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

2021 ◽  
Vol 151 ◽  
pp. 105964
Author(s):  
Muhammad Wisal Khattak ◽  
Ali Pirdavani ◽  
Pieter De Winne ◽  
Tom Brijs ◽  
Hans De Backer
Keyword(s):  
Regression Model ◽  
Negative Binomial ◽  
Negative Binomial Regression ◽  
Negative Binomial Regression Model ◽  
Poisson Regression Model ◽  
Generalized Poisson ◽  
Binomial Regression ◽  
Safety Performance Functions ◽  
Functional Forms ◽  
Generalized Poisson Regression

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 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 PENAKSIRAN PENJUALAN PRODUK BERDASARKAN PENDEKATAN MODEL REGRESI NEGATIF BINOMIAL

2019 ◽  
Vol 3 (1) ◽  
pp. 25
Author(s):  
Reny Rian Marliana
Keyword(s):  
Monte Carlo ◽  
Regression Model ◽  
Negative Binomial ◽  
Poisson Model ◽  
Negative Binomial Regression ◽  
Negative Binomial Regression Model ◽  
Generalized Poisson ◽  
Regression Parameters ◽  
Binomial Regression ◽  
Product Sales

AbstrakPenelitian bertujuan untuk membandingkan hasil penaksiran parameter model regresi binomial negative dengan model Poisson untuk underreported counts pada penelitian sebelumnya. Model regresi dibentuk pada data penjualan produk yang mengalami underreporting counts, akibat keterlambatan input data ke aplikasi penjualan produk (sales cycle). Pada penelitian sebelumnya, model yang digunakan merupakan gabungan antara distribusi Binomial dan distribusi Poisson. Parameter model regresi ditaksir menggunakan pendekatan Bayes dan simulasi Markov Chain Monte Carlo melalui Algoritma Gibbs Sampling. Hasil penaksiran menunjukkan adanya perbedaan antara banyaknya penjualan yang dilaporkan dengan banyaknya penjualan produk yang sebenarnya. Besar perbedaan tersebut merupakan banyaknya penjualan produk yang tidak terlaporkan. Pada penelitian lanjutan ini, model yang digunakan adalah Model Regresi Negatif Binomial. Parameter regresi ditaksir menggunakan metode Iterasi Newton Rapson. Hasil penaksiran menunjukkan selisih yang cukup besar dimana model Poisson untuk underreported counts lebih robust sesuai dengan komponen musiman yang ada.Kata Kunci: underreported, generalized poisson, negative binomial  AbstractThe goal of study is to compare the parameters of the negative Binomial regression model and the Poisson Model for underreported counts in the previous study. A model is a regression model for the number of product sales that run ito underreporting counts, caused by a delay on input process to the product sales applications (called sales cycle). The model used in the previous study is a mixture of the poisson and the binomial distributions developed by Winkelmann (1996). The regression parameters are estimated by a Bayesian approach and Markov Chain Monte Carlo simulation using Gibbs sampling algorithm. The results show the difference between the actual number and the reported number. This difference is the number of unreported product sales. In this study, the model used is the negative binomial regression model. The regression parameters are estimated using Newton Rapson iteration method. The results show a big gap from the previous study. It means that the Poisson Model for underreported counts is more robust in accordance with the seasonal components.Keywords: underreported, generalized poisson, negative binomial

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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