# Supervised dimension reduction with predictors of different nature

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*schedule*
le mardi 13 novembre 2018 de 12h00 à 13h00

**Organisé par :**Castillo, Fischer, Giulini, Gribkova, Levrard, Roquain, Sangnier

**Intervenant :**Pamela Llop (IMAL - Argentine)

**Lieu :**Paris-Diderot, salle 2015

**Sujet :**Supervised dimension reduction with predictors of different nature

**Résumé :**

In some areas of knowledge as economy and social sciences, it is common to model some

phenomenon of interest from explanatory variables of mixed nature; this is, continuous variables

(e.g. income, age, etc.), categorical variables (e.g. schooling, quality of roof, floor, etc.) and

binary variables (e.g. gender, TV, radio, auto, etc.). At the same time, many times it is

desirable to reduce the amount of predictors or to combine them in a simpler indicator in order

to simplify the analysis but without losing information about the phenomenon to be studied.

The sufficient dimension reduction approach (SDR) consists in reducing the dimension of the

p-dimensional space of the predictors X, combining them in a new set of variables that live

in an lower dimensional space without losing information about the response Y . Mostly, the

SDR methods assume continuos predictors ([5, 2, 3]). However, recently some extensions have

been developed for predictors whose distribution belongs to an exponential family ([1]) or for

ordinal predictors ([4]). Following this line, in this work we propose a supervised dimension

reduction technique for the case in which predictors are of different nature (continuous, binary

and ordinals) and we apply it to construct a socio-economic status index for real data coming

from the household suvey of Argentina.

References

[1] E. Bura, S. Duarte, and L. Forzani. Sufficient reductions in regressions with exponential

family inverse predictors. To appear in Journal of the American Statistical Association.

[2] R.D. Cook and L. Forzani. Principal fitted components for dimension reduction in regression.

Statistical Science, 23:485–501, 2008.

[3] R.D. Cook and L. Forzani. Likelihood-Based sufficient dimension reduction. Journal of the

American Statistical Association, 104(485):197–208, 2009.

[4] R. Garcı́a Arancibia, P. Llop, L. Forzani, and D. Tomassi Sufficient dimension reduction for

ordinal predictors. Submitted paper.

[5] K.C. Li. Sliced inverse regression for dimension reduction (with discussion). Journal of the

American Statistical Association, 86:316–342, 1991.