Type I multivariate zero-inflated COM-Poisson regression model.

In this paper, we present the Type I multivariate zero-inflated Conway-Maxwell-Poisson distribution, whose development is based on the extension of the Type I multivariate zero-inflated Poisson distribution. We developed important properties of the distribution and present a regression model. The AIC and BIC criteria are used to select the best fitted model. Two real data sets have been used to illustrate the proposed model. Moreover, we conclude by stating that the Type I multivariate zero-inflated Conway-Maxwell-Poisson distribution produces a better fitted model for multivariate count data with excess of zeros.

A new mixed-effects regression model for the analysis of zero-modified hierarchical count data.

Count data sets are traditionally analyzed using the ordinary Poisson distribution. However, such a model has its applicability limited as it can be somewhat restrictive to handle specific data structures. In this case, it arises the need for obtaining alternative models that accommodate, for example, (a) zero-modification (inflation or deflation at the frequency of zeros), (b) overdispersion, and (c) individual heterogeneity arising from clustering or repeated (correlated) measurements made on the same subject. Cases (a)-(b) and (b)-(c) are often treated together in the statistical literature with several practical applications, but models supporting all at once are less common. Hence, this paper's primary goal was to jointly address these issues by deriving a mixed-effects regression model based on the hurdle version of the Poisson-Lindley distribution. In this framework, the zero-modification is incorporated by assuming that a binary probability model determines which outcomes are zero-valued, and a zero-truncated process is responsible for generating positive observations. Approximate posterior inferences for the model parameters were obtained from a fully Bayesian approach based on the Adaptive Metropolis algorithm. Intensive Monte Carlo simulation studies were performed to assess the empirical properties of the Bayesian estimators. The proposed model was considered for the analysis of a real data set, and its competitiveness regarding some well-established mixed-effects models for count data was evaluated. A sensitivity analysis to detect observations that may impact parameter estimates was performed based on standard divergence measures. The Bayesian p -value and the randomized quantile residuals were considered for model diagnostics.

A New Regression Model for the Analysis of Overdispersed and Zero-Modified Count Data.

Count datasets are traditionally analyzed using the ordinary Poisson distribution. However, said model has its applicability limited, as it can be somewhat restrictive to handling specific data structures. In this case, the need arises for obtaining alternative models that accommodate, for example, overdispersion and zero modification (inflation/deflation at the frequency of zeros). In practical terms, these are the most prevalent structures ruling the nature of discrete phenomena nowadays. Hence, this paper's primary goal was to jointly address these issues by deriving a fixed-effects regression model based on the hurdle version of the Poisson-Sujatha distribution. In this framework, the zero modification is incorporated by considering that a binary probability model determines which outcomes are zero-valued, and a zero-truncated process is responsible for generating positive observations. Posterior inferences for the model parameters were obtained from a fully Bayesian approach based on the g-prior method. Intensive Monte Carlo simulation studies were performed to assess the Bayesian estimators' empirical properties, and the obtained results have been discussed. The proposed model was considered for analyzing a real dataset, and its competitiveness regarding some well-established fixed-effects models for count data was evaluated. A sensitivity analysis to detect observations that may impact parameter estimates was performed based on standard divergence measures. The Bayesian p-value and the randomized quantile residuals were considered for the task of model validation.

Zero-modified Poisson model: Bayesian approach, influence diagnostics, and an application to a Brazilian leptospirosis notification data.

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.