The simplicial generalized beta distribution. R-package and applications

A generalization of the Dirichlet and the scaled Dirichlet distributions is given by the simplicial generalized Beta, SGB (Graf, 2017). In the Dirichlet and the scaled Dirichlet distributions, the shape parameters are modeled with auxiliary variables (Maier, 2015, R-package DirichletReg) and Monti et al. (2011), respectively. On the other hand, in the ordinary logistic normal regression, it is the scale composition that is made dependent on auxiliary variables. The modeling of
scales seems easier to interpret than the modeling of shapes. Thus in the SGB regression:
- The scale compositions are modeled in the same way as for the logistic normal regression, i.e. each auxiliary variable generates D parameters, where D is the number of parts.
- The D Dirichlet shape parameters, one for each part in the compositions, are estimated as well.
- An additional overall shape parameter is introduced in the SGB that proves to have important properties in relation with non essential zeros.
- Use of survey weights is an option.
- Imputation of missing parts is possible.
An application to the United Kingdom Time Use Survey (Gershuny and Sullivan, 2017) shows the power of the method. The R-package SGB (Graf, 2019) makes the method accessible to users. See the package vignette for more information and examples.

, 2020