Hurdle Model Research Articles

Benthic studies adjacent to Sakhalin Island, Russia 2015 III: benthic energy density spatial models in the nearshore gray whale feeding area

Energy densities of six dominant benthic groups (Actinopterygii, Amphipoda, Bivalvia, Cumacea, Isopoda, and Polychaeta) and total prey energy were modeled for the nearshore western gray whale feeding area, Sakhalin Island, Russia, as part of a multi-disciplinary research program in the summer of 2015. Energy was modeled using generalized additive mixed models (GAMM) with accommodations for zero-inflation (logistic regression and hurdle models) and regression predictions combined with kriging to interpolate energy densities across the nearshore feeding area. Amphipoda energy density was the highest nearshore and in the south whereas Bivalvia energy density was the highest offshore and in the northern portion of the study area. Total energy was the highest in mid-range distances from shore and in the north. Amphipoda energy density was higher than minimum energy estimates defining gray whale feeding habitats (312–442 kJ/m2) in 13% of the nearshore feeding area whereas total prey energy density was higher than the minimum energy requirement in 49% of the habitat. Inverse distance-weighted interpolations of Amphipoda energy provided a broader scale representation of the data whereas kriging estimates were spatially limited but more representative of higher density in the southern portion of the study area. Both methods represented the general trend of higher Amphipoda energy density nearshore but with significant differences that highlight the value of using multiple methods to model patterns in highly complex environments.

Measuring the intensity of adoption of the system of rice intensification and improved rice seeds technologies in Geita district, Tanzania: An application of the adoption quotient and the double hurdle model approaches

The System of Rice Intensification (SRI) and Improved Rice (IRS) technologies are increasingly being disseminated to rice farmers in Tanzania to boost rice production [1, 2]. The use of these technologies is considered as an important milestone in improving rice productivity in the Country. However there remains a challenge in assessing and measuring the adoption of such technologies by farmers and their associated determinants. This study sought to apply the adoption quotient to assess the intensity of adoption of SRI and IRS technologies and examine the effects of institutional factors on the intensity of adoption using the double hurdle model. Data were collected using a structured questionnaire administered to 324 rice farmers from Nyamwilolelwa ward in Geita District, Tanzania, during the 2020 crop season. The research used cross-sectional survey method conducted and the questionnaire were administered using ODK – Kobo Collect technology. Data analysis for both, descriptive and inferential statistics was done on Stata version 14. The results from the adoption quotients estimates revealed a low adoption of SRI and IRS technologies whereby only 37.96% of rice farmers in the study area were found to have adopted the principles of SRI and IRS technologies, whereby on average the farmers adopted only 23.74% of the elements of SRI and IRS technologies. Results from the first hurdle regressions revealed that, extension visit, agriculture support, and the type of farming system, are significant in predicting the probability of adopting SRI and IRS technologies (p

Farmer adoption and intensity of use of extreme weather adaptation and mitigation strategies: evidence from a sample of Missouri farmers

Climate change and its associated weather extremes pose a threat to agriculture. To slow down climate change and reduce its associated risks, governments around the world are currently developing policies to encourage farmers to engage in adaptation and mitigation efforts. The aim of this study is to assess the adoption and intensity of use of extreme weather adaptation and mitigation strategies among a sample of Missouri farmers and to identify the factors that influence adaptation and mitigation behavior. Of particular interest is the influence of the 2019 Missouri River flooding on adaptation and mitigation efforts. An econometric hurdle model that separates the decision on whether to adopt adaptation/mitigation strategies from the decision on how many strategies to employ was used to achieve the study’s purpose. Improving field drainage or soil water retention capacity for potential flooding was found to be by far the most used adaptation. The most used mitigations were increasing use of minimum tillage, managing fertilizer, and planting cover crops. Types of crops grown, farm income, and opinions on extreme weather events were the most important determinants of both adaptation and mitigation decision. Direct experience with the 2019 Missouri River floods is found to only influence adaptation decision. Adaptation and mitigation intensity were found to be strongly influenced by opinions on government support for adaptation and CRP involvement, respectively. Directions for policy and outreach that can promote adaptation and mitigation efforts among farmers are discussed.

