Modeling COVID-19 Cases in Nigeria Using Some Selected Count Data Regression Models

The two most popular models inwell-known count regression models are Poisson and negative binomial regression models. Poisson regression is a generalized linear model form of regression analysis used to model count data and contingency tables. Poisson regression assumes the response variable Y has a Poisson distribution, and assumes the logarithm of its expected value can be modeled by a linear combination of unknown parameters. Negative binomial regression is similar to regular multiple regression except that the dependent (Y) variables an observed count that follows the negative binomial distribution. This research studies some factors affecting divorce using Poisson and negative binomial regression models. The factors are unemployment rate, inflation and Gini coefficient. The data were taken from the website of the Statistics Center for the years 2002 to 2023.Under the Poisson regression model, each factor has been reported to have an effect on the divorce rate. The two factors of inflation and unemployment had a direct effect and income inequality factors had an inverse effect on the divorce rate. But, under the negative binomial regression model, only inflation has an effect on the number of divorces. It is worth noting that according to the AIC values, the negative binomial regression model has a better fit than the Poisson regression model because its AIC value is lower.

Introduction: The need to model the impact of some demographic indicators on the frequency of household visits to healthcare centres in Nigeria's community is very important for preventing and spreading community diseases. This study aimed to investigate the effect of the patents' age, gender, marital status, type of illness and amount spent on the frequency of visits to community health care centres in Nigeria and to compared Negative Binomial Regression (NBR) and Generalized Poisson Regression (GPR) models to determine the preferred count regression model for the number of household visits to health centres in some communities in Nigeria. Methods: Survey of 132640 households in some Nigeria communities obtained from the 2018/2019 Nigeria Living Standard Survey (NLSS) were extracted from the National Bureau of Statistics (NBS) in collaboration with the World Bank. The Negative Binomial and Generalised Poisson regression models were used to investigate the five demographic variables on the frequency of visit to the community health centres. The performance of the count regression model was assessed using the Chi-square -2log Likelihood Statistic (2logL), Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) selection criteria. Results: Findings from the study showed that the type of illness and amount spent has a significantly positive effect on the number of household members' visits to the community health care centres in Nigeria while age, gender, and marital status was discovered to have a negative effect on the number of household members' visits to the community health care centres in Nigeria. Conclusion: The Nigeria Government, health centre management and community healthcare service providers' need to be aware that the amount spent and the nature of illness determines the level of health care services utilisation in the Nigeria community, hence the need for the drastic reduction in charges to encourage a household visit to the community health centres whenever the need arises.

The expansion of Poisson regression model which is used to solve the underdispersion data or overdispersion data known as Generalized Poisson (GP) regression model. The purpose of this final project is getting the parameter estimator of generalized linear model with response for GP distribution using maximum likelihood. This GP regression model can be applied on the data of number of Marasmus Kwashiorkorpatients in 25 subdistrict in Surabaya city in 2010. The variable response is the number of Marasmus Kwashiorkor patients, where as the predictor responses are the number of people who married at early age , the number of family heads who not graduated elementary school, the number of children who participated posyandu, the number of medical , the number of visits BKIA, and the number of poor population . The result of the GP regression model with statistic test can be concluded that the number of Marasmus Kwashiorkor patientsaffected by the number of visits BKIA and education levels of parents.The expansion of Poisson regression model which is used to solve the underdispersion data or overdispersion data known as Generalized Poisson (GP) regression model. The purpose of this final project is getting the parameter estimator of generalized linear model with response for GP distribution using maximum likelihood. This GP regression model can be applied on the data of number of Marasmus Kwashiorkorpatients in 25 subdistrict in Surabaya city in 2010. The variable response is the number of Marasmus Kwashiorkor patients, where as the predictor responses are the number of people who married at early age , the number of family heads who not graduated elementary school, the number of children who participated posyandu, the number of medical , the number of visits BKIA, and the number of poor population . The result of the GP regression model with statistic test can be concluded that the number of Marasmus Kwashiorkor patientsaffected by the number of visits BKIA and education levels of parents.

The generalized Poisson distribution has been found useful in fitting over-dispersed as well as under-dispersed count data. Since a number of models and methods have been proposed for the regression analysis of count data either with under-dispersion or with over-dispersion, we define and study a generalized Poisson regression (GPR) model which is useful in predicting a response variable affected by one or more covariates. This regression model is suitable for both types of dispersions. The methods of maximum likelihood and moments are given for the estimation of parameters. Approximate tests for the adequacy of the model are considered. Asymptotic tests are given for the significance of regression parameters. The GPR model has been applied to four observed data sets to which other regression models were applied earlier.

