Count Data Regression Research Articles

Copula-based bivariate count data regression models for simultaneous estimation of crash counts based on severity and number of vehicles

Statistical models of crash frequency typically apply univariate regression models to estimate total crash frequency or crash counts by various categories. However, a possible correlation between the dependent variables or unobserved variables associated with the dependent variables is not considered when univariate models are used to estimate categorized crash counts—such as different severity levels or numbers of vehicles involved. This may lead to inefficient parameter estimates compared to multivariate models that directly consider these correlations. This paper compares the results obtained from univariate negative binomial regression models of property-damage only (PDO) and fatal plus injury (FI) crash frequencies to models using traditional bivariate and copula-based bivariate negative binomial regression models. A similar comparison was made using models for the expected crash frequency of single- (SV) and multi-vehicle (MV) crashes. The models were estimated using two-lane, two-way rural highway segment-level data from an engineering district in Pennsylvania. The results show that all bivariate negative binomial models (with or without copulas) outperformed the corresponding univariate negative binomial models for PDO and FI, as well as SV and MV, crashes. Second, the statistical association of various traffic and roadway/roadside features with PDO and FI, as well as SV and MV crashes, were not the same relative to their corresponding relationships in the univariate models. The bivariate negative binomial model with normal copula outperformed all other models based on the goodness-of-fit statistics. The results suggest that copula-based bivariate negative binomial regression models may be a valuable alternative for univariate models when simultaneously modeling two disaggregate levels of crash counts.

Are Expensive Expressways in China Attractive to Businesses? Evidence From the Location Selections of Manufacturing Enterprises

Most expressways in China are tolled, making expressway transportation expensive for enterprises. Traditional location theory focuses only on transportation distances and transit costs, making it difficult to explain how expressways influence location decisions of enterprises. This research starts from the perspective of expressway travel times to explain how tolled expressways affect the location choices of new manufacturing enterprises. A geographic information system digital map of expressways for the years 2000–2013 was developed. The origin–destination matrix module was used to calculate the expressway travel times of 293 cities. Count data regression models, including probit, Poisson, zero-inflated Poisson, and negative binomial regression, were applied to empirically study the influence of expressway construction on the location selections of new manufacturing enterprises. The results show that reduced expressway travel time significantly attracts new enterprises and positively affects the location selections of manufacturing enterprises in China. Further, this finding reveals significant heterogeneity across different manufacturing industries.

Spatial association of Aedes aegypti with dengue fever hotspots in an endemic region

Background and objectiveDengue is a vector-borne viral disease usually transmitted by Aedes mosquitoes. Around the world, the relationship between local vector density and frequency of dengue cases is being explored and needs further evidence. This study aimed to analyze the potential spatial relationships between the dengue vector (Aedes aegypti) and dengue cases in the megacity of Bangladesh during the 2019 dengue outbreak. MethodsVector density measures were used to estimate spatial associations with dengue case distribution. Location was determined for 364 dengue cases who were admitted to Dhaka Medical College Hospital over a period of 4 months. Data were collected using a semi-structured questionnaire, and prior consent was ensured before participation. The Moran global index, Getis-Ord Gi∗, ordinary least squares regression, geographically weighted regression and count data regression methods were used for spatial analysis. ResultsWe found that dengue case distribution was not associated with immature Aedes aegypti mosquito (larvae) density across the city. The relationship between larval density measured by the Breteau Index (BI) and House Index (HI) with dengue cases was nonstationary and not statistically significant. ConclusionThe location of dengue cases appears to be unrelated to vector distribution and vector density. These findings should prompt the search for other transmission risk factors.

