Marginalized zero-inflated generalized Poisson regression

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.

COVID-19 is currently threatening countries in the world. Presently in Nigeria, there are about 29,286 confirmed cases, 11,828 discharged and 654 deaths as of 6th July 2020. It is against this background that this study was targeted at modeling daily cases of COVID-19’s deaths in Nigeria using count regression models like; Poisson Regression (PR), Negative Binomial Regression (NBR) and Generalized Poisson Regression (GPR) model. The study aim at fitting an appropriate count Regression model to the confirmed, active and critical cases of COVID-19 in Nigeria after 118 days. The data for the study was extracted from the daily COVID-19 cases update released by the Nigeria Centre for Disease Control (NCDC) online database from February 28th, 2020 – 6th, July 2020. The extracted data were used in the simulation of Poisson, Negative Binomial, and Generalized Poisson Regression model with a program written in STATA version 14 and fitted to the data at a 5% significance level. The best model was selected based on the values of -2logL, AIC, and BIC selection test/criteria. The results obtained from the analysis revealed that the Poisson regression could not capture over-dispersion, so other forms of Poisson Regression models such as the Negative Binomial Regression and Generalized Poisson Regression were used in the estimation. Of the three count Regression models, Generalized Poisson Regression was the best model for fitting daily cumulative confirmed, active and critical COVID-19 cases in Nigeria when overdispersion is present in the predictors because it had the least -2log-Likelihood, AIC, and BIC. It was also discovered that active and critical cases have a positive and significant effect on the number of COVID-19 related deaths in Nigeria.

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.

The Poisson regression model is widely used for count data. This model assumes equidispersion. In practice, equidispersion is seldom reflected in data. However, in real-life data, the variance usually exceeds the mean. This situation is known as overdispersion. Negative binomial distribution and other Poisson mix models are often used to model overdispersion count data. Another extension of the negative binomial distribution in another model for count data is the univariate generalized Waring. In addition, the model developed by Famoye can be used in the analysis of count data. When the count data contains a large number of zeros, it is necessary to use zero-inflated models. In this study, different generalized regression models are emphasized for the analysis of excessive zeros count data. For this purpose, a real data set was analysed with the generalized Poisson model, generalized negative binomial model, generalized negative binomial Famoye, generalized Waring model, and the foregoing zero-inflated models. Log-likelihood, Akaike information criterion, Bayes information criterion, Vuong statistics were used for model comparisons.

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.

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.

Estimation of safety performance functions for urban intersections using various functional forms of the negative binomial regression model and a generalized Poisson regression model

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.

Typically, a Poisson model is assumed for count data. In many cases, there are many zeros in the dependent variable, thus the mean is not equal to the variance value of the dependent variable. Therefore, Poisson model is not suitable anymore for this kind of data because of too many zeros. Thus, we suggest using a hurdle‐generalized Poisson regression model. Furthermore, the response variable in such cases is censored for some values because of some big values. A censored hurdle‐generalized Poisson regression model is introduced on count data with many zeros in this paper. The estimation of regression parameters using the maximum likelihood method is discussed and the goodness‐of‐fit for the regression model is examined. An example and a simulation will be used to illustrate the effects of right censoring on the parameter estimation and their standard errors.

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.

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.

A Poisson ridge regression estimator

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.

A crash-prediction model for multilane roads

Predicting Censored Count Data with COM-Poisson Regression