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In this paper the issue of variable selection with new approach in finite mixture of semi-parametric regression models is studying, although it is supposed that data have Poisson distribution. When we use Poisson distribution, two problems such as overdispersion and excess zeros will happen that can affect on variable selection and parameter estimation. Actually parameter estimation in parametric component of the semi-parametric regression model is done by penalized likelihood approach. However, in nonparametric component after local approximation using Teylor series, the estimation of nonparametric coefficients along with estimated parametric coefficients will be calculated. Using new approach leads to a properly variable selection results. In addition to representing related theories, overdispersion and excess zeros are considered in data simulation section and using EM algorithm in parameter estimation leads to increase the accuracy of end results.

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In this paper the mixed Poisson regression model is discussed and a Poisson Birnbaum-Saunders regression model is introduced consider the over-dispersion. The Birnbaum-Saunders distribution is the mixture of two the generalized inverse Gaussian distributions, therefore it can be considered as an extension of traditional models. Our proposed model has less dimensional parameter space than the Poisson- generalized inverse Gaussian regression model. We also show that the proposed model has a closed form for likelihood function and we obtain its moments. The EM algorithm is used to estimate the parameters and its efficiency is compared with conventional models by a simulation study. An analysis of a real data is provided for more illustration.

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Geostatistical spatial count data in finite populations can be seen in many applications, such as urban management and medicine. The traditional model for analyzing these data is the spatial logit-binomial model. In the most applied situations, these data have overdispersion alongside the spatial variability. The binomial model is not the appropriate candidate to account for the overdispersion. The proper alternative is a beta-binomial model that has sufficient flexibility to account for the extra variability due to the possible overdispersion of counts. In this paper, we describe a Bayesian spatial beta-binomial for geostatistical count data by using a combination of the integrated nested Laplace approximation and the stochastic partial differential equations methods. We apply the methodology for analyzing the number of people injured/killed in car crashes in Mashhad, Iran. We further evaluate the performance of the model using a simulation study.