TY - JOUR

T1 - Bayesian analysis of Poisson regression with lognormal unobserved heterogeneity

T2 - with an application to the patent-R&D relationship

AU - Tsionas, Michael

PY - 2010/5

Y1 - 2010/5

N2 - This article considers explicit and detailed theoretical and empirical Bayesian analysis of the well-known Poisson regression model for count data with unobserved individual effects based on the lognormal, rather than the popular negative binomial distribution. Although the negative binomial distribution leads to analytical expressions for the likelihood function, a Poisson-lognormal model is closer to the concept of regression with normally distributed innovations, and accounts for excess zeros as well. Such models have been considered widely in the literature (Winkelmann, 2008).The article also provides the necessary theoretical results regarding the posterior distribution of the model. Given that the likelihood function involves integrals with respect to the latent variables, numerical methods organized around Gibbs sampling with data augmentation are proposed for likelihood analysis of the model. The methods are applied to the patent-R&D relationship of 70 US pharmaceutical and biomedical companies, and it is found that it performs better than Poisson regression or negative binomial regression models.

AB - This article considers explicit and detailed theoretical and empirical Bayesian analysis of the well-known Poisson regression model for count data with unobserved individual effects based on the lognormal, rather than the popular negative binomial distribution. Although the negative binomial distribution leads to analytical expressions for the likelihood function, a Poisson-lognormal model is closer to the concept of regression with normally distributed innovations, and accounts for excess zeros as well. Such models have been considered widely in the literature (Winkelmann, 2008).The article also provides the necessary theoretical results regarding the posterior distribution of the model. Given that the likelihood function involves integrals with respect to the latent variables, numerical methods organized around Gibbs sampling with data augmentation are proposed for likelihood analysis of the model. The methods are applied to the patent-R&D relationship of 70 US pharmaceutical and biomedical companies, and it is found that it performs better than Poisson regression or negative binomial regression models.

KW - Bayesian analysis

KW - Count data

KW - Gibbs sampling

KW - Heterogeneity

KW - Lognormal distribution

KW - Poisson distribution

U2 - 10.1080/03610920802491774

DO - 10.1080/03610920802491774

M3 - Journal article

VL - 39

SP - 1689

EP - 1706

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

SN - 0361-0926

IS - 10

ER -