Bundling fertilizer trees and crops in Malawi's agro-based systems

Soil nutrient deficiency remains a significant challenge for improved agricultural productivity in the global south. Due to fast population growth and limited landholding sizes, most farmers search for affordable soil fertility enhancing options for their farms. With soaring inorganic fertilizer prices, farmers substitute inorganic fertilizer for fertilizer tree technologies in their cropping systems. Thus, understanding drivers of fertilizer trees adoption would provide requisite knowledge for State and non-State actors to promote the integration of fertilizer trees in crop farms. Therefore, this paper assessed the determinants and extent of adopting fertilizer tree technologies in agro-based systems. A Triple Hurdle model of Seemingly Unrelated Multivariate Probit and Tobit models were used to tune model parameter estimates from 962 farm households. The paper used both quantitative and qualitative analysis. The study found that seed availability, presence of technology suppliers, training, club membership, frequent extension contact, village bylaws, and household income deepens the adoption agenda. Revitalizing missing markets for agroforestry fertilizer tree seed at the community level is a plausible policy option

Maize Market Chain Analysis and the Determinants of Market Participation in the Gamo and Gofa Zones of Southern Ethiopia

The majority of farmers are producing maize in the Gamo and Gofa zones and they are not benefiting from it due to the marketing problem. Thus, this study was intended to analyze the maize market chain and determinants of market participation in the selected maize-producing districts of the Gamo and Gofa zones. To achieve this objective, multistage sampling techniques were followed to randomly select 151 sample respondents. The data were analyzed by using descriptive statistics, marketing margins, and the double hurdle model. The survey results revealed that approximately 35.88% of the maize from the total maize produced by the sampled farmers was marketed in the study area. The result indicates that among the five identified maize marketing channels, the largest volume of maize passed through channel V (producers, urban collectors, and consumers). In the marketing of maize, traders set the price due to poor market linkage and the low bargaining power of producers. The model regression result indicates that among the hypothesized factors, family size, allocated land size for maize, and market information have a significant effect on the quantity of maize market supply. Based on this finding, strengthening extension services through training and accessing inputs are recommended. Furthermore, market linkage through the cooperative establishment and the availability of market information by respective bodies is suggested.

Determinants of Displacement and Displacement Duration Following Hurricanes Katrina and Rita: A Hurdle Model Approach

In 2005, Hurricanes Katrina and Rita caused widespread destruction and displacement in parts of Louisiana, Alabama, and Mississippi. This research evaluates determinants of displacement and, conditional on being displaced, the duration of displacement for households living in areas affected by these hurricanes. Hurdle Models, which assume that different processes govern zero outcomes (i.e., no displacement) and positive outcomes (i.e., amount of time displaced), are used to model the likelihood of household displacement and its duration as a function of socioeconomic characteristics, hurricane-caused property and neighborhood damage, social support, and financial assistance. Results show that mobile home residence, marital status, educational attainment, the presence of children, and property and neighborhood damage affect the likelihood and expected length of displacement among sample respondents. Financial assistance and social support are also correlated with displacement and its duration, but endogeneity concerns complicate the interpretation of these results. The findings highlight the diversity of factors that slow households’ return following displacement and underscore the need for additional research on the role of social capital in determining hazard-related outcomes.

One or Many? Disentangling the Puzzle of Pro-Government Militia Deployment

Why do some countries harbor pro-government militias (PGMs), while others do not? We assert that the deployment of PGMs depends on topographic, social, and political structures within which governments and rebels operate. Drawing on the concept of opportunity structures, we postulate that structural conditions within which governments are embedded in constitute a contributing factor to the existence and multiplicity of PGMs. Data from the Pro-Government Militia Dataset along with a two-stage hurdle model reveal that personalist regime type and civil wars increase the likelihood of PGM emergence. In contrast, ethnic fractionalization, onshore oil fields, drug production, number of rebel groups, and military prowess influence the number of PGMs.

