In this article we want to show that the hurdle negative binomial regression model can be used to fit right censored data. In fact, the proposed model is suitable to solve the excess zeros problem in the response variable when the data are censored from the right side. The results from the fish data are summarized in Table 1-3. The goodness-of-fit measures are presented in the Table 3 according to different censoring points and it is obvious that we have a smaller value for −2 log L or AIC when the percentage of censoring increase and that is because of the number of the data which are used in the model. Also, the censored hurdle negative binomial model shows a better fit with respect to the censored negative binomial model for different censoring points as shown in Figure 2 and Figure 3.
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Seventh, a weakness of the paper is that a good fit of the Negative Binomial model does not provide a direct proof that political parties float independent candidates for electoral benefits. Our theories are based on incentives and empirical results are based on circumstantial evidence rather than rigorous proof. However, given the widespread actual existence of “strange bedfellows” in politics across countries and over time, more research is needed on the actual behavior of candidates in elections in India. For example, our study indicates the importance of electoral budgets in floating independent candidates. It, therefore, highlights the need for more credible auditing of the accounts of political parties and candidates, including independent candidates. Extending this argument further, a crucial part of our understanding of the incentives of all major players would also come from studies that observe post-election behavior and asset accumulation and not just during the election period.
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Analysis of count event data such as mortality cases, were often modelled using Poisson regression model. Maximum likelihood procedures were used by using SAS software to estimate the model parameters of a Poisson regression model. However, the Negative Binomial distribution has been widely suggested as the alternative to the Poisson when there is proof of overdispersion phenomenon. We modelled the mortality cases as the dependent variable using Poisson and Negative Binomial regression and compare both of the models. The procedures were done in SAS by using the function PROC GENMOD. The results showed that the mortality data in Poisson regression exhibit large ratio values between deviance to degree of freedom which indicate model misspecification or overdispersion. This large ratio was found to be reduced in Negative Binomial regression. The Normal probability plot of Pearson residual confirmed that the Negative Binomial regression is a better model than Poisson regression in modelling the mortality data. The objective of this study is to compare the goodness of fit of Poisson regression model and Negative Binomial regression model in the application of air pollution epidemiologic time series study by using SAS software.
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Although a number of indicators including oral health related behaviors, knowledge and attitudes were consid- ered in the negative binomial regression model on dental caries experience, only utilization of dental service dur- ing past three years were identified to be associated with the dental caries experience of the subjects. This finding is in agreement with review paper regarding risk factors of dental caries in some extent . Problem-oriented dental visiting pattern were found among these young adults. The majority of subjects in this study visited a dentist only when they had a problem that required treat- ment and not for preventive care. It was found that young adults who had a greater utilization of dental services had higher dental caries experience and a higher FT compo- nent. Due to the predominant item-based fee-for-service payment arrangement in the dental market in Hong Kong, dentists typically adopt a curative or restorative rather than a preventive approach when treating patients. Although Table 6 Relationship between mean numbers of sextants
The purpose of present study is to explore theoretically and empirically the impact of counterterrorism effectiveness on economic growth of Pakistan. The data for counter-terrorism components construct from GTD and data for growth variables gathered from WDI for the time 1980 to 2015. This study developed “negative binomial regression model” for investigatin g the magnitude and significance of counter-terrorism effectiveness. It also uses the ARDL bound test and causality analysis for examining the causal relationship between economic growth and counter-terrorism effectiveness. This study further identifies that there are three types of proactive strategies used by Government and military authorities to reduce violence: civilian policies, peace accords and military operations. The result shows that there are long term impacts of counter-terrorism policies on economic growth. The findings also imply that counter-terrorism strategies may not be able to restrict violence and incapacitate militant‟s organization and their sleeper cell if it lacks strong political support. The present work is raw evidence for the effort level of authorities and their preemptive strategies that leads to the significant breakdown effect to curb terrorism across the country.
