A weighted negative binomial Lindley distribution with applications to dispersed data

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.

Insights on the trend of the Novel Coronavirus 2019 series in some Small Island Developing States: A Thinning-based Modelling Approach

Undeniably, the Novel Coronavirus 2019, (COVID-19), has disrupted the routine functioning of the global economic and social activities. In particular, vulnerable economies such as the Small Island Developing states (SIDs) are facing unprecedented health and financial crisis. In such critical situation, some in-depth statistical models can be helpful for proper planning in terms of identifying factors that can influence significantly the number of infected COVID-19 cases and for forecasting. Modelling the COVID-19 infected series is a statistical challenge since the series are severely over-dispersed with lots of oscillations. This paper attempts a new integer-valued time series model based on the auto-regressive structure (INAR), with an oscillating Weighted Cosine Geometric (WCG) innovation term. The parameters in the proposed model constitute of the regression effects and serial auto-correlation coefficients and are estimated via likelihood and moment-based approaches. Monte Carlo simulation experiments are implemented to assess the performance and consistency of the different resulting estimators. Thereon, the INAR-WCG is applied to the COVID-19 series of various SIDs countries that include Singapore, Cape Verde, Bahrain, Mauritius and Maldives. The findings reveal that factors such as the transmission mode and the Government Stringency Index are the most influential. In terms of model fitting and forecasting, the INAR-WCG provides slightly better RMSEs than the other competing INAR-based processes.

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.