Predictors of adolescent truancy: The importance of cyberbullying, peer behavior, and parenting style

This study extends the truancy literature by exploring correlates of both committing truancy and the numbers of days truant among Spanish secondary school students. The study incorporates cyberbullying, peer truancy and parenting style as key predictors. Several count data regression models are estimated using a nationally representative survey of Spanish students (N = 37,476; Mage = 15.73; 50.9 % females). The results suggest that cyberbullying and parenting style play a significant role in a student’s decision to commit truancy, while peer truancy plays a significant role in both the decision of whether or not to commit truancy (OR = 1.61) and the number of days truant (IRR = 1.41). These results suggest that reducing cyberbullying and promoting specific parenting styles may serve to reduce truancy, and that this direct effect or reduction could be further increased indirectly via peer or social multipliers.

Quantile regression for count data: jittering versus regression coefficients modelling in the analysis of credits earned by university students after remote teaching

The extension of quantile regression to count data raises several issues. We compare the traditional approach, based on transforming the count variable using jittering, with a recently proposed approach in which the coefficients of quantile regression are modelled by parametric functions. We exploit both methods to analyse university students’ data to evaluate the effect of emergency remote teaching due to COVID-19 on the number of credits earned by the students. The coefficients modelling approach performs a smoothing that is especially convenient in the tails of the distribution, preventing abrupt changes in the point estimates and increasing precision. Nonetheless, model selection is challenging because of the wide range of options and the limited availability of diagnostic tools. Thus the jittering approach remains fundamental to guide the choice of the parametric functions.

Risk factors of under-five mortality in Ethiopia using count data regression models, 2021.

BackgroundDespite the global reduction in under-five mortality, still many children die before their fifth birthday in Ethiopia. The main aim of this study was to identify determinants of under-five mortality using count data regression models based on 2019 Ethiopia mini demography and health survey data.MethodsThe data source for this study was the 2019 Ethiopia mini demography and health survey data. Various count data regression models were applied to identify the determinants of under-five mortality.ResultsA total of 5,535 mothers with children aged 0–59 months were included in the study. Of the total, 1,277 (23.07%) women had lost at least one child by death before celebrating fifth birthday. Zero-Inflated Poisson model was found to be the best model, and it revealed that mother's age, marital status, mother's age at 1st birth, place of delivery, current contraceptive type used, type of cooking fuel, residence, region, religion, time to get drinking water, number of children at home, birth order, and birth type were significant factors that determine U5 mortality in Ethiopia.Mothers aged 15–24 years (IRR = 1.24, p = 0.007) and above 24 years (IRR = 1.66, p = 0.000) at their 1st births, mothers from rural area (IRR = 1.27, p = 0.000), mothers traveled for 1–30 min (IRR = 1.62, p = 0.000) and >30 min (IRR = 1.82, p = 0.000) to get drinking water, mothers used charcoal (IRR = 1.86, p = 0.009) and wood (IRR = 1.64, p = 0.033), children with birth order of 2nd-3rd (IRR = 3.91, p = 0.000), 4th -5th (IRR = 13.14, p = 0.000), 5th and above (IRR = 38.17, p = 0.000), and multiple born children (IRR = 1.5, p = 0.000) had higher risk of under-five mortality while mothers aged 25–34 years (IRR = 0.73, p = 0.000), unmarried mothers (IRR = 0.68, p = 0.004), mothers delivered in public health sectors (IRR = 0.59, p = 0.000), mothers used Pill/IUD (IRR = 0.64, p = 0.018), mothers who had 3 to 5 (IRR = 0.51, p = 0.000) and more than 5 (IRR = 0.27, p = 0.000) children at home had lower risk of under-five mortality.ConclusionsMothers should be encouraged to deliver at health institutions. Mothers also should be given awareness to use Pill/IUD contraceptive type. Moreover, facilitating rural areas to get electricity and drinking water near to homes helps to reduce the burden of U5M and to be in line with sustainable development goal.

