Modelling the Claim Count with Poisson Regression and Negative Binomial Regression

2005 ◽  
pp. 103-110
Author(s):  
Bartłomiej Bartoszewicz
Keyword(s):  
Poisson Regression ◽  
Negative Binomial ◽  
Negative Binomial Regression ◽  
Binomial Regression

scholarly journals Handling of Overdispersion in the Poisson Regression Model with Negative Binomial for the Number of New Cases of Leprosy in Java

2021 ◽  
Vol 5 (1) ◽  
pp. 1-13
Author(s):  
Yopi Ariesia Ulfa ◽  
Agus M Soleh ◽  
Bagus Sartono
Keyword(s):  
Regression Model ◽  
Poisson Regression ◽  
Negative Binomial ◽  
Negative Binomial Regression ◽  
Negative Binomial Regression Model ◽  
Explanatory Variables ◽  
Binomial Regression ◽  
Directorate General ◽  
The Republic ◽  
And Control

Based on data from the Directorate General of Disease Prevention and Control of the Ministry of Health of the Republic of Indonesia, in 2017, new leprosy cases that emerged on Java Island were the highest in Indonesia compared to the number of events on other islands. The purpose of this study is to compare Poisson regression to a negative binomial regression model to be applied to the data on the number of new cases of leprosy and to find out what explanatory variables have a significant effect on the number of new cases of leprosy in Java. This study's results indicate that a negative binomial regression model can overcome the Poisson regression model's overdispersion. Variables that significantly affect the number of new cases of leprosy based on the results of negative binomial regression modeling are total population, percentage of children under five years who had immunized with BCG, and percentage of the population with sustainable access to clean water.

PEMODELAN DENGAN GEOGRAPHICALLY WEIGHTED NEGATIVE BINOMIAL REGRESSION (Studi kasus: Banyaknya Penderita Kusta di Jawa Barat)

2021 ◽  
Vol 10 (3) ◽  
pp. 226-236
Author(s):  
Khusnul Khotimah ◽  
Itasia Dina Sulvianti ◽  
Pika Silvianti
Keyword(s):  
Regression Model ◽  
Count Data ◽  
Poisson Regression ◽  
Negative Binomial ◽  
Negative Binomial Regression ◽  
Kernel Weight ◽  
Negative Binomial Regression Model ◽  
West Java ◽  
Binomial Regression ◽  
Spatial Heterogenity

The number of leper in West Java is an example of the count data case. The analyzes commonly used in count data is Poisson regression. This research will determine the variables that influence the number of leper in West Java. The data used is the number of leper in West Java in 2019. This data has an overdispersion condition and spatial heterogenity. To handle overdispersion, the negative binomial regression model can be employed. While spatial heterogenity is overcome by adding adaptive bisquare kernel weight. This research resulted Geographically Weighted Negative Binomial Regression (GWNBR) with a weighting adaptive bisquare kernel classifies regency/city in West Java into ten groups based on the variables that sigfinicantly influence the number of leper. In general, the variable in the percentage of households with Clean and Healthy Behavior (PHBS) has a significant effect in all regency/city in West Java. Especially for Bogor Regency, Depok City, Bogor City, and Pangandaran Regency, the variable of the percentage of people poverty does not have a significant effect on the number leper.

scholarly journals PENERAPAN REGRESI BINOMIAL NEGATIF UNTUK MENGATASI OVERDISPERSI PADA REGRESI POISSON

2013 ◽  
Vol 2 (2) ◽  
pp. 6
Author(s):  
PUTU SUSAN PRADAWATI ◽  
KOMANG GDE SUKARSA ◽  
I GUSTI AYU MADE SRINADI
Keyword(s):  
Regression Analysis ◽  
Regression Model ◽  
Poisson Regression ◽  
Negative Binomial ◽  
Negative Binomial Regression ◽  
Poisson Regression Model ◽  
Response Variable ◽  
Poisson Regression Analysis ◽  
Binomial Regression ◽  
The Mean

Poisson regression was used to analyze the count data which Poisson distributed. Poisson regression analysis requires state equidispersion, in which the mean value of the response variable is equal to the value of the variance. However, there are deviations in which the value of the response variable variance is greater than the mean. This is called overdispersion. If overdispersion happens and Poisson Regression analysis is being used, then underestimated standard errors will be obtained. Negative Binomial Regression can handle overdispersion because it contains a dispersion parameter. From the simulation data which experienced overdispersion in the Poisson Regression model it was found that the Negative Binomial Regression was better than the Poisson Regression model.

