http://hdl.handle.net/10256/632 2025-07-02T03:49:12Z 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 2005-10-01T00:00:00Z 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 2005-10-01T00:00:00Z 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 2005-10-01T00:00:00Z 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 2005-10-01T00:00:00Z