A class of bivariate regression models for discrete and/or continuous responses

ABSTRACT

A general class of models for discrete and/or continuous responses is proposed in which joint distributions are constructed via the conditional approach. It is assumed that the distributions of one response and of the other response given the first one belong to exponential family of distributions. Furthermore, the marginal means are related to the covariates by link functions and a dependency structure between the responses is inserted into the model. Estimation methods, diagnostic analysis and a simulation study considering a Bernoulli-exponential model, a particular case of the class, are presented. Finally, this model is used in a real data set.

KEYWORDS:

• Bivariate regression models
• Conditional approach
• Dependency between the responses
• Discrete and/or continuous responses

MATHEMATICS SUBJECT CLASSIFICATION:

• 62J02
• 62J12
• 62F10

Acknowledgements

The research of Willian Luís de Oliveira was supported by the Brazilian organization Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) grant PDSE 99999.00 8230/ 2014-05. The work of Maria Durban was supported by the Spanish Ministry of Economy and Competitiveness grant MTM2014- 52184-P.

Additional information

Funding

Coordenação de Aperfeiçoamento de Pessoal de Nísvel Superior [PDSE 99999.00 8230/ 2014-05.]; Spanish Ministry of Economy and Competitiveness [MTM2014-52184-P].