Count Data Regression Models Research Articles

Broadband access and agritourism operations in the United States

AbstractAn online presence is crucial for agritourism operators to connect with consumers. In this study, we use count data regression models to examine the correlation between average broadband speed adopted and the number of agritourism operations. We found that adoption of fast broadband in 2012 was associated with a significantly higher number of agritourism operations nationally in 2017, underscoring the role of broadband connectivity in facilitating interactions between farmers and consumers, as well as in promoting agritourism. However, only a weak association exists in rural counties, indicating that the broadband–agritourism relationship does not extend to less populated areas.

Socio-environmental predictors of diabetes incidence disparities in Tanzania mainland: a comparison of regression models for count data

BackgroundDiabetes is one of the top four non-communicable diseases that cause death and illness to many people around the world. This study aims to use an efficient count data model to estimate socio-environmental factors associated with diabetes incidences in Tanzania mainland, addressing lack of evidence on the efficient count data model for estimating factors associated with disease incidences disparities.MethodsThis study analyzed diabetes counts in 184 Tanzania mainland councils collected in 2020. The study applied generalized Poisson, negative binomial, and Poisson count data models and evaluated their adequacy using information criteria and Pearson chi-square values.ResultsThe data were over-dispersed, as evidenced by the mean and variance values and the positively skewed histograms. The results revealed uneven distribution of diabetes incidence across geographical locations, with northern and urban councils having more cases. Factors like population, GDP, and hospital numbers were associated with diabetes counts. The GP model performed better than NB and Poisson models.ConclusionThe occurrence of diabetes can be attributed to geographical locations. To address this public health issue, environmental interventions can be implemented. Additionally, the generalized Poisson model is an effective tool for analyzing health information system count data across different population subgroups.

MODELING NOVEL COVID-19 PANDEMIC IN NIGERIA USING COUNT DATA REGRESSION MODELS

This study aimed to model COVID-19 daily cases in Nigeria, focusing on confirmed, active, critical, recovered, and death cases using count data regression models. Three count data regression models-Poisson regression, Negative Binomial regression, and Generalized Poisson regression were applied to predict COVID-19 related deaths based on the mentioned variables. Secondary data from the Nigeria Centre for Disease Control (NCDC) between February 29, 2020, and October 19, 2020, were used. The study found that Poisson Regression could not handle over-dispersion inherent in the data. Consequently, Negative Binomial Regression and Generalized Poisson Regression were considered, with Generalized Poisson Regression identified as the best model through performance criteria such as -2 log likelihood (-2logL), Akaike information criterion (AIC), and Bayesian information criterion (BIC). The study revealed positive and significant impacts of confirmed, active, and critical cases on COVID-19 related deaths, while recovered cases had a negative effect. Recommendations included increased attention to confirmed, active, and critical cases by relevant authorities to mitigate COVID-19-related deaths in Nigeria.

Count Data Regression Modelling: An Application to Monkeypox Confirmed Cases

Introduction: With the presence of COVID 19, some countries also faced an increase in number of cases due to Monkeypox virus. The main aim of this research was to investigate whether it is possible to fit count data regression models to predict the daily incidence of Monkeypox confirmed cases.
 Methods: In this study we have used two types of traditional count regression models like Poisson regression model and Negative binomial regression model using identity and logarithmic link function. Since our data was overdispersed, Negative binomial regression model with logarithmic link function fitted well as compared to other models. The parameters were estimated using SPSS, version 23.0.
 Results: The Negative Binomial Regression model with logarithm function fits well to the data related to Monkeypox cases. Therefore, the model shows that majority of the countries like Brazil, Canada, France, Germany, Peru, Spain, United Kingdom and United States of America shows significant decrease in number of cases with respect to time. The prediction line was plotted using this model where the line predicts well about the daily Monkeypox cases reported by different countries.
 Conclusion: From our study, we concluded that the count data regression model can be used widely to predict the incidence of any disease. The countries like Canada and Brazil have largest and smallest slope coefficient which shows maximum and minimum decrease in expected number of cases confirmed each day respectively.