A multi-environmental media approach to explore the association between metal exposure and the ability to identify smells among school-age children residing in Northern Italy

BACKGROUND AND AIM Inhalation of airborne particles can lead to olfactory dysfunction. We aimed to test the association between the exposure to a mixture of 12 metals measured in three environmental media and olfactory function among children and adolescents residing at different distances from ferromanganese alloy plants in the province of Brescia, Italy. METHODS We enrolled 130 children between 6 and 13 years old (51.5% females) residing in Valcamonica and Bagnolo Mella, respectively. The Burghart "Sniffin` Sticks” test was used to investigate olfactory performance in identifying smells. Metal concentrations in soil, indoor, and outdoor deposited dust samples from the subjects’ households were analyzed with a portable X-ray fluorescence instrument. A Multi Environmental Media (MEM) Weighted Quantile Sum (WQS) regression for count data was applied to test for the association between the exposure to metals and child olfactory function. All models were adjusted by age, sex, socio-economic status, area of residence, intelligence quotient, BMI and passive smoking. RESULTS The metal mixture was negatively associated with the identification score (=-0.229; 95%CI -0.439, -0.018). Cadmium (17.0%), iron (13.0%), lead (11.5%) and arsenic (8.5%) provided the strongest contribution to the association. Indoor dust resulted as the environmental media with the strongest contribution to the association with olfactory function for most of the elements considered in the mixture. CONCLUSIONS We identified metal concentrations in indoor dust as a risk factor for olfactory dysfunction in children and adolescents residing close to ferroalloy plants. Indoor pollution can be improved through public health interventions; moreover, the identification of the factors that can deteriorate olfactory functions can also prevent neurodegenerative disease. KEYWORDS Environmental exposure; olfactory function; metal exposure; soil; outdoor dust; indoor dust.

Estimating the Recreational Value and Setting Entrance Fees during Early Development of Ecotourism Sites: the Case of Bataan Natural Park

Ecotourism sites are established to provide “sustainable tourism,” bring economic opportunities to the local communities, and can potentially augment funding for conserving protected areas by charging entrance fees. A dilemma, however, faced by managers during the early stages of the development of ecotourism sites is the uncertain effect of increasing entrance fees on demand. This creates an apprehension to use entrance fees as a sustainable financing mechanism for conservation. This study used a combination of revealed and stated preference approaches to provide information on the recreational benefits and empirical guidance in setting entrance fee surcharges for proposed improvements in two eco-tourism sites of Bataan Natural Park – specifically, Ambon-Ambon and Lumutan Eco-trail and Tala River. Count data regression models were used to estimate the consumer surplus of visitors for the current conditions. In contrast, the contingent behavior method was used to measure the visitors’ willingness to pay (WTP) for improvements in the site attributes. Results of the count data models indicate the total consumer surplus from the ecotourism sites in their current state is significantly higher than the site's cost of improvement and maintenance. Furthermore, tourists are willing to pay more than the currently charged entrance fees. Protest and uncertainty corrected mean WTP for the improved condition are approximately PHP 130.90 for a visit to the eco-trail and PHP 108.50 for a visit to the river. The optimal and revenue-increasing entrance surcharge is estimated to be within PHP 15–76 for the Tala River and PHP 15–114 for the Falls. The results may have implications on providing alternative financing for protecting and conserving other natural parks and protected areas in their early stages of development in the Philippines.

Poisson and negative binomial regression models for zero-inflated data: an experimental study

Count data regression has been widely used in various disciplines, particularly health area. Classical models like Poisson and negative binomial regression may not provide reasonable performance in the presence of excessive zeros and overdispersion problems. Zero-inflated and Hurdle variants of these models can be a remedy for dealing with these problems. As well as zero-inflated and Hurdle models, alternatives based on some biased estimators like ridge and Liu may improve the performance against to multicollinearity problem except excessive zeros and overdispersion. In this study, ten different regression models including classical Poisson and negative binomial regression with their variants based on zero-inflated, Hurdle, ridge and Liu approaches have been compared by using a health data. Some criteria including Akaike information criterion, log-likelihood value, mean squared error and mean absolute error have been used to investigate the performance of models. The results show that the zero-inflated negative binomial regression model provides the best fit for the data. The final model estimations have been obtained via this model and interpreted in detail. Finally, the experimental results suggested that models except the classical models should be considered as powerful alternatives for modelling count and give better insights to the researchers in applying statistics on working similar data structures.

