FAMD interpretation and correlation matrix

[Athanasia Metoki]

Hello FactoMineR experts,

I have a dataset with ~2500 subjects and 13 variables (9 continuous, 4 categorical/dichotomous).

I ran an FAMD and decided to retain 7 factors/dimensions.

Here is my question:

In PCA (only continuous variables) we can calculate loadings (ie. correlations between the variables and the component).

• Are the results of "res$Dim.1$quanti" the loadings for the quantitative variables? For example in the table below, could we say that subjects with a high component 1 score will be those with high count of cigarettes per day before and after, high count of marijuana per day before and after, and low age of both parents?

• The results above are the quantitative variables for Dimension(component)1. The qualitative results are in the pictures below. So these results could be interpreted like this: Subjects with high scores in Dimension(component)1 are the ones with unplanned pregnancies (that is what =0 is in my dichotomous variables, and =1 means planned).
  

• So overall, could we sum up the above results for Dimension(component)1 like this: Subjects with a high component 1 score will be the subjects with high count of cigarettes per day before and after, high count of marijuana per day before and after, low age of both parents, and having mothers that had an unplanned pregnancy?

• In PCA one can create these nice correlation matrix plots (see picture below from here). I am assuming that would be impossible with FAMD since pearson correlation (R) is used for the qualitative variables but an ANOVA for the quantitative variables resulting in F-estimates and R2. Is there a way to get the R values for the quantitative variables, just so that I could compose a correlation matrix like the one below?

Thank you for your time, and looking forward to your response! (You have created a great tool!)

Best,

Nasia Metoki, PhD

[Francois Husson]

Hi,

In FAMD, you interpret the continuous variables as in PCA, and the categorical variables as in MCA. So all your interprtation are correct.
For the correlation matrix, it cannt be done with categorical variables, but you can consider the coordinates of the variables on the dimension with the object res$var$coord because the coordinates correspond to the R² between the coordinate of the individuals on the dimension and the continuous variable (so it is the square correlation coefficient) or between the coordinate of the individuals on the dimension and the categorical variable (and it is the square correlation ratio).

FH

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