Robust Multiple Correspondence Analysis (Robust MCA)

Classical MCA assigns equal weight to every respondent in the SVD. Robust MCA first estimates how unusual each respondent is — based on distances in a preliminary solution — and then downweights observations far from the bulk of the data. The resulting axes and maps are driven by the majority pattern rather than by outliers.

No. They are downweighted so that they have little influence on the axes, but they still appear as plotted points in the map. This lets you see where atypical respondents fall relative to the typical structure, which is often informative in itself.

Prefer Robust MCA when you have a priori reasons to expect data-quality problems — large online surveys with incentivized participants, administrative data with known entry errors, or any context where a small number of unusual response patterns is plausible. For clean, carefully collected data, classical MCA is simpler and equally valid.

Yes, in the same way classical MCA does — ordinal variables are treated as nominal (each level as a separate category) unless you apply a constrained (monotone) version. The robust re-weighting step is agnostic to whether the categories have an inherent order.

Robust distance estimation requires enough observations to obtain a stable covariance estimate in the reduced space. As a practical guideline, at least 100 respondents is advisable, and more is better. Very small samples make it difficult to distinguish outliers from normal variation in the tails.