Reparametrization of COM–Poisson regression models with applications in the analysis of experimental data

Soobhug²,

2020

PLoS ONE

Mauritius stands as one of the few countries in the world to have controlled the current pandemic, the novel coronavirus 2019 (COVID-19) to a significant extent in a relatively short lapse of time. Owing to uncertainties and crisis amid the pandemic, as an emergency announcement, the World Health Organization (WHO) solicits the help of health authorities, especially, researchers to conduct in-depth research on the evolution and treatment of COVID-19. This paper proposes an integer-valued time series model to analyze the series of COVID-19 cases in Mauritius wherein the corresponding innovation term accommodates for covariate specification. In this setup , sanitary curfew followed by sanitization and sensitization campaigns, time factor and safe shopping guidelines have been tested as the most significant variables, unlike climatic conditions. The over-dispersion estimates and the serial auto-correlation parameter are also statistically significant. This study also confirms the presence of some unobservable effects like the pathological genesis of the novel coronavirus and environmental factors which contribute to rapid propagation of the zoonotic virus in the community. Based on the proposed COM-Poisson mixture models, we could predict the number of COVID-19 cases in Mauritius. The forecasting results provide satisfactory mean squared errors. Such findings will subsequently encourage the policymakers to implement strict precautionary measures in terms of constant upgrading of the current health care and wellness system and re-enforcement of sanitary obligations.

Section: Methodsmentioning

confidence: 99%

Studying the trend of the novel coronavirus series in Mauritius and its implications

Soobhug²,

2020

PLoS ONE

WIREs Computational Stats

“…(Ribeiro Jr., Zeviani, Bonat, Demetrio, & Hinde, 2019) instead take the mean approximation provided in Equation ) and backsolve to get

λ = {(μ + \frac{ν - 1}{2 ν})}^{ν}

, and let ϕ = ln( ν ) to establish a second version of a mean‐parametrized CMP (hereafter MCMP2) distribution which has the pmf

P (() C = c | μ, ϕ) = {(μ + \frac{e^{ϕ} - 1}{2 e^{ϕ}})}^{{italicce}^{ϕ}} \frac{{((), c!)}^{- e^{ϕ}}}{η ((),, μ, ϕ)}, c = 0,1,2, \dots,

for μ > 0 where

η ((),, μ, ϕ) = \sum_{j = 1}^{\infty} {(μ + \frac{e^{ϕ} - 1}{2 e^{ϕ}})}^{{italicje}^{ϕ}} / {(j!)}^{e^{ϕ}}

is the normalizing constant. Both Huang (2017) and Ribeiro Jr. et al (2019) note that their respective MCMP parametrizations provide orthogonality between the mean μ and the dispersion (parametrized through ν or ϕ ), yet Ribeiro Jr. et al (2019) argue that the MCMP2 parametrization is simpler given the algebraic approach toward determining μ . At the same time, however, Ribeiro Jr. et al (2019) note that the mean and variance of the MCMP2 are accurate “for a large part of the parameter space.” This statement presumably stems from the recognized constraints necessary to satisfy these approximations; meanwhile, the MCMP1 parametrization does not appear to have any such restrictions.…”

Section: The Conway–maxwell–poisson Distributionmentioning

confidence: 99%

“…Both Huang (2017) and Ribeiro Jr. et al (2019) note that their respective MCMP parametrizations provide orthogonality between the mean μ and the dispersion (parametrized through ν or ϕ ), yet Ribeiro Jr. et al (2019) argue that the MCMP2 parametrization is simpler given the algebraic approach toward determining μ . At the same time, however, Ribeiro Jr. et al (2019) note that the mean and variance of the MCMP2 are accurate “for a large part of the parameter space.” This statement presumably stems from the recognized constraints necessary to satisfy these approximations; meanwhile, the MCMP1 parametrization does not appear to have any such restrictions.…”

Section: The Conway–maxwell–poisson Distributionmentioning

confidence: 99%

Conway–Maxwell–Poissonregression models for dispersed count data

Sellers

Premeaux

2020

While Poisson regression serves as a standard tool for modeling the association between a count response variable and explanatory variables, it is well‐documented that this approach is limited by the Poisson model's assumption of data equi‐dispersion. The Conway–Maxwell–Poisson (COM‐Poisson) distribution has demonstrated itself as a viable alternative for real count data that express data over‐ or under‐dispersion, and thus the COM‐Poisson regression can flexibly model associations involving a discrete count response variable and covariates. This work overviews the ongoing developmental knowledge and advancement of COM‐Poisson regression, introducing the reader to the underlying model (and its considered reparametrizations) and related regression constructs, including zero‐inflated models, and longitudinal studies. This manuscript further introduces readers to associated computing tools available to perform COM‐Poisson and related regressions. This article is categorized under: Statistical Models > Linear Models Statistical Models > Generalized Linear Models

“…However, the involved procedures are proned to numerical problems related to the repeated search (root finding) of the natural location parameter of the distribution. These numerical problems reduce the attractivity of the methods for applied scientists and have yet motivated backup to approximate inference using the CMP distribution [20]. Furthermore, the numerical instability will likely be amplified when extending these regression approaches to the generalized linear mixed model framework [21] to handle multilevel count data.…”

Section: Introductionmentioning

confidence: 99%

A Discrete Gamma Model Approach to Flexible Count Regression Analysis: Maximum Likelihood Inference

Cf¹,

Rl²

2021

Preprint

Most existing flexible count regression models allow only approximate inference. Balanced discretization is a simple method to produce a mean-parametrizable flexible count distribution starting from a continuous probability distribution. This makes easy the definition of flexible count regression models allowing exact inference under various types of dispersion (equi-, under- and overdispersion). This study describes maximum likelihood (ML) estimation and inference in count regression based on balanced discrete gamma (BDG) distribution and introduces a likelihood ratio based latent equidispersion (LE) test to identify the parsimonious dispersion model for a particular dataset. A series of Monte Carlo experiments were carried out to assess the performance of ML estimates and the LE test in the BDG regression model, as compared to the popular Conway-Maxwell-Poisson model (CMP). The results show that the two evaluated models recover population effects even under misspecification of dispersion related covariates, with coverage rates of asymptotic 95% confidence interval approaching the nominal level as the sample size increases. The BDG regression approach, nevertheless, outperforms CMP regression in very small samples (n = 15 − 30), mostly in overdispersed data. The LE test proves appropriate to detect latent equidispersion, with rejection rates converging to the nominal level as the sample size increases. Two applications on real data are given to illustrate the use of the proposed approach to count regression analysis.