Count compositions are vectors of non-negative integers summing to a fixed constant. This chapter briefly recalls the main results regarding two of the most popular distributions for count vectors, namely the multinomial and the Dirichlet-multinomial (DM). It proposes a new distribution for count compositions and develops a regression model based on it. The new distribution, flexible Dirichlet-multinomial is obtained by compounding the multinomial with the flexible Dirichlet, and it can be expressed as a structured finite mixture with particular DM components. The regression models are compared based on these new distributions through a simulation study and an application to a real dataset. Inferential issues are dealt with by a Bayesian approach through the Hamiltonian Monte Carlo algorithm. The chapter presents an application based on a real dataset concerning the results of the Italian general elections held in 2018.

Ascari, R., Migliorati, S. (2022). A New Regression Model for Count Compositions. In Data Analysis and Related Applications 2: Multivariate, Health and Demographic Data Analysis, Volume 10 (pp. 25-37). Wiley [10.1002/9781394165544.ch2].

A New Regression Model for Count Compositions

Ascari, R
Primo
;
Migliorati, S
Secondo
2022

Abstract

Count compositions are vectors of non-negative integers summing to a fixed constant. This chapter briefly recalls the main results regarding two of the most popular distributions for count vectors, namely the multinomial and the Dirichlet-multinomial (DM). It proposes a new distribution for count compositions and develops a regression model based on it. The new distribution, flexible Dirichlet-multinomial is obtained by compounding the multinomial with the flexible Dirichlet, and it can be expressed as a structured finite mixture with particular DM components. The regression models are compared based on these new distributions through a simulation study and an application to a real dataset. Inferential issues are dealt with by a Bayesian approach through the Hamiltonian Monte Carlo algorithm. The chapter presents an application based on a real dataset concerning the results of the Italian general elections held in 2018.
Capitolo o saggio
Multinomial data, Multivariate regression, Bayesian inference, Mixture model, Compound distribution
English
Data Analysis and Related Applications 2: Multivariate, Health and Demographic Data Analysis, Volume 10
9781786307729
Ascari, R., Migliorati, S. (2022). A New Regression Model for Count Compositions. In Data Analysis and Related Applications 2: Multivariate, Health and Demographic Data Analysis, Volume 10 (pp. 25-37). Wiley [10.1002/9781394165544.ch2].
Ascari, R; Migliorati, S
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/389899
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