Developing ridge estimators for the extended Poisson-Tweedie regression model: Method, simulation, and application

The extended Poisson-Tweedie (EPT) regression model is one of the count data regression models. It's a more flexible model in count data; since EPT model can be used in two situations: over-dispersion or under-dispersion but under assumption that this model uses second moment to be more flexible model. However, when the predictor (explanatory) variables of the EPT model are highly correlated, this means that there is the multicollinearity problem in the model. It causes inflation of the standard error of the maximum likelihood estimates and makes some of the significant variables insignificant. To handle and reduce the impact of the multicollinearity problem in the EPT model, we developed ridge estimators for this model. A theoretical comparison between the maximum likelihood and the proposed ridge estimators is done. The efficiency of the estimators is evaluated using the mean squared error (MSE). The simulation study and real-life application are used to evaluate the proposed estimators. We examined the performance of seven ridge estimators of the biasing parameter (k) to determine the most appropriate ridge estimator for this model. The simulation and application results showed that the proposed ridge estimator is superior to the maximum likelihood estimator, as it has the smallest MSE.

Determinants of Infant Mortality in Assam, India: Modelling with Generalised Linear Regression Model for Count Data

Determinants of Infant Mortality in Assam, India: Modelling with Generalised Linear Regression Model for Count Data

Zero-inflated Poisson regression analysis of factors associated with under-five mortality in Ethiopia using 2019 Ethiopian mini demographic and health survey data

Background Remarkable reduction in global under-five mortality has been seen over the past two decades. However, Ethiopia is among the five countries which account for about half (49%) of all under-five mortality worldwide. This study aimed at identifying factors associated with under-five children mortality in Ethiopia using the 2019 Ethiopia mini demography and health survey data. Methods The most recent national representative demography and health survey data of Ethiopia, 2019 Ethiopia mini demography and health survey data, were used for this study. Count data regression models were applied to identify the factors associated with under-five children mortality. Statistical significance was declared at P-value less than 0.05. Results Zero-Inflated Poisson (ZIP) regression model was found to be the best model compared to other count regression models based on models comparison Criteria. The ZIP model revealed that decreased risk of under-five mortality was associated with mothers aged 25–34 years, unmarried mothers, mothers delivered in health facility, mothers used Pill/IUD, mothers who had larger number of children at home whereas increased risk of under-five mortality was associated with older mothers at their first births, mothers from rural areas, mothers travel for 1–30 min and >30 min to get drinking water, mothers used charcoal and wood, children with higher birth order and multiple births. Conclusions In this study, place of residence, region, place of delivery, religion, age of mother, mother’s age at first birth, marital status, birth order, birth type, current contraceptive type used, type of cooking fuel, time to get drinking water, and number of children at home were statistically significant factors associated with under-five mortality in Ethiopia. Thus, the Ethiopian Ministry of Health and other concerned bodies are recommended to encourage mothers to deliver at health institutions, give awareness for mothers to use Pill/IUD contraceptive type, and facilitate rural areas to have electricity and drinking water near to homes so as to minimize the under-five mortality to achieve the sustainable development goal.

An implementation of Hurdle models for spatial count data. Study case: civil war as a risk factor for the development of childhood leukemia in Colombia

We propose a novel, efficient, and powerful methodology to deal with overdispersion, excess zeros, heterogeneity, and spatial correlation. It is based on the combination of Hurdle models and Spatial filtering Moran eigenvectors. Hurdle models are the best option to manage the presence of overdispersion and excess of zeros, separating the model into two parts: the first part models the probability of the zero value, and the second part models the probability of the non-zero values. Finally, gathering the spatial information in new covariates through a spatial filtering Moran vector method involves spatial correlation and spatial heterogeneity to improve the model fitting and explain spatial effects of variables that were not possible to measure. Thus, our proposal adapts usual regression models for count data so that it is possible to deal with phenomena where the usual theoretical assumptions, such as constant variance, independence, and unique distribution are not fulfilled. In addition, this research shows how a prolonged armed conflict can impact the health of children. The data includes children exposed to armed conflict in Colombia, a country enduring a non-international armed conflict lasting over 60 years. The findings indicate that children exposed to high levels of violence, as measured by the armed conflict index, demonstrate a significant association with the incidence and mortality rate of LAP in children. This fact is illustrated here using one of the most catastrophic conditions in childhood, as is Pediatric Acute Leukemia (LAP). The association between armed conflict and LAP has its conceptual basis in the epidemiology literature, given that, the incidence and mortality rates of neoplastic diseases increase with exposure to toxic and chronic stress during gestation and childhood. Our methodology provides a valuable framework for complex data analysis and contributes to understanding the health implications in conflict-affected regions.