Count Data Regression Models: An Application to the Major Rice Insect Pest Counts in the Terai Region of West Bengal

Count Data Regression Models: An Application to the Major Rice Insect Pest Counts in the Terai Region of West Bengal

Epidemiological Monitoring of COVID-19 in a Brazilian City: The Interface between the Economic Policies, Commercial Behavior, and Pandemic Control

The new Coronavirus disease (COVID-19) pandemic was responsible for one of the worst public health crises in Brazil, which led to the implementation of economic policies to keep social distance. Our aim is to perform an epidemiological analysis of the COVID-19 pandemic in Uberlândia, Minas Gerais, in 2021, highlighting the impact of government commercial policies on pandemic control. This is an epidemiological, observational, and analytical study with secondary data. We constructed a regression for count data using the Poisson model. Data adherence to the regression was verified by Cameron & Trivedi and the Likelihood Ratio tests. According to the Poisson model, there was a statistically significant association (p < 0.001) between the adoption of rigid commercial interventions and the drop in deaths. Moreover, we revealed a consistency between the economic policies and the number of screening tests applied, which may have contributed to the deaths behavior. This study shows the importance of institutionalizing economic policies and their positive impacts on pandemic control; however, it raises the discussion about the serious repercussions of these measures on population vulnerability.

Owner perception of health of North American dogs fed meat- or plant-based diets

BackgroundSome dog owners elect to feed their dog a plant-based food either as part of or for their entire dietary intake. Being omnivores or facultative carnivores, a strictly plant-based diet is not the natural type of food dogs evolved to consume, leaving some question as to whether this feeding management strategy is safe and healthy for dogs. ObjectivesThis study surveyed owner perceptions of health and wellbeing of dogs and compared between those fed meat-based and plant-based diets. MethodsA web-based questionnaire was distributed to pet owners to collect data on dog characteristics, husbandry, health and wellbeing. Univariate comparisons between diet groups was made by chi square analyses or Kaplan-Meier tests as appropriate, with a significance cut-off value of 0.05. Multivariate models were negative binomial and logistic regression for count and categorical data, respectively. ResultsOwners feeding plant-based diets to their dog reported fewer health disorders, specifically with respect to ocular or gastrointestinal and hepatic disorders. Dog longevity was reported to be greater for dogs fed plant-based diets. Owners feeding plant-based diets to their dogs relied less on veterinary associates for nutrition information, versus dog owners feeding meat-based diets. ConclusionsDog owners feeding a plant-based diet did not perceive adverse health effects in their dogs. The results might suggest an association between feeding a plant-based diet and perceived health and longevity, however inherent bias and limitations associated with surveys of owner perception must be considered, and objective research is required to determine if plant-based diets truly affect canine health.

Heterogeneous Overdispersed Count Data Regressions via Double-Penalized Estimations

Recently, the high-dimensional negative binomial regression (NBR) for count data has been widely used in many scientific fields. However, most studies assumed the dispersion parameter as a constant, which may not be satisfied in practice. This paper studies the variable selection and dispersion estimation for the heterogeneous NBR models, which model the dispersion parameter as a function. Specifically, we proposed a double regression and applied a double ℓ1-penalty to both regressions. Under the restricted eigenvalue conditions, we prove the oracle inequalities for the lasso estimators of two partial regression coefficients for the first time, using concentration inequalities of empirical processes. Furthermore, derived from the oracle inequalities, the consistency and convergence rate for the estimators are the theoretical guarantees for further statistical inference. Finally, both simulations and a real data analysis demonstrate that the new methods are effective.