From staple food to market-oriented crop: commercialization level of smallholder teff (Eragrostis teff) growers in Jamma District, Ethiopia

IntroductionIn countries like Ethiopia where the selling of staple food crops is the common way of earning cash income; the concept of agricultural commercialization is never restricted to cash crops. Among the staple food crops, teff is becoming a market-oriented crop in Ethiopia. This paper investigated the challenges, opportunities, and intensity of teff commercialization in the study area.MethodsData were collected from 155 randomly selected teff growers, four focus group discussion participants encompassing both women and men farmers, and twelve key informant interviewees from the local leader, development agents, and head of the Woreda agriculture office. Data were analyzed by descriptive statistics, Value of teff sale, Crop Output Market Participation Index (COMPI), double hurdle model, and qualitative data analysis.ResultsThe average teff commercialization in terms of the value of teff sale by sample households was 6005 ETB (Ethiopian Birr). The double hurdle model result revealed that sex of the household head, application of agricultural inputs, and row sowing technology positively affected the commercialization decision of farmers in the teff output whilst the size of land allocated to teff, chemical fertilizer, row sowing technology, and frequency of contact with extension agents positively influenced the intensity of teff commercialization. Adjunct to this high input price, lack of input availability, and frost were identified as major hinders to teff production in the study area.ConclusionsThe finding of this study showed that there is a direct relationship between agricultural inputs utilization for teff and farmers’ decision to commercialize it and the level of its commercialization. Therefore, the timely provision of agricultural inputs and possible subsidization of these inputs will increase the productivity of teff since farmland expansion is unthinkable due to scarcity of land. Moreover, the District office of agriculture should collaboratively work with the nearby research centers to reduce the problem of frost by introducing a frost-resistant variety.

Environmental drivers of the occurrence and abundance of the Irukandji jellyfish (Carukia barnesi).

Understanding the links between species and their environment is critical for species management. This is particularly true for organisms of medical and/or economic significance. The ‘Irukandji’ jellyfish (Carukia barnesi) is well known for its small size, cryptic nature, and highly venomous sting. Being the namesake of the Irukandji syndrome, contact with this marine stinger often leads to hospitalization and can be fatal. Consequently, the annual occurrence of this organism is believed to cost the Australian government an estimated $AUD3 billion annually in medical costs and losses for tourism. Despite its economic importance the logistical difficulties related to surveying C.barnesi in situ has led to a paucity of knowledge regarding its ecology and significantly impeded management strategies to date. In this study, we use six years of direct C. barnesi capture data to explore patterns pertaining to the annual occurrence and abundance of this species in the nearshore waters of the Cairns coast. We provide novel insights into trends in medusae aggregations and size distribution and primarily focus on the potential role of environmental drivers for annual C. barnesi occurrence patterns. Using a two-part hurdle model, eight environmental parameters were investigated over four time periods for associations with records of medusa presence and abundance. Final models showed a small amount of variation in medusa presence and abundance patterns could be accounted for by long-term trends pertaining to rainfall and wind direction. However, the assessed environmental parameters could not explain high annual variation or site location effects. Ultimately best-fit models had very low statistical inference power explaining between 16 and 20% of the variance in the data, leaving approximately 80% of all variation in medusa presence and abundance unexplained.

Beliefs about harms of cigarette smoking among Norwegian adults born from 1899 to 1969. Do variations across education, smoking status and sex mirror the decline in smoking?