A new regression model for count data with applications to health care data

A new regression model for count data with applications to health care data

A Flexible Dispersed Count Model Based on Bernoulli Poisson–Lindley Convolution and Its Regression Model

Count data are encountered in real-life dealings. More understanding of such data and the extraction of important information about the data require some statistical analysis or modeling. One innovative technique to increase the modeling flexibility of well-known distributions is to use the convolution of random variables. This study examines the distribution that results from adding two independent random variables, one with the Bernoulli distribution and the other with the Poisson–Lindley distribution. The considered distribution is named as the two-parameter Bernoulli–Poisson–Lindley distribution. Many of its statistical properties are investigated, such as moments, survival and hazard rate functions, mode, dispersion behavior, mean deviation about the mean, and parameter inference based on the maximum likelihood method. To evaluate the effectiveness of the bias and mean square error of the produced estimates, a simulation exercise is carried out. Then, applications to two practical data sets are given. Finally, we construct a flexible count data regression model based on the proposed distribution with two practical examples.

Determinants of the duration of sick leave due to occupational injuries: Evidence from Spanish manufacturing

Introduction: Despite the significant economic impact of occupational injuries on companies and society, studies focused on analyzing the determinants of workdays lost due to sick leave remain scarce and incomplete. This paper contributes to this issue by (a) analyzing the drivers of sick leave duration, distinguishing factors that explain the health recovery time from those that could lead workers to a voluntary extension of the absence period, and (b) formulating and empirically testing the effect of gender, citizenship, temporary work, job tenure, amount of disability benefit, and size of the injured worker's firm on the number of days the employee is off work after the injury. Method: Hypotheses are tested on a comprehensive dataset that includes all nonfatal occupational injuries causing sick leave that occurred in the manufacturing sector in Spain during 2015–2019, with more than 400,000 injuries. We conduct ordinary least squares and count data regression models in which the number of days off work is regressed on employees and work characteristics while accounting for a set of variables to control the injury's nature and severity. Results: The results show that after considering the intrinsic characteristics of the injury and the severity of the worker's injuries, women, native workers, workers with more seniority, workers with higher salaries, and those working in larger companies have longer periods of sick leave. The results suggest that moral hazard considerations significantly impact the time to return to work after an occupational injury. Practical applications: Based on the findings, several insights for company managers and public decision-makers are discussed. Specifically, interventions aimed at improving the organization of work and the working conditions of workers in manufacturing industries are highlighted, as well as the need to improve control and supervision mechanisms during the recovery process of injured workers.

Estimating the Number of Unemployed Months for Individuals in Turkey with the Poisson and Negative Binomial Regression Models

Unemployment is one of the greatest economic and social problems in Turkey, as well as it is in many other countries in the world. Unemployment is often explained by macroeconomic factors. However, demographic and individual characteristics also have an effect on the unemployment duration of individuals, in addition to the macroeconomic factors. The present study aims to find the factors that have an effect on the duration of unemployment of individuals in Turkey with count data regression models. Therefore, the present study examined Poisson Regression (PR) and Negative Binomial Regression (NBR) models, which are used in cases that the dependent variable is count data. The study also aims to determine the model with the best fit to the dataset among the estimated models. In the study, the number of months in which individuals were unemployed was modeled, using the data obtained from the Survey of Income and Living Conditions (SILC) micro dataset of the Turkish Statistical Institute (TURKSTAT) in 2019. 62713 people aged 15 and over participated in the SILC, of which 5889 reported that they were unemployed for one month or more. A model with the best fit and with the independent variables of marital status, education status, and general health status was determined among the seven models determined by the forward selection method. It has been determined that the model that best fits the dataset among the predicted models is the NBR model according to the Akaike Information Criterion (AIC).
 Key Words: Count data, Poisson Regression Model, Negative Binomial Regression Model
 JEL Classification: C10, C46, D30

Modeling the Effect of Population Density and Some Related Factors on Covid-19 Pandemic in Nigeria: An Application of Count Data Regression

