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 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.

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 ANALISIS REGRESI COUNT DATA UNTUK PEMODELAN JUMLAH KASUS PENYAKIT TUBERKULOSIS DI KABUPATEN BANYUMAS

2021 ◽  
Vol 13 (2) ◽  
pp. 57
Author(s):  
Kristy Kristy ◽  
Jajang Jajang ◽  
Nunung Nurhayati
Keyword(s):  
Regression Model ◽  
Count Data ◽  
Poisson Regression ◽  
Negative Binomial ◽  
Predictor Variable ◽  
Negative Binomial Regression ◽  
Negative Binomial Regression Model ◽  
Binomial Regression ◽  
The Mean ◽  
Generalized Poisson Regression

Tuberculosis is an infectious disease caused by Mycobacterium tuberculosis. Banyumas Regency is one of the districts with quite high Tuberculosis cases in Central Java. This study aims to analyze the factors that affect the number of tuberculosis cases in Banyumas Regency using regression analysis of count data. Poisson regression is the simplest count data regression model that has the assumption of equidispersion, that is, the mean value equal to the variance. However, in its application, these assumption is often not fulfilled, for example, there are cases of overdispersion (variance value is greater than the mean). In this study, to overcome the case of overdispersion, an approach was used using Generalized Poisson Regression (GPR) and negative binomial regression. The results showed that the data on the number of tuberculosis cases in Banyumas Regency in 2019 was overdispersion. The data modeling of the number of tuberculosis cases in Banyumas Regency with the negative binomial regression model is better than the GPR model. Meanwhile, the only predictor variable that affects the number of tuberculosis cases in Banyumas Regency is the sex ratio of productive age (15-49 years).

scholarly journals Mean-parametrized Conway–Maxwell–Poisson regression models for dispersed counts

2017 ◽  
Vol 17 (6) ◽  
pp. 359-380 ◽  
Author(s):  
Alan Huang
Keyword(s):  
Poisson Regression ◽  
Regression Models ◽  
Negative Binomial ◽  
Asymptotic Properties ◽  
Poisson Model ◽  
Finite Sample ◽  
Generalized Poisson ◽  
The Mean ◽  
Generalized Poisson Regression ◽  
Log Linear

Conway–Maxwell–Poisson (CMP) distributions are flexible generalizations of the Poisson distribution for modelling overdispersed or underdispersed counts. The main hindrance to their wider use in practice seems to be the inability to directly model the mean of counts, making them not compatible with nor comparable to competing count regression models, such as the log-linear Poisson, negative-binomial or generalized Poisson regression models. This note illustrates how CMP distributions can be parametrized via the mean, so that simpler and more easily interpretable mean-models can be used, such as a log-linear model. Other link functions are also available, of course. In addition to establishing attractive theoretical and asymptotic properties of the proposed model, its good finite-sample performance is exhibited through various examples and a simulation study based on real datasets. Moreover, the MATLAB routine to fit the model to data is demonstrated to be up to an order of magnitude faster than the current software to fit standard CMP models, and over two orders of magnitude faster than the recently proposed hyper-Poisson model.

scholarly journals PENERAPAN REGRESI GENERALIZED POISSON UNTUK MENGATASI FENOMENA OVERDISPERSI PADA KASUS REGRESI POISSON

2013 ◽  
Vol 2 (2) ◽  
pp. 49
Author(s):  
I PUTU YUDANTA EKA PUTRA ◽  
I PUTU EKA NILA KENCANA ◽  
I GUSTI AYU MADE SRINADI
Keyword(s):  
Poisson Regression ◽  
Discrete Data ◽  
Mean Value ◽  
Regression Method ◽  
Response Variable ◽  
Generalized Poisson ◽  
The Mean ◽  
Generalized Poisson Regression ◽  
Better Than

The Poisson regression is generally used to analyze the response variable that is a discrete data. Poisson regression has assumption which must be met, that is condition equidispersion. But in fact this assumption is often violated, that is the value of the variance is greater or less than the mean value. The condition when value of the variance is greater than the mean value is called overdispersion. One method that can be used for overdispersion data is Generalized Poisson regression. In this research, it was found that the Generalized Poisson regression method was better than Poisson regression method.

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.

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