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The Poisson Regression Model, GPR, and NBR were conducted to determine the better model to use in modeling data on number of road traffic crashes within the Anambra state Command of Federal Road Safety Commission, Nigeria. The criterion for selection of the best model used is the AIC. The best model is that with the smallest AIC value. This happened to be the NBR model. The deviance for the Poisson regression model (Table C) is larger than the deviance of the Negative Binomial Regression and the Generalized Poisson Regression models (Tables E and G) thus indicating the existence of significant over-dispersion if the Poisson Regression Model were adopted. To test for over-dispersion, AIC of Poisson against Negative Binomial Regression model and Generalized Poisson Regression are obtained and compared. On the basis of the AIC values in tables C, E and G the estimated AIC for GPR model (Table G) is 3508.595 whereas it is 6266 for the PR (Table C) and 2742 for the NBR model (Table E). The smallest AIC value is that of the negative binomial regression model. Therefore, the best model for the number of road traffic crashes in Anambra state road safety command is best modeled and described using the negative binomial regression model.
Abstract— The Poisson Regression and Negative Binomial Regression models are the conventional statistical models for count data. This paper presents using decision tree to model motorcycle accident occurrences and compared its classification performance with Poisson Regression and Negative Binomial Regression model. The frequency of motorcycle accidents that involve death or serious injury based were converted into a categorical dependent variable (zero, low and high frequency) and the factors considered are collision types, road geometry, time, weather condition, road surface condition and type of days. Based on classification accuracy, results show that the decision tree model using CART (Classification and Regression Tree) slightly performs better (78.1%) than Poisson Regression (76.3%) with Negative Binomial Regression (77.6%) models. The CART decision rules revealed that the most significant factor contributing to high frequency of motorcycle accidents that result in death or serious injury is when the accidents happen on a straight road, junction or bend.
The OR is a commonly used measure of uncertainty in a binary decision (e.g., zero or non-zero). When data are obtained from a count process, there is information in the counts that is lost when the data are dichotomized. We proposed a method for estimating the OR that does not require dichotomizing the count data. We demonstrated analytically the gain in information using this approach and the resulting increase in precision when making infer- ences on the OR. For a given p, the probability of a positive count, the information gain increases as the count data become more dispersed from zero and one. The ana- lytic methods we propose can be implemented easily by biomedical researchers. For geometric and Poisson mod- els, any software fitting GLMs can be used provided it allows the user to modify the link function. For NB mod- els, an optimization routine can be used to maximize the likelihood. In our examples, the optimization always con- verged because the logistic regression of the dichtomized data provides initial values that are very close to the solutions for the count data.
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Actually, the occurrence of HRI is a comprehensive impact of weather factors and other factors, such as physical activities, the lack of environmental acclima- tization, poor physical fitness, and illness  . In consensus, if the count of HRI is abnormally high, it implies a high possibility that other than weather fac- tors have stepped in. For example, according to our collected HRI counts (2002-2010) on the dates when Standard Chartered Marathon was held in Sin- gapore (see Table 3), the counts of HRI cases were in a range from 4 to 12 com- pared to the overall mean of 0.34 cases (see Table 2). We need to arrange dif- ferent models to reflect the different scenarios. Here, the separation line was as- sumed to be at the location where the counts of HRI cases were zero or more as more than normal zeros were observed. Therefore, the hurdle model was em- ployed where the zero counts and the positive counts of HRI cases were modeled by different distributions.
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Understanding whether part of the population would remain malaria-free regardless of protective measures may be particularly important for studies of preventive inter- ventions, such as a vaccine, when absence of an episode may be considered a success . Failure to account for an unexposed fraction can lead to biased estimates of intervention effects. For interventions that may partially protect some individuals and completely protect others, differentiating partial and complete protection may be of particular interest [15-17]. This is possible within the zero-inflated model framework by including covariates in the count or binary sections of the model, respectively. Understanding what factors are associated with remaining malaria-free, particularly in areas of apparently high trans- mission, may be important in understanding where mal- aria control efforts should, and should not, be focused.
