http://hdl.handle.net/10256/150 2025-06-03T09:37:10Z http://hdl.handle.net/10256/24828 Book of Abstract of the 10th International Workshop on Compositional Data Analysis (CoDaWork2024): 3-7 June 2024, Girona, Spain CoDaWork. International Workshop on Compositional Data Analysis (10è : 2024 : Girona, Catalunya) Comas Cufí, Marc; Palarea Albaladejo, Javier CoDaWork 2024, the 10th International Workshop on Compositional Data analysis, offers an open forum for discussing the latest advances in the methodology and applications of compositional data analysis and related methods in different fields. The primary goal of the workshop is to present the state of the art and identify relevant lines of future methodological research and areas of applications; bringing together researchers from varied disciplines, academic mathematicians and statisticians, applied data analysts and modellers, research students, as well as those with a general interest in the field, to share their ideas, experiences, and developments CoDaWork 2024 held in Girona on 3-7 June 2024, and organised by Statistics and Compositional Data Analysis Research Group from the Department of Computer Sciences, Applied Mathematics and Statistics of the University of Girona 2024-06-03T00:00:00Z http://hdl.handle.net/10256/10558 Proceedings of the 6th International Workshop on Compositional Data Analysis: Girona, 1-7 de juny de 2015 CoDaWork. International Workshop on Compositional Data Analysis (6è : 2015 : L'Escala, Catalunya) Thió i Fernández de Henestrosa, Santiago; Martín Fernández, Josep Antoni Llibre d'actes del 6è International Workshop on Compositional Data Analysis, celebrat a Girona els dies 1 a 7 de juny de 2015 Workshop on Compositional Data analysis. CoDaWork (6è: 2015: L'Escala, Girona) 2015-06-01T00:00:00Z http://hdl.handle.net/10256/753 Experimental design on the simplex Atkinson, A.C. Martín Fernández, Josep Antoni; Daunis-i-Estadella, Pepus Optimum experimental designs depend on the design criterion, the model and the design region. The talk will consider the design of experiments for regression models in which there is a single response with the explanatory variables lying in a simplex. One example is experiments on various compositions of glass such as those considered by Martin, Bursnall, and Stillman (2001). Because of the highly symmetric nature of the simplex, the class of models that are of interest, typically Scheff´e polynomials (Scheff´e 1958) are rather different from those of standard regression analysis. The optimum designs are also rather different, inheriting a high degree of symmetry from the models. In the talk I will hope to discuss a variety of modes for such experiments. Then I will discuss constrained mixture experiments, when not all the simplex is available for experimentation. Other important aspects include mixture experiments with extra non-mixture factors and the blocking of mixture experiments. Much of the material is in Chapter 16 of Atkinson, Donev, and Tobias (2007). If time and my research allows, I would hope to finish with a few comments on design when the responses, rather than the explanatory variables, lie in a simplex. References Atkinson, A. C., A. N. Donev, and R. D. Tobias (2007). Optimum Experimental Designs, with SAS. Oxford: Oxford University Press. Martin, R. J., M. C. Bursnall, and E. C. Stillman (2001). Further results on optimal and efficient designs for constrained mixture experiments. In A. C. Atkinson, B. Bogacka, and A. Zhigljavsky (Eds.), Optimal Design 2000, pp. 225–239. Dordrecht: Kluwer. Scheff´e, H. (1958). Experiments with mixtures. Journal of the Royal Statistical Society, Ser. B 20, 344–360. 1 2008-05-30T00:00:00Z http://hdl.handle.net/10256/752 Robust Factor Analysis for Compositional Data Filzmoser, Peter; Hron, Karel; Reimann, Clemens; Garrett, Robert G. Daunis-i-Estadella, Pepus; Martín Fernández, Josep Antoni Factor analysis as frequent technique for multivariate data inspection is widely used also for compositional data analysis. The usual way is to use a centered logratio (clr) transformation to obtain the random vector y of dimension D. The factor model is then y = Λf + e (1) with the factors f of dimension k < D, the error term e, and the loadings matrix Λ. Using the usual model assumptions (see, e.g., Basilevsky, 1994), the factor analysis model (1) can be written as Cov(y) = ΛΛT + ψ (2) where ψ = Cov(e) has a diagonal form. The diagonal elements of ψ as well as the loadings matrix Λ are estimated from an estimation of Cov(y). Given observed clr transformed data Y as realizations of the random vector y. Outliers or deviations from the idealized model assumptions of factor analysis can severely effect the parameter estimation. As a way out, robust estimation of the covariance matrix of Y will lead to robust estimates of Λ and ψ in (2), see Pison et al. (2003). Well known robust covariance estimators with good statistical properties, like the MCD or the S-estimators (see, e.g. Maronna et al., 2006), rely on a full-rank data matrix Y which is not the case for clr transformed data (see, e.g., Aitchison, 1986). The isometric logratio (ilr) transformation (Egozcue et al., 2003) solves this singularity problem. The data matrix Y is transformed to a matrix Z by using an orthonormal basis of lower dimension. Using the ilr transformed data, a robust covariance matrix C(Z) can be estimated. The result can be back-transformed to the clr space by C(Y ) = V C(Z)V T where the matrix V with orthonormal columns comes from the relation between the clr and the ilr transformation. Now the parameters in the model (2) can be estimated (Basilevsky, 1994) and the results have a direct interpretation since the links to the original variables are still preserved. The above procedure will be applied to data from geochemistry. Our special interest is on comparing the results with those of Reimann et al. (2002) for the Kola project data 2008-05-30T00:00:00Z