Aim: Nigeria's population density and other factors like confirmed, admitted, and discharged cases have adversely impacted health behaviors and the management of the COVID-19 pandemic. This study aims to investigate how population, population density, confirmed, admitted, and discharged cases affect the prevalence of the COVID-19 pandemic in the 36 states of Nigeria, including the FCT. Method: The number of COVID-19-related deaths, confirmed, admitted, and discharged individuals, from June 20, 2021, to December 31, 2022, were extracted from the Nigeria Centre for Disease Control (NCDC) online database, while data set on the Nigeria population and density were collected from Nigeria’s National Population Commission (NPC) website. Three count data regression techniques; Poisson, Negative Binomial, and Generalized Poisson Regression models were employed to analyze these count data. Result: It was found that the number of admitted patients has a significant negative impact on COVID-19, whereas the number of confirmed laboratory COVID-19 cases has a significant positive effect on the number of deaths related to COVID-19. Additionally, the result showed that Nigeria's COVID-19 death rate is negatively impacted by discharged cases, population, and population density. Conclusion: It is inferred that the Generalized Poisson Regression model is the most suitable count data regression model for over-dispersion and is the best model for predicting the number of COVID-19-related deaths in Nigeria between June 20, 2021, and December 31, 2022.

Parallel dynamics in the yield of universal SARS-CoV-2 admission screening and population incidence

The majority of SARS-CoV-2 transmissions originates from either asymptomatic or presymptomatic individuals. To prevent unnoticed introduction of SARS-CoV-2, many hospitals have implemented universal admission screening during the COVID-19 pandemic. The present study aimed to investigate associations between results of an universal SARS-CoV-2 admission screening and public SARS-CoV-2 incidence. Over a study period of 44 weeks, all patients admitted to a large tertiary care hospital were tested for SARS-CoV-2 by polymerase chain reaction. SARS-CoV-2 positive patients were retrospectively categorized as symptomatic or asymptomatic at admission. Cantonal data were used to calculate weekly incidence rates per 100,000 inhabitants. We used regression models for count data to assess the association of the weekly cantonal incidence rate and the proportion of positive SARS-CoV-2 tests in the canton with (a) the proportion of SARS-CoV-2 positive individuals and (b) the proportion of asymptomatic SARS-CoV-2 infected individuals identified in universal admission screening, respectively. In a 44-week period, a total of 21,508 admission screenings were performed. SARS-CoV-2 PCR was positive in 643 (3.0%) individuals. In 97 (15.0%) individuals, the positive PCR reflected residual viral replication after recent COVID-19, 469 (72.9%) individuals had COVID-19 symptoms and 77 (12.0%) SARS-CoV-2 positive individuals were asymptomatic. Cantonal incidence correlated with the proportion of SARS-CoV-2 positive individuals [rate ratio (RR): 2.03 per 100 point increase of weekly incidence rate, 95%CI 1.92–2.14] and the proportion of asymptomatic SARS-CoV-2 positive individuals (RR: 2.40 per 100 point increase of weekly incidence rate, 95%CI 2.03–2.82). The highest correlation between dynamics in cantonal incidence and results of admission screening was observed at a lag time of one week. Similarly, the proportion of positive SARS-CoV-2 tests in the canton of Zurich correlated with the proportion of SARS-CoV-2 positive individuals (RR: 2.86 per log increase in the proportion of positive SARS-CoV-2 tests in the canton, 95%CI 2.56–3.19) and the proportion of asymptomatic SARS-CoV-2 positive individuals (RR: 6.50 per log increase in the proportion of positive SARS-CoV-2 tests in the canton, 95%CI 3.93–10.75) in admission screening. Around 0.36% of admission screenings were positive in asymptomatic patients. Admission screening results paralleled changes in population incidence with a brief lag.