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The last issue to be addressed in this study is modelling interactions. We represented here the interaction between ageman × gender which was statistically signiﬁ cant and can be also explained in rational terms. Thus, by adding this interaction in the claim frequency model, we extended the NB2 model involving fractional polynomials. The LR test determining the statistically signiﬁ cant diﬀ erence from the NB2 model without interaction term yielded the chi2, with 2 degrees of freedom, 43.45 and the corresponding p-value was less than 0.0001 which indicated better ﬁ t of the model. In addition,
Methods: We initially use the Poisson generalized linear model (GLM) with polynomial effect functions of relevant covariates. If the time series of residuals from fitting the Poisson GLM reveals significant serial correlation, a Poisson generalized linear autoregressive moving average (GLARMA) model is refitted to the data to account for the auto-correlation among the time series of daily call numbers. If the data is overdispersed relative to the best fitting Poisson GLARMA model, then the negative binomial GLARMA model is refitted to account for any overdispersion. In all the models, dummy variables for weekdays and months are included to account for any cyclic trends due weekday effect or month of the year effect. The secular time trend is modeled by a polynomial function of calendar time over the study period. Finally any critical temperatures are identified by visually inspecting the graph of the effect function of temperature.
The frequency of zero counts in the previous literature was much larger than frequency of any other counts. The model fitted the data very well, and the authors suggested choosing a model based on dispersion of the non-zero counts. Hence, (Warton, 2005) fit the data existing a large probabilities at zero with transformed distribution, log-linear distribution, negative binomial distribution using method of moment estimation (MME) and maximum likelihood estimation (MLE) ZIP and ZINB. Thus, the large zero counts in abudance data were move likley to have arisen from a negative binomial distribution with a small mean than from a ZINB distribution. In addition, (Welsh.A.H et al., 1996) suggested testing whether the zero inflation term was necessary and importantly that NB distribution gen- erally abudance modeling data better than other distributions even when there were more zeros than predicted by the models.
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we performed both Poisson and negative binomial re- gression analyses (Additional file 2). When evaluating the model, the Akaike and Bayesian information criteria (AIC and BIC, respectively) are often used, where lower values indicate a better model (Additional file 3) . We evaluated the relationship between COC and hos- pital admissions in each COC group using a negative bi- nomial regression analysis, which was chosen due to over-dispersion. Finally, factors affecting continuity of care and the relationship between continuity of care and healthcare costs were examined through a multiple re- gression analysis. All statistical analyses were performed using SAS software version 9.4 (SAS, Inc., Cary, NC, USA). The results were considered statistically signifi- cant when the p-value was less than 0.05.
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Having established that ZINB regression model was best suited to determine the effect of month on the disease occurrence in Oyo state, months of reporting also had significant effect on the incidence of new cases of childhood pneumonia. Previous studies have shown that pneumonia illness is most common in the winter months and the greatest incidence during the rainy season [8, 9]. The geographical locations were also predictors of the occurrence of childhood pneumonia. In Nigeria, several environmental factors that could predispose children to pneumonia vary across geographic locations. The variation may be occasioned by seasonal and or occupational differences. A previous study on acute respiratory infections among un-der-five children in Indian slums  has identified the role of hazardous environment in the incidence of pneumonia while the impact of seasonal variation in pneumonia infection was noted by  who highlighted the increase in episodes typically occurring during the rainy season.
This study applies the Poisson and Negative Binomial Regression models to investigate the influence of household factors on car ownership in Akure metropolis, the capital of Ondo State located in south west Nigeria. The decision to buy a car is one of the most significant decisions made by a consumer. Not only is it one of the most significant financial investments for many people, but it also represents a dramatic increase in mobility and is often viewed as a status symbol. It is also a key feature of the transportation system that to a great extent influences travel behaviour and participation in out-of-home activities. The increase in utilization patterns and high-levels of household car ownership have a direct effect on energy consumption and air quality levels in local and global scales .
