A latent Gaussian model for compositional data with zeros

Journal of the Royal Statistical Society. Series C: Applied Statistics

Volumn 57, Issue 5, 2008, Pages 505-520

  Butler, Adam ^a   Glasbey, Chris ^a  

^a BIOMATHEMATICS AND STATISTICS SCOTLAND   (United Kingdom)

Author keywords

Dietary composition; Euclidean projection; Gibbs sampling; Multivariate normal; Nutrition; Unit sum constraint

Indexed keywords

EID: 52049120582     PISSN: 00359254     EISSN: 14679876     Source Type: Journal    
DOI: 10.1111/j.1467-9876.2008.00627.x     Document Type: Article

References (29)

1. Adolph, C. (2004) Succession in the temple: central banker careers and the politics of appointment. Working Paper. University of Washington, Seattle.
2. Agricultural Research Service (2006) USDA Nutrient Database for Standard Reference, Release 19. Washington DC : US Department of Agriculture Available from http://www.ars.usda.gov/nutrientdata.)
3. Aitchison, J. (1986) The Statistical Analysis of Compositional Data. London : Chapman and Hall.
4. Aitchison, J. Egozcue, J. J. (2005) Compositional data analysis: where are we and where should we be heading? Math. Geol., 37, 829 850.
5. Aitchison, J Kay, J. W. (2003) Possible solutions of some essential zero problems in compositional data analysis. In Proc. CODAWORK'03, 1st Compositional Data Analysis Wrkshp (eds S. Thió-Henestrosa J. A. Martín- Fernández Girona, Oct. 15th-17th. (Available from http://ima.udg.edu/ Activats/CoDaWork03.)
6. Allcroft, D. J. Glasbey, C. A. (2003a) Analysis of crop lodging using a latent variable model. J. Agric. Sci., 140, 383 393.
7. Allcroft, D. J. Glasbey, C. A. (2003b) A latent Gaussian Markov random-field model for spatiotemporal rainfall disaggregation. Appl. Statist., 52, 487 498.
8. Bacon-Shone, J 2003) Modelling structural zeros in compositional data. In Proc. CODAWORK'03, 1st Compositional Data Analysis Wrkshp (eds S. Thió-Henestrosa J. A. Martín-Fernández Girona, Oct. 15th-17th. (Available from http://ima.udg.edu/Activats/CoDaWork03.)
9. Bull, K., Wanless, S., Elston, D. A., Daunt, F., Lewis, S. Harris, M. P. (2004) Local-scale variability in the diet of Black-legged Kittiwakes rissa tridactyla. Ardea, 92, 43 52.
10. Butler, A., Glasbey, C. A. Wanless, S. (2007) Approximate Bayesian inference for a latent Gaussian model for compositional data. Technical Report. Biomathematics and Statistics Scotland, Edinburgh.
11. Casella, G. George, E. I. (1992) Explaining the Gibbs sampler. Am. Statistn, 46, 167 174.
12. Cowles, M. K. Carlin, B. P. (1996) Markov chain Monte Carlo convergence diagnostics: a comparative review. J. Am. Statist. Ass., 91, 883 904.
13. Egozcue, J. J., Diaz Barrero, J. L. Pawlowsky-Glahn, V. (2006) Hilbert spaces of probability density functions based on Aitchison geometry. Acta Math. Sin., 22, 1175 1182.
14. Elston, D. A., Illius, A. W. Gordon, I. J. (1996) Assessment of preference among a range of options using log ratio analysis. Ecology, 77, 2538 2548.
15. von Eynatten, H., Pawlowsky-Glahn, V. Egozcue, J. J. (2002) Understanding perturbation on the simplex: a simple method to better visualise and interpret compositional data in ternary diagrams. Math. Geol., 34, 249 257.
16. Fletcher, R. (1981) Practical Methods of Optimization. Chichester : Wiley.
17. Fry, T. R. L Chong, D 2005) A tale of two logits, compositional data analysis and zero observations. In Proc. CODAWORK'05, 2nd Compositional Data Analysis Wrkshp (eds G. Mateu-Figueras C. Barceló-Vidal Girona, Oct. 19th-21st. (Available from http://ima.udg.edu/Activats/CoDaWork05.)
18. Fry, J., Fry, T. R. L. McLaren, K. R. (2000) Compositional data analysis and zeros in micro data. Appl. Econ., 32, 953 959.
19. Gilks, W. R., Richardson, S. Spiegelhalter, D. J. (1996) Markov Chain Monte Carlo in Practice. Boca Raton : Chapman and Hall-CRC.
20. Jeffreys, H. (1946) An invariant form for the prior probability in estimation problems. Proc. R. Soc. Lond. A, 186, 453 461.
21. Martín-Fernández, J. A., Barceló-Vidal, C. B Pawlowsky-Glahn, V 2000) Zero replacement in compositional data. In Advances in Data Science and Classification: Proc. 7th Conf. International Federation of Classification Societies (eds H. A. L. Kiers, J. P. Rasson, P. J. F. Groenen M. Schader pp. 155 160. Berlin : Springer.
22. Martín-Fernández, J. A., Barceló-Vidal, C. B. Pawlowsky-Glahn, V. (2003a) Dealing with zeros and missing values in compositional data sets using nonparametric imputation. Math. Geol., 35, 253 278.
23. Martín-Fernández, J. A., Palarea-Albaladejo, J Gómez-García, J 2003b) Markov chain monte carlo method applied to rounding zeros of compositional data: first approach. In Proc. CODAWORK'03, 1st Compositional Data Analysis Wrkshp (eds S. Thió-Henestrosa J. A. Martín-Fernández Girona, Oct. 15th-17th. (Available from http://ima.udg.edu/Activats/CoDaWork03.)
24. Palarea-Albaladejo, J., Martín-Fernández, J. A Gómez-García, J. A 2007a) A modified EM alr-algorithm for replacing rounded zeros in compositional data sets. Comput. Geosci., to be published.
25. Palarea-Albaladejo, J., Martín-Fernández, J. A Gómez-García, J. A. (2007b) Parametric approach for dealing with compositional rounded zeros. Math. Geol., 39, 625 645.
26. R Development Core Team (2006) R: a Language and Environment for Statistical Computing. Vienna : R Foundation for Statistical Computing.
27. Robert, C. P. Casella, G. (1999) Monte Carlo Statistical Methods. New York : Springer.
28. Salter-Townshend, M. Haslett, J 2006) Zero-inflation of compositional data. In Proc. 21st Int. Wrkshp Statistical Modelling, Galway, July 3rd-7th, pp. 448 456. Statistical Modelling Society.
29. Tobin, J. (1958) Estimation for relationships with limited dependent variables. Econometrica, 26, 24 36.