scholarly journals Overdisp: A Stata (and Mata) Package for Direct Detection of Overdispersion in Poisson and Negative Binomial Regression Models

2020 ◽  
Vol 8 (3) ◽  
pp. 773-789
Author(s):  
Luiz Paulo Lopes Fávero ◽  
Patrícia Belfiore ◽  
Marco Aurélio dos Santos ◽  
R. Freitas Souza
Keyword(s):  
Count Data ◽  
Data Model ◽  
Regression Models ◽  
Negative Binomial ◽  
Direct Detection ◽  
Negative Binomial Regression ◽  
The Other ◽  
Explanatory Variables ◽  
Data Regression ◽  
Binomial Regression

Stata has several procedures that can be used in analyzing count-data regression models and, more specifically, in studying the behavior of the dependent variable, conditional on explanatory variables. Identifying overdispersion in countdata models is one of the most important procedures that allow researchers to correctly choose estimations such as Poisson or negative binomial, given the distribution of the dependent variable. The main purpose of this paper is to present a new command for the identification of overdispersion in the data as an alternative to the procedure presented by Cameron and Trivedi [5], since it directly identifies overdispersion in the data, without the need to previously estimate a specific type of count-data model. When estimating Poisson or negative binomial regression models in which the dependent variable is quantitative, with discrete and non-negative values, the new Stata package overdisp helps researchers to directly propose more consistent and adequate models. As a second contribution, we also present a simulation to show the consistency of the overdispersion test using the overdisp command. Findings show that, if the test indicates equidispersion in the data, there are consistent evidence that the distribution of the dependent variable is, in fact, Poisson. If, on the other hand, the test indicates overdispersion in the data, researchers should investigate more deeply whether the dependent variable actually exhibits better adherence to the Poisson-Gamma distribution or not.

Managing Inflation

2016 ◽  
Vol 63 (1) ◽  
pp. 77-87 ◽  
Author(s):  
William H. Fisher ◽  
Stephanie W. Hartwell ◽  
Xiaogang Deng
Keyword(s):  
Count Data ◽  
Regression Models ◽  
Negative Binomial ◽  
Negative Binomial Regression ◽  
Excess Zeros ◽  
Binomial Regression ◽  
Negative Binomial Models ◽  
Using Data ◽  
Over Dispersion ◽  
Binomial Models

Poisson and negative binomial regression procedures have proliferated, and now are available in virtually all statistical packages. Along with the regression procedures themselves are procedures for addressing issues related to the over-dispersion and excessive zeros commonly observed in count data. These approaches, zero-inflated Poisson and zero-inflated negative binomial models, use logit or probit models for the “excess” zeros and count regression models for the counted data. Although these models are often appropriate on statistical grounds, their interpretation may prove substantively difficult. This article explores this dilemma, using data from a study of individuals released from facilities maintained by the Massachusetts Department of Correction.

scholarly journals A Study of Count Regression Models for Mortality Rate

CAUCHY ◽  
2021 ◽  
Vol 7 (1) ◽  
pp. 142-151
Author(s):  
Anwar Fitrianto
Keyword(s):  
Mortality Rate ◽  
Regression Model ◽  
Count Data ◽  
Bayesian Information Criterion ◽  
Regression Models ◽  
Negative Binomial ◽  
Negative Binomial Regression ◽  
Information Criterion ◽  
Poisson Regression Model ◽  
Binomial Regression

This paper discusses how overdispersed count data to be fit. Poisson regression model, Negative Binomial 1 regression model (NEGBIN 1) and Negative Binomial regression 2 (NEGBIN 2) model were proposed to fit mortality rate data. The method used is comparing the values of Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) to find out which method suits the data the most. The results show that the data indeed display higher variability. Among the three models, the model preferred is NEGBIN 1 model.

scholarly journals Analysis of the correlation of socioeconomic, sanitary, and demographic factors with homicide deaths - Bahia, Brazil, 2013-2015

2020 ◽  
Vol 73 (6) ◽  
Author(s):  
Tiago Oliveira de Souza ◽  
Edinilsa Ramos de Souza ◽  
Liana Wernersbach Pinto
Keyword(s):  
Regression Models ◽  
Ecological Study ◽  
Negative Binomial ◽  
Demographic Factors ◽  
Negative Binomial Regression ◽  
Legal Intervention ◽  
Explanatory Variables ◽  
Binomial Regression ◽  
Education Levels ◽  
Using Data

ABSTRACT Objective: To analyze the correlation of socioeconomic, sanitary, and demographic factors with homicides in Bahia, from 2013 to 2015. Methods: Ecological study, using data from the Information System on Mortality and from the Superintendence of Economic and Social Studies. The depending variable is the corrected homicide rate. Explanatory variables were categorized in four axes. Simple and multiple negative binomial regression models were used. Results: Positive associations were found between homicides and the Index of Economy and Finances (IEF), the Human Development Index, the Gini Index, population density, and legal intervention death rates (LIDR). The variables Index of Education Levels (IEL), rates of death with undetermined intentions (RDUI), and the proportion of ill-defined causes (IDC) presented a negative association with the homicide rates. Conclusion: The specific features of the context of each community, in addition to broader socioeconomic municipal factors, directly interfere in life conditions and increase the risk of dying by homicide.

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.

scholarly journals Transition models for count data: a flexible alternative to fixed distribution models

2021 ◽  
Author(s):  
Moritz Berger ◽  
Gerhard Tutz
Keyword(s):  
Count Data ◽  
Regression Models ◽  
Negative Binomial ◽  
Real Data ◽  
Distribution Models ◽  
Explanatory Variables ◽  
Excess Zeros ◽  
Proposed Model ◽  
Transition Models ◽  
Fixed Distribution

AbstractA flexible semiparametric class of models is introduced that offers an alternative to classical regression models for count data as the Poisson and Negative Binomial model, as well as to more general models accounting for excess zeros that are also based on fixed distributional assumptions. The model allows that the data itself determine the distribution of the response variable, but, in its basic form, uses a parametric term that specifies the effect of explanatory variables. In addition, an extended version is considered, in which the effects of covariates are specified nonparametrically. The proposed model and traditional models are compared in simulations and by utilizing several real data applications from the area of health and social science.

scholarly journals Analysis of Nonsevere Crashes on Two- and Four-Lane Urban and Rural Highways: Effects of Wet Pavement Surface Condition

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Aschalew Kassu ◽  
Michael Anderson
Keyword(s):  
Negative Binomial ◽  
Surface Condition ◽  
Negative Binomial Regression ◽  
Segment Length ◽  
Mean Values ◽  
Rural Highways ◽  
Explanatory Variables ◽  
Crash Data ◽  
Pavement Surface ◽  
Binomial Regression

This study examines the effects of wet pavement surface conditions on the likelihood of occurrences of nonsevere crashes in two- and four-lane urban and rural highways in Alabama. Initially, sixteen major highways traversing across the geographic locations of the state were identified. Among these highways, the homogenous routes with equal mean values, variances, and similar distributions of the crash data were identified and combined to form crash datasets occurring on dry and wet pavements separately. The analysis began with thirteen explanatory variables covering engineering, environmental, and traffic conditions. The principal terms were statistically identified and used in a mathematical crash frequency models developed using Poisson and negative binomial regression models. The results show that the key factors influencing nonsevere crashes on wet pavement surfaces are mainly segment length, traffic volume, and posted speed limits.

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.

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