On the identifiability in the latent budget model

The latent budget model (LBM) is a reduced rank model for the analysis of c ompositional data In the social sciences the LBM was originally proposed fo r the analysis of two-way contingency tables. The rows of the table are mod elled as a mixture of typical or latent distributions (budgets). The mixing parameters can be used to classify the rows into typical groups. In geolog y the model is used for the analysis of physical mixing processes, and in t his context it is known as the end-member model. A major drawback of the latent budget model is that, in general, the model is not identifiable, which complicates the interpretation of the model cons iderably. This paper studies the geometry and identifiability of the latent budget model. Knowledge of the geometric structure of the model is used to specify an appropriate criterion to identify the model. The results are il lustrated by an empirical data set.