A Score Test for Testing a Marginalized Zero-Inflated Poisson Regression Model Against a Marginalized Zero-Inflated Negative Binomial Regression Model

2017 ◽  
Vol 23 (1) ◽  
pp. 113-128 ◽  
Author(s):  
Gul Inan ◽  
John Preisser ◽  
Kalyan Das
Keyword(s):  
Regression Model ◽  
Poisson Regression ◽  
Negative Binomial ◽  
Score Test ◽  
Negative Binomial Regression ◽  
Negative Binomial Regression Model ◽  
Poisson Regression Model ◽  
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.

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 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.

scholarly journals Modeling Frequency of Truck Crashes on Limited-Access Highways

2013 ◽  
Author(s):  
Niranga Amarasingha ◽  
Sunanda Dissanayake
Keyword(s):  
Regression Model ◽  
Negative Binomial ◽  
Model Fitting ◽  
Negative Binomial Regression ◽  
Negative Binomial Regression Model ◽  
Poisson Regression Model ◽  
Limited Access ◽  
Related Data ◽  
Binomial Regression ◽  
Serious Injuries

Freight can be efficiently transported between most locations in the U.S. using large trucks. Involvement of large trucks in crashes can cause much damage and serious injuries, due to their large sizes and heavy weights. The purpose of this study was to identify the relationships between large truck crashes and traffic and geometric characteristics on limited access highways. Crash and traffic and geometric-related data for Kansas were utilized to develop a Poisson regression model and a negative binomial regression model for understanding the relationships. Based on model-fitting statistics, the negative binomial model was found to be the better model, which was used to identify the important characteristics. By addressing identified factors, safety could be promoted through introduction of appropriate engineering improvements.

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 Statistical models for analyzing count data: predictors of length of stay among HIV patients in Portugal using a multilevel model

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Ahmed Nabil Shaaban ◽  
Bárbara Peleteiro ◽  
Maria Rosario O. Martins
Keyword(s):  
Length Of Stay ◽  
Regression Model ◽  
Random Effects ◽  
Count Data ◽  
Negative Binomial ◽  
Negative Binomial Regression ◽  
Comprehensive Approach ◽  
Negative Binomial Regression Model ◽  
Hiv Patients ◽  
Binomial Regression

Abstract Background This study offers a comprehensive approach to precisely analyze the complexly distributed length of stay among HIV admissions in Portugal. Objective To provide an illustration of statistical techniques for analysing count data using longitudinal predictors of length of stay among HIV hospitalizations in Portugal. Method Registered discharges in the Portuguese National Health Service (NHS) facilities Between January 2009 and December 2017, a total of 26,505 classified under Major Diagnostic Category (MDC) created for patients with HIV infection, with HIV/AIDS as a main or secondary cause of admission, were used to predict length of stay among HIV hospitalizations in Portugal. Several strategies were applied to select the best count fit model that includes the Poisson regression model, zero-inflated Poisson, the negative binomial regression model, and zero-inflated negative binomial regression model. A random hospital effects term has been incorporated into the negative binomial model to examine the dependence between observations within the same hospital. A multivariable analysis has been performed to assess the effect of covariates on length of stay. Results The median length of stay in our study was 11 days (interquartile range: 6–22). Statistical comparisons among the count models revealed that the random-effects negative binomial models provided the best fit with observed data. Admissions among males or admissions associated with TB infection, pneumocystis, cytomegalovirus, candidiasis, toxoplasmosis, or mycobacterium disease exhibit a highly significant increase in length of stay. Perfect trends were observed in which a higher number of diagnoses or procedures lead to significantly higher length of stay. The random-effects term included in our model and refers to unexplained factors specific to each hospital revealed obvious differences in quality among the hospitals included in our study. Conclusions This study provides a comprehensive approach to address unique problems associated with the prediction of length of stay among HIV patients in Portugal.

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