A penalized likelihood approach for dealing with separation in count data regression model

Separation or monotone likelihood can be observed in fitting process of both Poisson or generalized Poisson (GP) regression, particularly in case of small and/or sparse count data, using maximum likelihood estimation (MLE) when one or more regression coefficients diverge to infinity. The study investigates the consequence of separation in the MLE based standard Poisson or GP model and addressed the problems by introducing a penalized likelihood approach. The penalized likelihood function is derived by adding a penalty term to the standard maximum likelihood function, which was originally proposed by Firth (1993) for reducing first order bias in MLE. The corresponding penalized likelihood score equation has shown to achieve convergence and provide finite estimate of the regression coefficient, which was not possible for the maximum likelihood method score equation. The simulation study, with different forms of separation, showed that penalized Poisson model or penalized GP outperform the standard Poisson and even the Zero-inflated Poisson (ZIP) in the presence of complete or quasi-complete separation by achieving convergence and providing finite estimate of the regression coefficients. Even in the presence of near-to-quasi-complete separation, which is very common in practice, the penalized method showed better results than the standard Poisson, GP and ZIP in all simulation scenarios. The method was illustrated using antenatal care data extracted from database of the Bangladesh demographic health survey 2018.

Striking sex differences in magnetic resonance imaging findings in the sacroiliac joints in the population

BackgroundIn patients with axial spondyloarthritis (axSpA), magnetic resonance imaging (MRI) is used to detect bone marrow edema (BME) in sacroiliac joints (SIJ) but SIJ BME are also detected in the population. Not much is known about sex differences in that regard.ObjectiveTo explore sex-specific differences associated with the extent of BME in the SIJ suggestive of axSpA in a general population cohort study.MethodsTaking advantage of 793 recently evaluated MRIs of subjects < 45 years taking part in the SHIP cohort, we used negative-binomial (NB) count data regression to analyze factors associated with the extent of SIJ BME. Predictors were explored by model-based boosting (MBB), a machine learning approach.ResultsEstimates of NB regression showed strong effects of sex in interaction with age, BMI, back pain, and particularly HLA-B27. The NB regression model showed incidence rate ratios (IRR) for the main effect of sex (females vs. males): 0.94 [95% CI: 0.63; 1.41], HLA-B27: 4.32 [2.09; 9.8], and for the interaction of sex to HLA-B27: 0.22 [0.06; 0.75]. According to MBB, HLA-B27 positivity, BMI, current smoking, back pain in the last 3 months, the interaction of sex and HLA-B27, and delivery in the last 12 months were of highest importance to explain the extent of SIJ BME.ConclusionsDifferent factors were associated with the extent of SIJ BME in females and males. Most importantly, HLA-B27 was relevant only in males but not in females in whom a postpartal state was important. This finding may be relevant for the pathogenesis of axSpA.

Elastic-net Regularized High-dimensional Negative Binomial Regression: Consistency and Weak Signal Detection

We study a sparse negative binomial regression (NBR) for count data by showing the non-asymptotic advantages of using the elastic-net estimator. Two types of oracle inequalities are derived for the NBR's elastic-net estimates by using the Compatibility Factor Condition and the Stabil Condition. The second type of oracle inequality is for the random design and can be extended to many $\ell_1 + \ell_2$ regularized M-estimations, with the corresponding empirical process having stochastic Lipschitz properties. We derive the concentration inequality for the suprema empirical processes for the weighted sum of negative binomial variables to show some high--probability events. We apply the method by showing the sign consistency, provided that the nonzero components in the true sparse vector are larger than a proper choice of the weakest signal detection threshold. In the second application, we show the grouping effect inequality with high probability. Third, under some assumptions for a design matrix, we can recover the true variable set with a high probability if the weakest signal detection threshold is large than the turning parameter up to a known constant. Lastly, we briefly discuss the de-biased elastic-net estimator, and numerical studies are given to support the proposal.