Identifying predictors of frequency of 1-year readmission in adult patients with diabetes using count data regression models

Identifying predictors of frequency of 1-year readmission in adult patients with diabetes using count data regression models

Seasonality of presentation and birth in catatonia

BackgroundCatatonia is a neuropsychiatric syndrome associated with both psychiatric disorders and medical conditions. Understanding of the pathophysiology of catatonia remains limited, and the role of the environment is unclear. Although seasonal variations have been shown for many of the disorders underlying catatonia, the seasonality of this syndrome has not yet been adequately explored. MethodsClinical records were screened to identify a cohort of patients suffering from catatonia and a control group of psychiatric inpatients, from 2007 to 2016 in South London. In a cohort study, the seasonality of presentation was explored fitting regression models with harmonic terms, while the effect of season of birth on subsequent development of catatonia was analyzed using regression models for count data. In a case-control study, the association between month of birth and catatonia was studied fitting logistic regression models. ResultsIn total, 955 patients suffering from catatonia and 23,409 controls were included. The number of catatonic episodes increased during winter, with a peak in February. Similarly, an increasing number of cases was observed during summer, with a second peak in August. However, no evidence for an association between month of birth and catatonia was found. ConclusionsThe presentation of catatonia showed seasonal variation in accordance with patterns described for many of the disorders underlying catatonia, such as mood disorders and infections. We found no evidence for an association between season of birth and risk of developing catatonia. This may imply that recent triggers may underpin catatonia, rather than distal events.

DGLMExtPois: Advances in Dealing with Over and Under-dispersion in a Double GLM Framework

In recent years the use of regression models for under-dispersed count data, such as COM-Poisson or hyper-Poisson models, has increased. In this paper the DGLMExtPois package is presented. DGLMExtPois includes a new procedure to estimate the coefficients of a hyper-Poisson regression model within a GLM framework. The estimation process uses a gradient-based algorithm to solve a nonlinear constrained optimization problem. The package also provides an implementation of the COM-Poisson model, proposed by @huang, to make it easy to compare both models. The functionality of the package is illustrated by fitting a model to a real dataset. Furthermore, an experimental comparison is made with other related packages, although none of these packages allow you to fit a hyper-Poisson model.

New modified two-parameter Liu estimator for the Conway–Maxwell Poisson regression model

The Conway–Maxwell–Poisson (COMP) model is one of the count data regression models used in over- and underdispersion cases. Thus, COMP regression is a flexible model in the count data models. In the regression analysis, when the explanatory variables are correlated with each other, multicollinearity exists; this inflates the standard error of the maximum likelihood estimates. To handle the effect of multicollinearity, we proposed a new modified Liu estimator for the COMP regression model based on two shrinkage parameters. This estimator is proposed to reduce the effect of multicollinearity on the standard error of the estimates. To evaluate the performance of the proposed estimator, the mean squared error (MSE) criterion is employed. Theoretical comparison of the proposed estimator with existing estimators (ridge, Liu, and modified one-parameter Liu estimators) is made. The results of the simulation study and real-life application indicate the superiority of the proposed estimator.

Is Job Stability Declining in Germany? Evidences from Count Data Models

The macro evidence of increased adjustment pressure since the early seventies suggests that job mobility should have increased. Hence, retrospective and spell data from the German Socio-Economic Panel are combined in order to test the hypothesis that job stability for German workers declined between 1974 and 1994. Using count data regression models in which we control for labour market experience, various demographic factors, and occupation, we find that job stability did not decrease, but if anything increase, between 1974 and 1994. Our finding suggests that labour market inflexibility is an important factor in explaining the European unemployment problem.

A hybrid model of spatial autoregressive-multivariate adaptive generalized Poisson regression spline

Several Multivariate Adaptive Regression Spline (MARS) approaches are available to model categorical and numerical (especially continuous) data. Currently, there are other numerical data types—discrete or count data—that call for specific consideration in modeling. Additionally, spatially correlated count data is frequently observed. This has been seen in the case of health data, for example, the number of newborn fatalities, tuberculosis patients, hospital visitors, etc. However, currently no structurally consistent nonparametric regression and MARS model for count data incorporating spatial lag autocorrelation. The SAR-MAGPRS estimator (Spatial Autoregressive - Multivariate Adaptive Generalized Poisson Regression Spline) is developed to fill this gap. Although it can be applied to different count distributions, the estimator was developed in this study under the assumption of a Generalized Poisson distribution. This paper provides an information-theoretic framework for incorporating knowledge of the spatial structure and non-parametric regression models, especially MARS for the count data types. Moreover, the proposed method can assist in modeling the number of diseases while health policies are being developed. The framework presents an application of the Penalized Least Square (PLS) method to estimate the SAR – MAGPRS model.