In this paper, we develop diagnostic methods for generalized Poisson regression (GPR) models with errors in variables based on the corrected likelihood. The one-step approximations of the estimates in the case-deletion model are given and case-deletion and local influence measures are presented. Meanwhile, based on a corrected score function, the testing statistics for the significance of dispersion parameters in GPR models with measurement errors are investigated. Finally, illustration of our methodology is given through numerical examples.

Tuberculosis (TB) remains a major public health concern in many parts of the world, including Benue State, Nigeria, where agricultural communities are particularly vulnerable. This study aims to model the monthly mortality incidence of tuberculosis (TB) among farmers in Benue State, Nigeria, focusing on serologically confirmed, active, severe, recovered, and mortality cases using count data regression models. Three count data regression models: Poisson Regression (PR), Negative Binomial Regression (NBR), and Generalized Poisson Regression (GPR) were employed to predict TB-related mortality based on these variables. Secondary data from the Benue State Epidemiological Unit, Makurdi, spanning from January 2010 to December 2023, served as the basis for analysis. The study found the presence of over-dispersion in the Poisson Regression model which necessitated the use of NBR and GPR. Model performance was evaluated using -2 Log-Likelihood (-2 logL), Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC). Among the three competing models, NBR provided the best fit, with a -2 logL value of -901.92, an AIC of 1203.85, and a BIC of 1223.70, effectively addressing the over-dispersion in the data. The analysis identified confirmed, active, and severe TB cases as significant predictors of TB-related mortality in Benue State. Additionally, a strong negative and significant relationship was observed between recovered cases and mortality, indicating that an increase in recoveries correlates with a decline in TB-related deaths. The study recommends that policymakers and researchers should prioritize the Negative Binomial Regression model for TB analysis, enhance TB case management and treatment adherence, improve TB data collection, and design targeted interventions to reduce severe cases and increase recovery rates among vulnerable populations like farmers.

Infant Mortality is one of the issues that can affect the number and age composition of the population. The Government pays special attention to reduce the amount of Infant Mortality Rate in Central Java, so the role of data and information becomes very important. Poisson regression is a nonlinear regression which is often used to model the relationship between the response variable in the form of discrete data with predictor variables in the form of continuous or discrete data. Poisson regression models have equidispersi assumption, a condition in which the mean and variance of the response variable have equal value. In practice, the assumption is sometimes violated in the analysis of discrete data in the form of overdispersi (value of variance greater than the mean value) so that Poisson regression model is not appropriate to be used. Overdispersi is a condition in which the data of response variable shows. One model that can be used to solve the overdispersi problem is generalized Poisson regression model. The regression model is an extension of the Poisson regression and part of the Generalized Linear Model (GLM) which does not require constancy of variance to test the hypothesis. From the data of Infant Mortality Rate in Central Java on 2007 known that there overdispersi. And the factors affecting Infant Mortality Rate is the number of health facilities, the number of medical personnel, and the percentage of households with clean water each county / city.

Maternal mortality is one indicator to describing prosperity in a country and indicator of women's health. Most of the maternal mortality caused by postpartum maternal mortality. The number of postpastum maternal mortality is events that the probability of the incident is small, where the incident depending on a certain time or in a certain regions with the results of the observation are variable diskrit and between variable independent each other that follows the Poisson distribution, so that the proper statistical method is Poisson regression. However, in Poisson regression model analysis sometimes assumptions can occur violations, where the value of variance is greater than the mean value called overdispersion. Generalized Poisson Regression (GPR) is one model that can be used to handle overdispersion problems. This modeling produces global parameters for all locations (regions), so to overcome this we need a method of statistical modeling with due regard to spatial factors. The analytical method used to determine the factors that influence the number of postpartum maternal mortality in Central Java that have overdispersion and there are spatial factors, is Geographically Weighted Generalized Poisson Regression (GWGPR) using the Maximum Likelihood Estimation method and Adaptive Bisquare weighting. Poisson regression and GPR modeling produces a variable percentage of pregnant women doing K1 which has a significant effect on the number of postpartum maternal mortality, while for GWGPR modeling is divided into four cluster in all regency/city in Central Java based on the same significant variable. From the comparison of AIC values, it was found that the GWGPR model is better for analyzing postpartum maternal mortality in Central Java because it has the smallest AIC value.Keywords: The Number of Postpartum Maternal Mortality, Overdispersion, Generalized Poisson Regression, Spatial, Geograpically Weighted Generalized Poisson Regression, AIC

Homogeneity of dispersion parameters and zero-inflation parameters is a standard assumption in zero-inflated generalized Poisson regression (ZIGPR) models. However, this assumption may be not appropriate in some situations. This work develops a score test for varying dispersion and/or zero-inflation parameter in the ZIGPR models, and corresponding test statistics are obtained. Two numerical examples are given to illustrate our methodology, and the properties of score test statistics are investigated through Monte Carlo simulations.

