In this paper, a Bayesian method for inference is developed for the zero-modified Poisson (ZMP) regression model. This model is very flexible for analyzing count data without requiring any information about inflation or deflation of zeros in the sample. A general class of prior densities based on an information matrix is considered for the model parameters. A sensitivity study to detect influential cases that can change the results is performed based on the Kullback-Leibler divergence. Simulation studies are presented in order to illustrate the performance of the developed methodology. Two real datasets on leptospirosis notification in Bahia State (Brazil) are analyzed using the proposed methodology for the ZMP model.
This paper proposes a statistical generalized species-area model (GSAM) to represent various patterns of species-area relationship (SAR), which is one of the fundamental patterns in ecology. The approach enables the generalization of many preliminary models, as power-curve model, which is commonly used to mathematically describe the SAR. The GSAM is applied to simulated data set of species diversity in areas of different sizes and a real-world data of insects of Hymenoptera order has been modeled. We show that the GSAM enables the identification of the best statistical model and estimates the number of species according to the area.
In this article, we propose a class of zero-modified Poisson mixture models as an alternative to model overdispersed count data exhibiting inflation or deflation of zeros. A relevant feature of this class is that the zero modification can be incorporated using a zero truncation process and consequently, the proposed models can be expressed in the hurdle version. This procedure leads to the fact that the proposed models can be fitted without any previous information about the zero modification present in agiven dataset. A fully Bayesian approach has been considered for estimation and inference concerns. Three different simulation studies have been conducted to illustrate the performance of the developed methodology. The usefulness of the proposed class of models has been assessed by using three real datasets provided by the literature. A general model comparison with some well-known discrete distributions has been presented.
The present paper consists of using the Chapman-Richard generalized growth model to functionally relate the number of people infected by COVID-19 with the number of days. The objective of this work is to estimate the instant that the number of infected people stops growing using the dataset of the accumulated amount of infected. For this propose, one conducted a comparative study of the performances of three models of Richard in eight Brazilian States. In the methodological context, the Gauss Newton procedure was used to estimate the parameters. In addition, selection criteria of the models were used to select the one that best fits the dataset. The methodology used allowed consistent estimates of the number of people infected by COVID-19 as a function of time and, consequently, it was possible to conclude that the projections provided by the growth curves point to a scenario of general contamination acceleration. Besides, the models predict that the epidemic is close to reaching its peak in Amazonas, Ceará, Maranhão, Pernambuco, and São Paulo States.
The primary goal of this paper is to introduce the zero-modified Poisson-Lindley regression model as an alternative to model overdispersed count data exhibiting inflation or deflation of zeros in the presence of covariates. The zero-modification is incorporated by considering that a zerotruncated process produces positive observations and consequently, the proposed model can be fitted without any previous information about the zeromodification present in a given dataset. A fully Bayesian approach based on the g-prior method has been considered for inference concerns. An intensive Monte Carlo simulation study has been conducted to evaluate the performance of the developed methodology and the maximum likelihood estimators. The proposed model was considered for the analysis of a real dataset on the number of bids received by 126 U.S. firms between 1978-1985, and the impact of choosing different prior distributions for the regression coefficients has been studied. A sensitivity analysis to detect influential points has been performed based on the Kullback-Leibler divergence. A general comparison with some well-known regression models for discrete data has been presented.
IntroductionThe standard Poisson (P) distribution is the most adopted discrete model for the analysis of count data in several research fields, mainly due to its great simplicity and by having its computational implementation available for many statistical packages. However, it is well-known that such model is not a suitable choice for the analysis of counts in which the variance-to-mean ratio is not (at least) close to 1, that is, when the equidispersion property is violated. Apart from data transformation, the most popular way to circumvent such an issue is the use of finite mixture models (McLachlan and Peel, 2000) that can accommodate, for example, overdispersion (Karlis and Xekalaki, 2005). The Negative Binomial (N B) distribution (that may arise as a P mixture model by using a Gamma distribution for the continuous part) is undoubtedly the most famous alternative to model extra-P variability. However, the literature concerning discrete models, which can handle different
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