Semiparametric count data regression for self-reported mental health.

''For how many days during the past 30 days was your mental health not good?" The responses to this question measure self-reported mental health and can be linked to important covariates in the National Health and Nutrition Examination Survey (NHANES). However, these count variables present major distributional challenges: The data are overdispersed, zero-inflated, bounded by 30, and heaped in 5- and 7-day increments. To address these challenges-which are especially common for health questionnaire data-we design a semiparametric estimation and inference framework for count data regression. The data-generating process is defined by simultaneously transforming and rounding (star) a latent Gaussian regression model. The transformation is estimated nonparametrically and the rounding operator ensures the correct support for the discrete and bounded data. Maximum likelihood estimators are computed using an expectation-maximization (EM) algorithm that is compatible with any continuous data model estimable by least squares. star regression includes asymptotic hypothesis testing and confidence intervals, variable selection via information criteria, and customized diagnostics. Simulation studies validate the utility of this framework. Using star regression, we identify key factors associated with self-reported mental health and demonstrate substantial improvements in goodness-of-fit compared to existing count data regression models.

Resilience of Railway Transport to Four Types of Natural Hazards: An Analysis of Daily Train Volumes

A crucial step in measuring the resilience of railway infrastructure is to quantify the extent of its vulnerability to natural hazards. In this paper, we analyze the vulnerability of the German railway network to four types of natural hazards that regularly cause disruptions in German rail operations: floods, mass movements, slope fires, and tree falls. Using daily train traffic data matched with various data on disruptive events, we quantify the extent to which these four types of natural hazard reduce daily train traffic volumes. With a negative binomial count data regression, we find evidence that the track segments of the German railway network are most vulnerable to floods, followed by mass movements and tree-fall events. On average, floods reduce traffic on track segments by 19% of the average daily train traffic, mass movements by 16%, and tree fall by 4%. Moreover, when more than one type of natural hazard affects the track segment on the same day, train traffic on that segment falls by 34% of the average train traffic. Slope fires have an ambiguous and nonrobust effect on train traffic due to the reverse causality due to its triggering factors. This is the first study that attempts to rank different natural hazards according to their impact on railway traffic. The results have implications for the selection of resilience strategy and can help prioritize policy measures.

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

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).

Use of Penalized Count Regression to Determine Factors Affecting the Length of Stay of Trauma Patients in the Intensive Care Unit

Background: Trauma is considered an important issue in most countries. Identification of the factors affecting the length of stay (LOS) in the intensive care unit (ICU) plays a crucial role in controlling the costs and complications of prolonged hospitalization. Objectives: This study aimed to identify the factors affecting the LOS of trauma patients in the ICU using stepwise and new penalized variable selection methods in count data regression. Methods: The patients’ information was evaluated in Emtiaz Hospital and Shahid Rajaee trauma center in Shiraz from March 2016 to September 2017. Count regression model was used to determine the factors affecting the LOS of patients in the ICU using penalized variable selection including, Enet, Snet, and Mnet. Results: The mean age of the patients (n=382) was obtained at 36.7±16.7 years, and the majority (88.4%) of the patients were male. The mean LOS in the ICU was determined at 6.2±6.6 days. Mnet with a negative binomial distribution outperformed the other penalized variable selection methods. A Glasgow Coma Scale (GCS) of less than 9 (IRR=1.7), blunt brain trauma (IRR=1.8), chest trauma (IRR=2.2), and oxygen saturation of less than 90 (IRR=1.2) increased the LOS of trauma patients in the ICU. Conclusions: Penalized variable selection methods effectively ignore or control the existing correlations between predictors. Amongst the penalized models, Mnet provided more acceptable results with smaller Akaike information criterion and fewer predictors. According to this penalty, the most important factors affecting the length of stay were chest trauma, blunt brain trauma, GCS, and oxygen saturation rate. Most clinical studies on trauma have also shown the importance of these factors.