Interpreting Factor Maps of Categorical Variables from MCA

[Larry John]

Fellow Group Members,

I'm a new FactorMineR user conducting MCA on a set of categorical variables. I've created FactorMaps of the variable categories, but want to be sure I am interpreting the graphic correctly. I used factoextra’s fviz_mca_var command to create the biplots (Factor Maps).

Could one of you please take a look at the attached file (Cat biplot with arrows Dims 1 and 2) and tell me whether or not the following descriptive analysis is correct? It would also be helpful if someone could provide the arguments and values that will keep the labels from conflicting with each other. I tried to use the jitter argument, but the system refused to accept it.

This biplot displays the correlation of each variable category with Dimensions 1 and 2, which, taken together, address approximately 56% of the variance. The following variables are well correlated with Dimension 1, as they are within 0.5 SD of the dashed horizontal line representing the dimension: fearcat_low, greedcat_low, trustcat_mod, fearcat_mod. The following variables, which are between 0.5 and 1 SD, are less well coordinated with Dimension 1: greedcat_none, sympcat_mod, A (which represents the choice of an anti-cooperative strategy), greedcat_mod, trustcat_low and fearcat_high. Five variable categories are more than 1 SD from the horizontal line, leading to the conclusion that they are at best poorly coordinated with Dimension 1: sympcat_high, trustcat_high, fearcat_none, sympcat_low and trustcat_none (trustcat none is almost certainly a low mass-high inertia outlier, as it contains less than 2% of the total number of individuals in the sample).

The following variable categories are well correlated with Dimension 2, as they are all within 0.5 SD of the dashed vertical line representing the dimension: fearcat_none, trustcat_high, sympcat_high, greedcat_none, and A (which represents the choice of an anti-cooperative strategy). The following variables are less well correlated with Dimension 2, as they are between 0.1 and 1 SD of the vertical line: fearcat_low, trsutcat_mod, sympcat_mod, and greedcat_mod. Five variable categories are more than 1 SD from the vertical line, leading to the conclusions that they are at best poorly correlated with Dimension 2: trustcat_none, sympcat_low, fearcat_high, trustcat_low and greedcat_low.

In terms of interactions, the following pairs of variable categories appear well correlated with each other based on their angular distance, indicating that interactions may exist between the variables of which they are levels: fearcat_mod and trustcat_mod, fearcat_high and trustcat_low, fearcat_none and trustcat_high, trustcat_high and sympcat_high, sympcat_high and greedcat_none, greedcat_mod and fearcat_high, greedcat_mod and trustcat_low.

Many thanks for any help you can provide.

Larry John.  

[Larry John]

You will be happy (or completely unconcerned) to know that I answered my questions myself by finding and reading Husson, Le and Pages, 2011. I got the interpretation of distance from the axes completely backwards. The angular distance stuff is correct, although the actual measure to use is the cosine of the angular difference.

Very sorry to have troubled you all with my uninformed question.

Larry