Session 1: Theoretical advances in compositional data analysis.
http://hdl.handle.net/10256/632
Mon, 09 Sep 2024 22:46:37 GMT2024-09-09T22:46:37Zalr approach for replacing values below the detection limit
http://hdl.handle.net/10256/667
alr approach for replacing values below the detection limit
Palarea Albaladejo, Javier; Martín Fernández, Josep Antoni; Gómez García, Juan
Mateu i Figueras, Glòria; Barceló i Vidal, Carles
All of the imputation techniques usually applied for replacing values below the
detection limit in compositional data sets have adverse effects on the variability. In this
work we propose a modification of the EM algorithm that is applied using the additive
log-ratio transformation. This new strategy is applied to a compositional data set and the
results are compared with the usual imputation techniques
Sat, 01 Oct 2005 00:00:00 GMThttp://hdl.handle.net/10256/6672005-10-01T00:00:00ZThe Dirichlet distribution with respect to the Aitchison measure on the simplex - a first approach
http://hdl.handle.net/10256/666
The Dirichlet distribution with respect to the Aitchison measure on the simplex - a first approach
Mateu i Figueras, Glòria; Pawlowsky-Glahn, Vera
Mateu i Figueras, Glòria; Barceló i Vidal, Carles
The algebraic-geometric structure of the simplex, known as Aitchison geometry, is used
to look at the Dirichlet family of distributions from a new perspective. A classical
Dirichlet density function is expressed with respect to the Lebesgue measure on real
space. We propose here to change this measure by the Aitchison measure on the
simplex, and study some properties and characteristic measures of the resulting density
Sat, 01 Oct 2005 00:00:00 GMThttp://hdl.handle.net/10256/6662005-10-01T00:00:00ZWeighted Logratio Biplots, Correspondence Analysis and Spectral Maps
http://hdl.handle.net/10256/664
Weighted Logratio Biplots, Correspondence Analysis and Spectral Maps
Greenacre, Michael J.; Lewi, Paul
Mateu i Figueras, Glòria; Barceló i Vidal, Carles
Starting with logratio biplots for compositional data, which are based on the principle of subcompositional coherence, and then adding weights, as in correspondence analysis, we rediscover Lewi's spectral map and many connections to analyses of two-way tables of non-negative data. Thanks to the weighting, the method also achieves the property of distributional equivalence
Sat, 01 Oct 2005 00:00:00 GMThttp://hdl.handle.net/10256/6642005-10-01T00:00:00ZA tale of two logits, compositional data analysis and zero observations
http://hdl.handle.net/10256/662
A tale of two logits, compositional data analysis and zero observations
Fry, Tim R.L.; Chong, Derek
Mateu i Figueras, Glòria; Barceló i Vidal, Carles
The application of compositional data analysis through log ratio trans-
formations corresponds to a multinomial logit model for the shares themselves.
This model is characterized by the property of Independence of Irrelevant Alter-
natives (IIA). IIA states that the odds ratio in this case the ratio of shares
is invariant to the addition or deletion of outcomes to the problem. It is exactly
this invariance of the ratio that underlies the commonly used zero replacement
procedure in compositional data analysis. In this paper we investigate using the
nested logit model that does not embody IIA and an associated zero replacement
procedure and compare its performance with that of the more usual approach of
using the multinomial logit model. Our comparisons exploit a data set that com-
bines voting data by electoral division with corresponding census data for each
division for the 2001 Federal election in Australia
Sat, 01 Oct 2005 00:00:00 GMThttp://hdl.handle.net/10256/6622005-10-01T00:00:00Z