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

2020 ◽  
pp. 64-73
Author(s):  
Samuel Olorunfemi Adams ◽  
Muhammad Ardo Bamanga ◽  
Samuel Olayemi Olanrewaju ◽  
Haruna Umar Yahaya ◽  
Rafiu Olayinka Akano
Keyword(s):  
Regression Model ◽  
Poisson Regression ◽  
Regression Models ◽  
Negative Binomial ◽  
Negative Binomial Regression ◽  
Significance Level ◽  
Generalized Poisson ◽  
Binomial Regression ◽  
Selection Test ◽  
Generalized Poisson Regression

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.

Penanganan Overdispersi pada Regresi Poisson dengan Regresi Binomial Negatif pada Kasus Kemiskinan di Indonesia

2019 ◽  
Vol 8 (1) ◽  
Author(s):  
Lulu Mahdiyah Sandjadirja ◽  
Muhammad Nur Aidi ◽  
Akbar Rizki
Keyword(s):  
Regression Model ◽  
Poisson Regression ◽  
Negative Binomial ◽  
Negative Binomial Regression ◽  
External Factors ◽  
Poor People ◽  
Negative Binomial Regression Model ◽  
Average Value ◽  
Binomial Regression ◽  
Working Age

Poisson regression can be used to model rare events that consist of count data. Poisson regression application is carried out to find out external factors that affect the number of poor people in Indonesia by the province in 2016. The assumptions that must be met in this analysis are equdispersion. However, in real cases there is often a problem of overdispersion, ie the value of the variance is greater than the average value. High diversity can be caused by outliers. Expenditures on outliers have not been able to deal with the problem of overdispersion in Poisson Regression. One way to overcome this problem is to replace the Poisson distribution assumption with the Negative Binomial distribution. The results of the analysis show that the Negative Binomial Regression model without outliers is better than the Poisson Regression without outliers model indicated by a smaller AIC value. Based on the Negative Binomial Regression model without this outlier the external factors that affect the number of poor people in Indonesia by the province in 2016 are the percentage of households with floor conditions of houses with soil by province, population by province, percentage of unemployment to the total workforce by province and the percentage of the workforce against the working age population.

scholarly journals Driving Risk Assessment Using Near-Miss Events Based on Panel Poisson Regression and Panel Negative Binomial Regression

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 829
Author(s):  
Shuai Sun ◽  
Jun Bi ◽  
Montserrat Guillen ◽  
Ana M. Pérez-Marín
Keyword(s):  
Risk Score ◽  
Poisson Regression ◽  
High Speed ◽  
Negative Binomial ◽  
Negative Binomial Regression ◽  
Near Miss ◽  
Risk Scores ◽  
Data Set ◽  
Binomial Regression ◽  
Driving Risk

This study proposes a method for identifying and evaluating driving risk as a first step towards calculating premiums in the newly emerging context of usage-based insurance. Telematics data gathered by the Internet of Vehicles (IoV) contain a large number of near-miss events which can be regarded as an alternative for modeling claims or accidents for estimating a driving risk score for a particular vehicle and its driver. Poisson regression and negative binomial regression are applied to a summary data set of 182 vehicles with one record per vehicle and to a panel data set of daily vehicle data containing four near-miss events, i.e., counts of excess speed, high speed brake, harsh acceleration or deceleration and additional driving behavior parameters that do not result in accidents. Negative binomial regression (AICoverspeed = 997.0, BICoverspeed = 1022.7) is seen to perform better than Poisson regression (AICoverspeed = 7051.8, BICoverspeed = 7074.3). Vehicles are separately classified to five driving risk levels with a driving risk score computed from individual effects of the corresponding panel model. This study provides a research basis for actuarial insurance premium calculations, even if no accident information is available, and enables a precise supervision of dangerous driving behaviors based on driving risk scores.

scholarly journals Count Regression Models for Analyzing Crime Rates in The East Java Province

2021 ◽  
Vol 2123 (1) ◽  
pp. 012028
Author(s):  
Dian Handayani ◽  
A F Artari ◽  
W Safitri ◽  
W Rahayu ◽  
V M Santi
Keyword(s):  
Poisson Regression ◽  
Crime Rate ◽  
Negative Binomial ◽  
Negative Binomial Regression ◽  
Crime Rates ◽  
Poor People ◽  
Explanatory Variables ◽  
Generalized Poisson ◽  
Binomial Regression ◽  
Generalized Poisson Regression

