About MCA and PCA

[Mahmood Naderan]

Hi,
As I read the MCA [1] and PCA examples, I came across some questions
where the answers can help better understand the concept. So, I
appreciate any further explanation.

- In the MCA example, it is stated that "Except for the age, all the
variables are categorical". I want to know if categorizing is a manual
process or that is determined by some algorithms? Why is age excluded?
and what does continuous variable mean exactly?

- What information MCA shows that PCA doesn't show? I mean, what is
the shortcoming of PCA? Categorical variables?

- How can PCA results help to better categorizing variables in MCA? I
mean which case is correct?
1) Use raw variables -> do PCA -> figure out the variable categories
-> do MCA -> analyze results
2) Use raw variables -> do PCA -> analyze results
3) Preprocess variables by definitions and categorize them -> do MCA
-> analyze results


[1] http://factominer.free.fr/factomethods/multiple-correspondence-analysis.html
[2] http://factominer.free.fr/factomethods/principal-components-analysis.html

Regards,
Mahmood

[Womble]

Hi.  You really need to go and consult any of the many standard text books on multivariate statistical analysis.  These questions are not related to FactoMineR.

The short answer is:  PCA is mainly concerned with analysing continuous variables such as length, width, weight.

Multiple Correspondence Analysis is concerned with mulitiple categories: e.g.,

object 1 is green, oval and has a flower on it

object 2 is yellow, oval and has a cat on it

object 3 is yellow, square and has a flower on it

and so on.

You can have supplementary  qualitative variables in a PCA.  So, for example, if you have objects described by length, width and weight, you could have colour as a supplementary qualitative variable.  The colour is not used in the analysis, but the results are compared to it.

For beginners in multivariate analysis I always suggest sticking to:

PCA: continuous data.

CA: cross-tabulated count data

MCA: multistate descriptive categorical data

Compositional data (i.e., data which sums to 100%) are a whole other can of worms.

Hope this helps.