Si avvisa che in data 06-04-2017, alle ore 14:00
precise,
presso l'Aula Seminari "F. Saleri" VI piano -
Dipartimento di
Matematica, Politecnico di Milano,
nell'ambito delle iniziative MOX, si svolgerā il
seguente seminario:
Relatori:
Eva
Fiserova e Karel
Hron, Palacky University, Olomouc, Czech Republic
Titolo:
Regression analysis for
compositional data
from perspective of the logratio approach
Sommario:
Regression analysis is an
important tool for
analysing the relationships between the response variable and
known explanatory
variables. When the response variables or explanatory
variables are
compositional,
i.e.
multivariate observations carrying only relative information
(proportions,
percentages),
a
special treatment in
regression is necessary. Compositional data are characterized
by the simplex
sample space with the Aitchison geometry that forms the
Euclidean structure.
Proper statistical methodology for this kind of observations
is the logratio
methodology that enables to express the data isometrically in
the real
Euclidean space where it is possible to apply standard
statistical tools
(Aitchison, 1986; Pawlowsky-Glahn et al., 2015). The lecture
is focused on
three main regression tasks, where compositional data are
involved: either
regression with a compositional response variable, or
regression with
compositional explanatory variables, or regression between
parts of a
composition. The main methodological approach for dealing with
compositional regression
is based on orthonormal logratio coordinates. Although
regression models in orthonormal
logratio coordinates are theoretically well justified, both
the normalizing
constants to reach orthonormality and the natural logarithm
itself result in
quite a complex interpretation of the regression parameters.
In the lecture, we
will present new orthogonal logratio coordinates (Muller et
al., 2017) in order
to achieve better interpretability of regression parameters
while preserving
all important features of regression models for compositional
data. Theoretical
results will be applied to real-world examples.
Docente di riferimento:
Alessandra Menafoglio, alessandra.menafoglio@polimi.it
Tutti gli interessati sono invitati a partecipare.
Cordiali saluti,
Laura Sangalli
-- Laura Maria Sangalli MOX - Dipartimento di Matematica Politecnico di Milano Piazza Leonardo da Vinci 32 20133 Milano - Italy tel: +39 02 2399 4554 fax: +39 02 2399 4568 email: laura.sangalli@polimi.it url: http://mox.polimi.it/~sangalli