Dealing with Rounded Zeros in Compositional Data under Dirichlet Models
Mar 01, 2010
DOI:
Published in: The 10th Islamic Countries Conference on Statistical Sciences, Cairo
Publisher: Islamic Countries Society of Statistical Sciences
One of the obstacles facing the application of the Dirichlet modeling of compositional data is the occurrence of zero. In the Dirichlet model, the presence of zeros makes the probability density function vanish. Zeros in compositional data are classified into “rounded” zeros and “essential” or true zeros. The rounded zero corresponds to a small proportion or below detection limit value while the essential zero is an indication of the complete absence of the component in the composition. Several parametric and non-parametric imputation techniques have been proposed to replace rounded zeros and model the essential zeros under logratio model. In this paper, a new method based on Beta regression is proposed for replacing rounded zeros in compositional data. The performance of the proposed method is analyzed using Monte Carlo simulation and an illustrative example using real data is given.