Lognormal vs. Gamma: Extra variations
Within a Bayesian framework of hierarchical modeling, the inclusion of extra variation effects becomes popular with Poisson and Binomial sampling processes. For the less populated areas, mortality rates are heterogeneous due to environmental effects or other socio-economic status. Thus, the extra variation in the frequency of deaths will usually exceed that expected from sampling distributions. In this paper, we propose a quasi-multiplicative spatio-temporal model (PGC) with gamma extra variation effects. Then we compare the performance of proposed model to loglinear model (PLC) with lognormal extra variation effects in SUN et al. (2000). Gibbs sampling is used to compute the posterior moments and marginal posterior densities. The numerical results based on Missouri male lung cancer data show that PGC and PLC models are almost interchangeable. The extra variation effects are important to predict the mortality rates adequately under both models.
Bayesian spatio-temporal model, Gibbs sampling, Loglinear model, Mortality rates, Quasi-multiplicative model
Kim, Hoon, Dongchu Sun, and Robert K. Tsutakawa. "Lognormal vs. gamma: extra variations." Biometrical Journal: Journal of Mathematical Methods in Biosciences 44, no. 3 (2002): 305-323.