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Cross-sectional study was utilized in this study in order to identify several geometric characteristics effect compared to speed limit increase .The Negative Binomial (NB) regression model is the standard approach for modeling the yearly crash frequency based on Highway Safety Manual (HSM) recommenda- tion . This approach is implemented using any of several commercially available software packages. In this research, the STATA statistical software package  was utilized to conduct the NB regression and estimate CMF by computing the exponential of treatment factor coefficient. The NB regression approach is commonly used to develop crash prediction models. Considering the number of crashes occurring per year at several intersections in a city. In a Poisson regression model, the probability of intersection i having y i crashes
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medicine and health. Poisson regression is of the models which is used in count varia- bles such as the number of blood donations, the number of stopping addiction, the num- ber of failed courses or semester etc. and is applicable in many medical researches. In this method we build a model on the mean of the response variable using statistical methods. The Poisson regression is a subset of a large set of statistical modeling which is called Generalized Linear Model (GLM). Sometimes the count variables which are used to build a statistical modeling, have an inflation in zero which are divided into
Cultivating and developing strategic emerging industry is the key point of promoting China’s social and eco- nomic sustainable development at present. Financial support plays a key role of the core and foundation in fos- tering strategic emerging industries. Gu, H.F. (2011)   proposed finance supporting frame and system for the developing of strategic emerging industries, which would render important theory guide and strategy refer- ence to China establishing scientifically high-efficiency industry development policy and finance economic pol- icy. Wu, J.X. and Li, X.Z. (2012)  argued that the local governments should take more active roles to re- sponse to market failure, commit to strategic mission, construct regional innovation system, and take advantage of opportunity window during the development of strategic emerging industries. And they proposed suggestions that included soliciting the support of central government, fostering the local big enterprises, helping to build industrial ecosystem, promoting to the establishment of non-profitable industry research labs, leading consump- tion, which would give the beneficial reference to policy formation from the local governments. Using the data of 112 listed companies from 7 strategic emerging industries and based on the DEA efficiency measurement form 2009 to 2011, Zhai, H.Y. (2012)  found that the mean overall efficiency, pure technical efficiency and scale efficiency were growing in 2011 compared to 2010 and 2009. The equity financing efficiency of energy saving and environmental protection, new energy, new materials and IT industry increased much, while the eq- uity financing efficiency of high-end technology and equipment industry showing no growth, but was still at a high level though, and the equity financing efficiency of biological and new energy automotive industry de- creased slightly. After examined by Logit model
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In applications in the area of survival analysis, the hrf is often U-shaped or unimodal, i.e., the function is not monotonic. The regression models commonly used for survival data are the log-Weibull, monotonic failure rate, log-logistic, decreasing failure rate and unimodal functions. One of the objectives of this work is to propose a new regres- sion model, in location and scale form, called the log-power-Cauchy negative-binomial (LPCNB) regression model, which presents different failure rate functional forms. The proposed model is an alternative to the traditional extreme value (or log-Weibull), logistic and log-normal models, among others. One way to study the effect of these explanatory variables on the response variable Y is through a location-scale regression model, also known as a model of accelerated lifetime. These models consider that the response vari- able belongs to a family of distributions characterized by a location parameter and a scale parameter. Further details on this class of regression models can be found in Cox and Oakes (1984), Kalbfleisch and Prentice (2002) and Lawless (2003). In the context of sur- vival analysis, some distributions have been used to analyze censored data. For example, more recently, Cruz et al. (2016) proposed the log-odd log-logistic Weibull regression model with censored data, Lanjoni et al. (2016) defined an extended Burr XII regres- sion model and Ortega et al. (2016) introduced the odd Birnbaum-Saunders regression model with applications to lifetime data. In a similar manner, we define a location-scale regression model using the LPCNB regression model.
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