Weather Variability and the Incidence of Cryptosporidiosis: Comparison of Time Series Poisson Regression and SARIMA Models

Background: Under-five mortality rate, often known by its acronym U5MR, indicates the probability of dying between birth and five years of age, expressed per 1,000 live births. Globally, 16,000 children under-five still die every day. Especially in Sub-Saharan Africa every 1 child in 12, dying before his or her fifth birthday. This study aims to identify the determinants of under-five mortality among women in child bearing age group of Tach-Armachiho district using count regression models. Methods: For achieving the objective, a two-stage random sampling technique (simple random sampling and systematic random sampling techniques in the first and second stages respectively) was used to select women respondents. The sample survey conducted in Tach-Armachiho district considered a total of 3815 households of women aged 15 to 49 years out of which the information was collected from 446 selected women through interviewer administrated questionnaire. Results: The descriptive statistics result showed that in the district 16.6% of mothers have faced the problem of at least one under-five death. In this study, Poisson regression, negative binomial, zero-inflated Poisson and zero-inflated negative binomial regression models were applied for data analysis. Each of these count models were compared by different statistical tests. So that, zero-inflated poisson regression model was found to be the best fit for the collected data. Results of the zero-inflated Poisson regression model showed that education of husband, source of water, mother occupation, kebele of mother, prenatal care, place of delivery, place of residence, wealth of house hold, average birth interval and average breast feeding were found to be statistically significant determinants of under-five mortality. Conclusions: In this study, it was found that the factors like average birth interval and average breast feeding were found to be statistically significant factors in both groups (not always zero category and always zero category) with under-five child deathwhereas education of husband, source of water, place of delivery, mother occupation and wealth index of the household have significant effect on under-five mortality under not always zero group. Place of residence, kebele of mother and prenatal care have a significant effect on under-five mortality in TachArmachiho district on inflated group

ABSTRACTThe generalized Poisson (GP) regression model has been used to model count data that exhibit over-dispersion or under-dispersion. The zero-inflated GP (ZIGP) regression model can additionally handle count data characterized by many zeros. However, the parameters of ZIGP model cannot easily be used for inference on overall exposure effects. In order to address this problem, a marginalized ZIGP is proposed to directly model the population marginal mean count. The parameters of the marginalized zero-inflated GP model are estimated by the method of maximum likelihood. The regression model is illustrated by three real-life data sets.

The coronavirus disease 2019 (COVID-19) pandemic was defined by the World Health Organization (WHO) as a global epidemic on March 11, 2020, as the infectious disease that threatens public health fatally. In this study, the main aim is to model the impact of various air pollution causes on mortality data due to the COVID-19 pandemic by Generalized Linear Mixed Model (GLMM) approach to make global statistical inferences about 174 WHO member countries as subjects in the six WHO regions. “Total number of deaths by these countries due to the COVID-19 pandemic” until July 27, 2022, is taken as the response variable. The explanatory variables are taken as the WHO regions, the number of deaths from air pollution causes per 100.000 population as “household air pollution from solid fuels,” “ambient particulate matter pollution,” and “ambient ozone pollution.” In this study, Poisson, geometric, and negative binomial (NB) regression models with “country” taken as fixed and random effects, as special cases of GLMM, are fitted to model the response variable in the aspect of the above-mentioned explanatory variables. In the Poisson, geometric, and NB regression models, Iteratively Reweighted Least Squares parameter estimation method with the Fisher-Scoring iterative algorithm under the log-link function as canonical link function is used. In the GLMM approach, Laplace approximation is also used in the prediction of random effects. In this study, six different Poisson, geometric, and NB regression models with fixed and random effects are established for 174 countries all over the world to make global statistical inferences for investigating the relationships between “total number of deaths” by these countries due to the COVID-19 pandemic and “air pollution causes.” As a result of this study, “NB mixed-effects regression model” as the most appropriate GLMM is used to make global statistical inferences about the impact of the various air pollution causes on the mortality data due to the COVID-19 pandemic.

Predicting Censored Count Data with COM-Poisson Regression

Methodologic Challenges in the Analysis of Count Data in Radiology Health Services Research