Smoking is one of the most important causes of socioeconomic disparities in morbidity and mortality. The aim of this study was to examine if beliefs about harms of smoking differed across gender, smoking status and education among Norwegian adults born between 1899 and 1969. Using data from a nationally representative survey of smoking habits and a multinomial logit/negative binomial two-stage hurdle model design, we examined (first hurdle) the associations between birth cohort, gender, education and smoking status and four beliefs about cigarette smoking: i) smoking is not harmful, ii) do not know if smoking is harmful, iii) any number of cigarettes per day (CPD) is harmful and iv) smoking more than a given nonzero number of CPD is harmful, and (second hurdle) the predicted number of CPD that could be smoked without causing harm (from outcome iv). The probability of believing that smoking was not harmful was close to zero, regardless of birth cohort, sex, education and smoking status. The probability of not knowing if smoking was harmful decreased from around 0.7 to almost zero across cohorts. The probability of believing that smoking more than zero CPD was harmful increased from less than 0.1 to around 0.7, while the probability of believing that there is some safe level of smoking increased with cohorts born from 1900 to 1930 before declining. Respondents with primary/secondary education consistently believed smoking to be less harmful compared to respondents with tertiary education, but cohort trajectories were similar. The similar birth cohort trajectories in beliefs about the harms of smoking do not support the idea that Norwegian adults with lower education has had qualitatively different beliefs about the harmfulness of smoking compared to those with higher education. The persistent and large socioeconomic gradient is likely a result of other factors.

Intra-household Gender Disparity in Private Tuition: Evidence from West Bengal

The article focuses on intra-household gender disparity in private tuition in West Bengal. By employing Engel curve framework and hurdle model with household-level data from NSS 71st Round (2014–2015), the article establishes that there is significant gender bias in favour of girls for the age group 15–20 years. This is contrary to the general perception of gender bias against girls. It has also been found that at the same age group, there is a significant difference in enrolment of girls and boys in private schools where boys are mostly enrolled in private schools. This finding suggests that girls are discriminated at the decision of formal schooling, but there is an attempt to compensate for it at a later stage when credentials become important to signal in the labour market or marriage market.

Negative emotion and nonacceptance of emotion in daily life.

Nonacceptance of emotion is consistently linked with increased levels of psychopathology and diminished well-being. Research has found that negative emotion and nonacceptance of emotion are positively associated cross-sectionally but has yet to directly investigate temporal associations between these constructs. Given that negative emotions are frequently the target of negative thoughts and other emotions, and that acceptance of emotion is associated with prospective decreases in negative emotion, we hypothesized that the temporal relation between negative emotion and nonacceptance of emotion is bidirectional. The present study examined the association between these variables during people's daily lives using an experience sampling methodology. Multilevel modeling was used for all analyses, including hierarchical generalized linear modeling and log-normal hurdle modeling. A total of 187 women from the United States and Australia reported negative emotion and nonacceptance of emotion 14 times a day for 5 days. Negative emotion and nonacceptance of emotion were positively associated contemporaneously. Across time, nonacceptance of emotion was prospectively and positively associated with the intensity of negative emotion independent of immediately prior negative emotion, and negative emotion intensity was prospectively and positively associated with nonacceptance of emotion independent of immediately prior nonacceptance. Results support a bidirectional model of negative emotion and nonacceptance of emotion wherein each variable predicts increases in the other across time. Our findings elucidate how individuals fall into maladaptive emotional patterns that are difficult to break and could possibly pave the way to the development and maintenance of psychopathology. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Intellectual Capital in Cross Border Mergers & Acquisitions: An Exaptation Perspective

Exaptation, in internationalization, is defined as the re-use of capabilities that a firm developed through domestic geographical dispersion in the process of cross border mergers and acquisitions (CBMA). This study tests the impacts of exaptation with a firm’s first and subsequent cross border mergers and acquisition engagements. The study is based on the 10 years of data from 2009 to 2019 of 99 manufacturing sector companies of Malaysia to test the relationship between the firm’s domestic geographical dispersion and chances to engage in first-time and subsequent CBMA. We applied pooled regression to estimate hurdle models. The results showed a positive and statistically significant influence of exaptation of control and coordination capabilities on the firm’s probability of engaging first-time cross-border mergers and acquisitions; however, these capabilities become irrelevant in subsequent CBMA involvement. The findings imply that firms operating in geographically dispersed business units can have higher chances of success in cross border mergers and acquisitions.

