  Compositional data are met in many different fields, such as economics,
archaeometry, ecology, geology and political sciences. Regression where the
dependent variable is a composition is usually carried out via a log-ratio
transformation of the composition or via the Dirichlet distribution. However,
when there are zero values in the data these two ways are not readily
applicable. Suggestions for this problem exist, but most of them rely on
substituting the zero values. In this paper we adjust the Dirichlet
distribution when covariates are present, in order to allow for zero values to
be present in the data, without modifying any values. To do so, we modify the
log-likelihood of the Dirichlet distribution to account for zero values.
Examples and simulation studies exhibit the performance of the zero adjusted
Dirichlet regression.
