A latent Gaussian model for compositional data with zeros

Author

Listed:
• Chris Glasbey

Abstract

Compositional data record the relative proportions of different components within a mixture and arise frequently in many fields. Standard statistical techniques for the analysis of such data assume the absence of proportions which are genuinely zero. However, real data can contain a substantial number of zero values. We present a latent Gaussian model for the analysis of compositional data which contain zero values, which is based on assuming that the data arise from a (deterministic) Euclidean projection of a multivariate Gaussian random variable onto the unit simplex. We propose an iterative algorithm to simulate values from this model and apply the model to data on the proportions of fat, protein and carbohydrate in different groups of food products. Finally, evaluation of the likelihood involves the calculation of difficult integrals if the number of components is more than 3, so we present a hybrid Gibbs rejection sampling scheme that can be used to draw inferences about the parameters of the model when the number of components is arbitrarily large. Copyright (c) 2008 Royal Statistical Society.

Suggested Citation

• Adam Butler & Chris Glasbey, 2008. "A latent Gaussian model for compositional data with zeros," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 57(5), pages 505-520.
as

File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-9876.2008.00627.x
File Function: link to full text

As the access to this document is restricted, you may want to search for a different version of it.

References listed on IDEAS

as
1. Jane Fry & Tim Fry & Keith McLaren, 2000. "Compositional data analysis and zeros in micro data," Applied Economics, Taylor & Francis Journals, vol. 32(8), pages 953-959.
2. David J. Allcroft & Chris A. Glasbey, 2003. "A latent Gaussian Markov random-field model for spatiotemporal rainfall disaggregation," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(4), pages 487-498.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as

Cited by:

1. Paulo Rodrigues & Ana Lima, 2009. "Analysis of an European union election using principal component analysis," Statistical Papers, Springer, vol. 50(4), pages 895-904, August.
2. Tsagris, Michail & Preston, Simon & T.A. Wood, Andrew, 2016. "Improved classi cation for compositional data using the $\alpha$-transformation," MPRA Paper 67657, University Library of Munich, Germany.
3. Michail Tsagris & Simon Preston & Andrew T. A. Wood, 2016. "Improved Classification for Compositional Data Using the α-transformation," Journal of Classification, Springer;The Classification Society, vol. 33(2), pages 243-261, July.

Corrections

All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:jorssc:v:57:y:2008:i:5:p:505-520. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley-Blackwell Digital Licensing) or (Christopher F. Baum). General contact details of provider: http://edirc.repec.org/data/rssssea.html .

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.