Decline, adopt or compromise? A dual hurdle model for advice utilization

Research on advice utilization often operationalizes the construct via Judge Advisor Systems (JAS), where a judge’s belief is elicited, they are provided advice, and given an opportunity to revise their belief. Belief change, or weight of advice (WOA), is measured as the shift in the judge’s belief proportional to the difference between their original belief and the advice. Several JAS studies have found WOA typically takes on a trimodal distribution, with inflation at the boundary values of 0 (indicating a judge declined advice) and 1 (adoption of advice). A dual hurdle beta model is proposed to account for these inflations. In addition to being an innovative computational model to address this methodological challenge, it also serves as a descriptive theoretical model which posits that the decision process happens in two stages: an initial discrete “choosing” stage, where the judge opts to either decline, adopt, or compromise with advice; and a subsequent continuous “averaging” stage, which occurs only if the judge opts to compromise. The approach was assessed via reanalysis of three recent JAS studies reflective of popular topics in the literature, such as algorithmic advice utilization, egocentric discounting effects, and judgmental forecasting. In each case new results were uncovered about how different correlates of advice utilization influence the decision process at either or both of the discrete and continuous stages, often in quite different ways, providing support for the descriptive theoretical model. A Bayesian graphical analysis framework is provided that can be applied to future research on advice utilization.

Addressing overdispersion and zero-inflation for clustered count data via new multilevel heterogenous hurdle models

ABSTRACT Unobserved heterogeneity causing overdispersion and the excessive number of zeros take a prominent place in the methodological development on count modeling. An insight into the mechanisms that induce heterogeneity is required for better understanding of the phenomenon of overdispersion. When the heterogeneity is sourced by the stochastic component of the model, the use of a heterogenous Poisson distribution for this part encounters as an elegant solution. Hierarchical design of the study is also responsible for the heterogeneity as the unobservable effects at various levels also contribute to the overdispersion. Zero-inflation, heterogeneity and multilevel nature in the count data present special challenges in their own respect, however the presence of all in one study adds more challenges to the modeling strategies. This study therefore is designed to merge the attractive features of the separate strand of the solutions in order to face such a comprehensive challenge. This study differs from the previous attempts by the choice of two recently developed heterogeneous distributions, namely Poisson–Lindley (PL) and Poisson–Ailamujia (PA) for the truncated part. Using generalized linear mixed modeling settings, predictive performances of the multilevel PL and PA models and their hurdle counterparts were assessed within a comprehensive simulation study in terms of bias, precision and accuracy measures. Multilevel models were applied to two separate real world examples for the assessment of practical implications of the new models proposed in this study.

Influence of Rising Water Temperature on the Temperate Seagrass Species Eelgrass (Zostera marina L.) in the Northeast USA

Sea surface temperature (SST) has increased worldwide since the beginning of the 20th century, a trend which is expected to continue. Changes in SST can have significant impacts on marine biota, including population-level shifts and alterations in community structure and diversity, and changes in the timing of ecosystem events. Seagrasses are a group of foundation species that grow in shallow coastal and estuarine systems, where they provide many ecosystem services. Eelgrass, Zostera marina L., is the dominant seagrass species in the Northeast United States of America (USA). Multiple factors have been cited for losses in this region, including light reduction, eutrophication, and physical disturbance. Warming has the potential to exacerbate seagrass loss. Here, we investigate regional changes in eelgrass presence and abundance in relation to local water temperature using monitoring data from eight sites in the Northeastern USA (New Hampshire to Maryland) where a consistent monitoring protocol, SeagrassNet, has been applied. We use a hurdle model consisting of a generalized additive mixed model (GAMM) with binomial and beta response distributions for modeling eelgrass presence and abundance, respectively, in relation to the local summer average water temperature. We show that summer water temperature one year prior to monitoring is a significant predictor of eelgrass presence, but not abundance, on a regional scale. Above average summer temperatures correspond to a decrease in probability of eelgrass presence (and increased probability of eelgrass absence) the following year. Cooler than average temperatures in the preceding year, down to approximately 0.5°C below the site average, are associated with the highest predicted probability of eelgrass presence. Our findings suggest vulnerability in eelgrass meadows of the Northeast USA and emphasize the value of unified approaches to seagrass monitoring, conservation and management at the seascape scale.