Abstract Crime rate is the number of reported crimes divided by total population. Several factors could contribute the variability of crime rates among areas. This study aims to model the relationship between crime rates among regencies and cities in the East Java Province (Indonesia) and some potentially explanatory variables based on Statistics Indonesia publication in 2020. The crime rate in the East Java Province was consistently at the top three after DKI Jakarta and North Sumatra during 2017 to 2019. Therefore, it is interesting for us to study further about the crime rate in the East Java. Our preliminary analysis indicates that there is an overdispersion in our sample data. To overcome the overdispersion, we fit Generalized Poisson and Negative Binomial regression. The ratio of deviance and degree of freedom based on Negative Binomial is slightly smaller (1.38) than Generalized Poisson (1.99). The results indicate that Negative Binomial and Generalized Poisson regression, compared to standard Poisson regression, are relatively fit to model our crime rate data. Some factors which contribute significantly (α=0.05) for the crime rate in the East Java Province under Negative Binomial as well as Generalized Poisson regression are percentage of poor people, number of households, unemployment rate, and percentage of expenditure.

scholarly journals PERBANDINGAN REGRESI BINOMIAL NEGATIF DAN REGRESI GENERALISASI POISSON DALAM MENGATASI OVERDISPERSI (Studi Kasus: Jumlah Tenaga Kerja Usaha Pencetak Genteng di Br. Dukuh, Desa Pejaten)

2014 ◽  
Vol 3 (3) ◽  
pp. 107 ◽  
Author(s):  
NI MADE RARA KESWARI ◽  
I WAYAN SUMARJAYA ◽  
NI LUH PUTU SUCIPTAWATI
Keyword(s):  
Nonlinear Regression ◽  
Poisson Regression ◽  
Negative Binomial ◽  
Negative Binomial Regression ◽  
Response Variable ◽  
Generalized Poisson ◽  
Binomial Regression ◽  
Count Response ◽  
The Mean ◽  
Generalized Poisson Regression

Poisson regression is a nonlinear regression that is often used to model count response variable and categorical, interval, or count regressor. This regression assumes equidispersion, i.e., the variance equals the mean. However, in practice, this assumption is often violated. One of this violation is overdispersion in which the variance is greater than the mean. There are several  methods to overcome overdispersion. Two of these methods are negative binomial regression and generalized Poisson regression. In this research, binomial negative regression and generalized Poisson regression statistically equally good in handling overdispersion.

scholarly journals Comparison between Efficiency of Poisson Regression Model and Negative Binomial Regression in the Analysis of Factors Affecting Mortality from Cardiovascular Diseases in Yazd Province in 2017

2021 ◽  
Author(s):  
Mohammad Mirjani Arjenan ◽  
Mohsen Askarshahi ◽  
Mahmud Vakili
Keyword(s):  
Cardiovascular Diseases ◽  
Regression Model ◽  
Poisson Regression ◽  
Regression Models ◽  
Negative Binomial ◽  
Negative Binomial Regression ◽  
Poisson Regression Model ◽  
Registration System ◽  
Factors Affecting ◽  
Binomial Regression

Introduction: Despite the advances in cardiovascular diseases, death caused by these diseases is still considered as the leading cause of mortality. In this study, some of the effective factors on the deaths caused by cardiovascular diseases were investigated Methods: This cross-sectional analytical study investigated the efficacy of Poisson regression models and negative binomial regression models on factors affecting mortality from cardiovascular diseases. The death data were extracted from the death registration system for Yazd province in 2017.Gender, age, education, occupation, location, and city of death were also extracted for each deceased. The two regression models were then fitted to the data Results:  A total of 5,015 deaths were recorded, of which 1,642 were due to cardiovascular diseases. Cardiovascular disease mortality rates were significant using negative binomial regression in terms of the educational variables, place of residence, type of residence, and age. Death rates caused by cardiovascular diseases were not significant for age and occupational, educational, and residential variables. Conclusion: If the time of death is considered as an offset variable, the regression model of two negative sentences is more effective in showing the factors affecting death due to cardiovascular diseases according to AIC and BIC criteria. In the case that the total number of deaths is considered as the offset variable, the Poisson regression model is more efficient.

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