A Dirichlet Regression Model for Compositional Data with Zeros
Tóm tắt
Từ khóa
Tài liệu tham khảo
J. Aitchison, “The statistical analysis of compositional data,” J. R. Stat. Soc., Ser. B 44, 139–177 (1982).
J. Aitchison, The Statistical Analysis of Compositional Data (Chapman and Hall, London, 2003).
I. J. Bear and D. Billheimer, “A logistic normal mixture model allowing essential zeros,” in Proceedings of the 6th Compositional Data Analysis Workshop, Girona, Spain, 2015.
A. Butler and C. Glasbey, “A latent Gaussian model for compositional data with zeros,” J. R. Stat. Soc., Ser. C 57, 505–520 (2008).
G. Campbell and J. E. Mosimann, “Multivariate analysis of size and shape: modelling with the Dirichlet distribution,” in ASA Proceedings of Section on Statistical Graphics (San Francisco, USA, 1987), pp. 93–101.
P. J. Davis, “Leonhard Euler’s integral: a historical profile of the gamma function: In memoriam: Milton Abramowitz,” Am.Math. Mon. 66, 849–869 (1959).
D. M. Endres and J. E. Schindelin, “A new metric for probability distributions,” IEEE Trans. Inform. Theory 49, 1858–1860 (2003).
R. Gueorguieva, R. Rosenheck, and D. Zelterman, “Dirichlet component regression and its applications to psychiatric data,” Comput. Stat. Data Anal. 52, 5344–5355 (2008).
C. Gourieroux, A. Monfort, and A. Trognon “Pseudo maximum likelihood methods: theory,” Econometrica 52, 681–700 (1984).
R. H. Hijazi, “An EM-algorithm based method to deal with rounded zeros in compositional data under Dirichlet models,” in Proceedings of the 1st Compositional Data Analysis Workshop, Girona, Spain, 2011.
R. H. Hijazi and R.W. Jernigan, “Modelling compositional data using Dirichlet regression models,” J. Appl. Probab. Stat. 4, 77–91 (2009).
S. Kullback, Information Theory and Statistics (Dover, New York, 1997).
T. J. Leininger, A. E. Gelfand, J. M. Allen, and J. A. Silander, Jr., “Spatial regression modeling for compositional data with many zeros,” J. Agricult., Biol. Environ. Stat. 18, 314–334 (2013).
J. M. Maier, DirichletReg: Dirichlet Regression in R (2014). http://dirichletreg.r-forge.r-project.org/.
J. A. Martín-Fernández, K. Hron, M. Templ, P. Filzmoser, and J. Palarea-Albaladejo, “Model-based replacement of rounded zeros in compositional data: Classical and robust approaches,” Comput. Stat. Data Anal. 56, 2688–2704 (2012).
W. Lin, P. Shi, R. Feng, and H. Li, “Variable selection in regression with compositional covariates,” Biometrika 101, 785–797 (2014).
M. R. Murteira Joséand J. J. S. Ramalho, “Regression analysis of multivariate fractional data,” Econometric Rev. 35, 515–552 (2016).
K. W. Ng, G. L. Tian, and M. L. Tang, Dirichlet and Related Distributions: Theory, Methods and Applications (Wiley, Chichester, 2011).
F. Österreicher and I. Vajda, “A new class of metric divergences on probability spaces and its applicability in statistics,” Ann. Inst. Stat. Math. 55, 639–653 (2003).
J. Palarea-Albaladejo and J. A. Martín-Fernández, “Amodified EMalr-algorithm for replacing rounded zeros in compositional data sets,” Comput. Geosci. 34, 902–917 (2008).
J. L. Scealy and A. H. Welsh, “Regression for compositional data by using distributions defined on the hypersphere,” J. R. Stat. Soc., Ser. B 73, 351–375 (2011).
R. L. Smith, “A statistical assessment of Buchanan’s vote in Palm Beach county,” Stat. Sci. 17, 441–457 (2002).
M. A. Stephens, “Use of the vonMises distribution to analyse continuous proportions,” Biometrika 69, 197–203 (1982).
C. Stewart and C. Field, “Managing the essential zeros in quantitative fatty acid signature analysis,” J. Agricult., Biol., Environ. Stat. 16, 45–69 (2011).
M. Templ, K. Hron, and P. Filzmoser, robCompositions: Robust Estimation for Compositional Data, R PackageVersion 0.8-4.
H. Theil, Economics and Information Theory (North-Holland, Amsterdam, 1967).
T. W. Yee, VGAM: Vector Generalized Linear and Additive Models. R Package Version 0.8-4 (2011). http://CRAN. R-project.org/package=VGAM.
G. Zadora, T. Neocleous, and C. Aitken, “A two-level model for evidence evaluation in the presence of zeros,” J. Forensic Sci. 55, 371–384 (2010).
M. Tsagris and G. Athineou, Compositional: Compositional Data Analysis. R package version 2.8 (2017). https://CRAN.R-project.org/package=Compositional.