CHENG -0.5906299 0.000000e+00


$`Dim 2`
$`Dim 2`$quali
R2 p.value
TYPE.OF.MARKER 1 0

$`Dim 2`$category
Estimate p.value
modal 0.09405465 0
adverb 1.10990324 0
lexical verb -1.01227334 0
adjective -0.19168455 0

############################################################

[François Husson]

Dear Eloiz,

The results in the MCA function correspond to the eigenvalue, the percentage of variance explained by each dimension, the results for the individuals (coordinates, contribution to the construction of the dimension, quality of representation), you also have results for the categories and the variables.
The you have used the dimdesc function which does not correspond to MCA but is a function that is used as a help to interpret the data. This function is specific to the FactoMineR package. The results of this function help to interpret each dimension. You can see first which variables are linked to each dimension (variables are sorted and only significant variables are given), and then you have the categories that are linked to the dimensions (once again, categories are sorted from the most linked with a positive coordinate, then categories less linked but with a positive coordinate, the less linked with a negative coordinate and then the most linked with a negative coordinate).
You can have more details in this book: Exploratory Multivariate Analysis by Example Using R. Husson, Lê, Pagès (2011) CRC Press.
http://www.crcpress.com/product/isbn/9781439835807;jsessionid=k2EBx4fAHXxoTd8m4nPygg**
or on the website of FactoMineR on this page :
http://factominer.free.fr/classical-methods/multiple-correspondence-analysis.html

Best
FH

[eloiz]

Thanks a lot!!

Eloiz

On Feb 26, 1:34 am, François Husson <francois.hus...@agrocampus-

ouest.fr> wrote:
> Dear Eloiz,
>
> The results in the MCA function correspond to the eigenvalue, the
> percentage of variance explained by each dimension, the results for the
> individuals (coordinates, contribution to the construction of the
> dimension, quality of representation), you also have results for the
> categories and the variables.
> The you have used the dimdesc function which does not correspond to MCA but
> is a function that is used as a help to interpret the data. This function
> is specific to the FactoMineR package. The results of this function help to
> interpret each dimension. You can see first which variables are linked to
> each dimension (variables are sorted and only significant variables are
> given), and then you have the categories that are linked to the dimensions
> (once again, categories are sorted from the most linked with a positive
> coordinate, then categories less linked but with a positive coordinate, the
> less linked with a negative coordinate and then the most linked with a
> negative coordinate).
> You can have more details in this book: Exploratory Multivariate Analysis

> by Example Using R. Husson, Lê, Pagès (2011) CRC Press.http://www.crcpress.com/product/isbn/9781439835807;jsessionid=k2EBx4f...
> or on the website of FactoMineR on this page :http://factominer.free.fr/classical-methods/multiple-correspondence-a...

[Rajib Saha]

Hello François,

It has been very useful to understand the dimdesc function. I have a question on this. Similar to the principle components derived from PCA, can we define linear algebraic expression to present each dimension ? an example in this conetxt would be very helpful.

Regards,

Rajib

[François Husson]

Dear Rajib,

The dimdesc function allows us to interpret and understand the dimensions. It doesn't give the coefficient of the linear algebraic expression.

It would be difficult to give these coefficients in the context of MCA because the variables are transformed (in a disjunctive data table and then the variables are centred and divided by the margins).

FH

[Ling]

Hi François,

After reading through the discussions on imdesc() function, I still have some questions hope you you can explain.

What is R2 column in the output of imdesc() function.

Can you elaborate on how the R2 is calculated and how the P.values are obtained? 

Likewise, what are the values in the Estimate column? How are they calculated?

In addition, as you explained: categories are sorted from the most linked with a positive 

 coordinate, then categories less linked but with a positive coordinate, the 
 less linked with a negative coordinate and then the most linked with a 
 negative coordinate

What values should I refer to in order to see the level of linkness ? 

Are the values somewhere in the summary of the MCA results ? 

What are the values you used to sort the orders of the categories?

$`Dim 1`$quali

                   R2     p.value

road      0.427237795 0.00000e+00

Injury    0.549534867 0.00000e+00

sex       0.021139614 0.00000e+00

failure   0.226984763 0.00000e+00

dayofweek 0.005094197 9.47807e-96

$`Dim 1`$category

                             Estimate       p.value

Skidding Swerving Sliding  0.34812814  0.000000e+00

M                          0.07718872  0.000000e+00

No Injury                  0.65657373  0.000000e+00

Urban                      0.32657907  0.000000e+00

Minor                      0.04139532 3.606934e-177

Severe                     0.30615850  4.038540e-56

day_5                      0.06391134  6.173988e-50

day_1                      0.01400856  5.870761e-05

day_4                      0.01233542  3.823904e-03

day_3                     -0.03350085  7.568507e-13

day_6                     -0.05987254  8.748975e-53

Moderate                  -0.29433865 7.332291e-297

Rule of Road              -0.23428552  0.000000e+00

F                         -0.07718872  0.000000e+00

Serious                   -0.39204985  0.000000e+00

Fatal                     -0.31773906  0.000000e+00

Rural                     -0.32657907  0.000000e+00

Thank you for your help in advance!

Ling

[Emily Choy]

I also would like to know what the R2 values for qualitative variables in the PCA or MCA represent? Why do qualitative variables have R2 values while quantitative values have R values?

Thank you for your help!
Emily

[François Husson]

R2 values are used for qualitative variables because it is the indicator that is used in anova. For quantitative variable, one can use the R-squared also, but the sign of the correlation coefficient is useful. That'is why we prefer to use the R values.

[Anne-Marie Dion-Cote]

Dear all,

I was wondering if a correction for multiple testing might be appropriate when using the dim.desc() function?

If not, why?

Thanks in advance,

Anne-Marie

[josse]

Dear Anne Marie,
Sure, it is not a bad idea at all and we thought about it many times but have not yet investigated and implemented this...
But sure, a good idea,
Best,
JJ

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[Anne-Marie Dion-Cote]

Great, thank you for your quick answer. I have used the function p.adjust().