Factors affecting adoption of technical, organisational and institutional dairy innovations in selected milksheds in Kenya

ABSTRACT Technical dairy innovations (TDI), such as improved cow feeding, health management and genetic improvement, could boost milk production. At the same time, organisational and institutional dairy innovations (OIDI), including group milk sales, feed and credit access, could boost dairy supply chain efficiency. This study examined the TDI adoption determinants and the OIDI adoption intensity. Data were collected from 1146 farmers (410, 382 and 354 in the milksheds of Mukurweini Wakulima Dairy Limited [MWDL], Happy Cow Limited [HCL] and New Kenya Co-operative Creameries [NKCC], respectively) and analysed using a double hurdle model. Access to credit positively influenced the TDI adoption in the three milksheds. Adoption of TDI was influenced by hired employees, dairy records, total dairy cows and household head education. The empirical evidence from the study supports the observation that OIDI adoption intensity is influenced by income, farm size, dairy records, and dairy information access. To boost TDI adoption, the dairy development partners should link cooperative society members with agricultural credit lenders. Additionally, the dissemination of dairy information to farmers by the dairy stakeholders could spur TDI adoption, while providing dairy information and training farmers on dairy record keeping should be promoted to boost TDI and OIDI adoption.

Determinants of Teff Row Planting Technology Adoption: The Case of North Shewa Zone, Oromia National Regional State, Ethiopia

Row planting is one of the technologies introduced in Ethiopia to improve production and productivity of the major crops. However, the rate of adopting the technology decline from time to time. Thus, this study aims to identify factors affecting adoption level and intensity use of Teff row planting technology in the selected districts of North Shewa Zone, Ethiopia. Multi-stage random sampling techniques were used to select 400 respondents. Adoption index, independent sample mean t-test, chi-square test and double hurdle model were used for data analysis. The results of adoption index reveals that among 400 sample households, 79.8% was non-adopter while 20.2% were adopter of Teff row planting technology. A total of 10 variables were hypothesized to affect the adoption level and intensity use of Teff row planting technology in the study area. Among these, 6 variables had significant effect on adoption level of Teff row planting technology while 4 variables had significant effect on the intensity use of Teff row planting technology. Accordingly, the experience of household in Teff production, education level of household head, family size, extension contact, credit utilization and demonstration site visit had positive and significant effect on the adoption level of Teff row planting technology adoption at 1, 1, 5, 1, 1 and 1% significance level respectively. Moreover, family size, education level of household head, frequency of extension contacts and demonstration site visit had positive and significant effect on the intensity use of Teff row planting technology at 10, 1, 1 and 1% significant level respectively. Hence, in order to increase the households’ adoption level and intensity use of Teff row planting technology in the study area, strengthening the extension services, improving the education level of the households, strengthening the credit services and expanding the demonstration site should be the focus area of the policy makers.

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.

Sayma Verileri ile Kantil Regresyon: Aşırı Yayılım Veri Örneği

Sayma modellerinde klasik regresyon varsayımları sağlanamamaktadır. Bu nedenle sayma verileri için Poisson ve negatif binom dağılım en bilinen yöntemlerdir. Poisson model eşit yayılım durumunda, negatif binom dağılım aşırı yayılım durumunda kullanılabilir. Uygulamada veriler genellikle aşırı yayılım göstermektedir. Eğer sayma verilerinde fazla sıfır değerli varsa eşit yayılım durumunda zero-inflated Poisson, aşırı yayılım durumunda zero-inflated negatif binom modelleri, Poisson Hurdle ve negatif binom Hurdle modelleri veya bunların genelleştirilmiş modelleri tercih edilebilir. Bu modeller genel olarak bağımlı değişkenin koşullu ortalamasını modellemeye odaklanır. Ancak koşullu ortalama regresyon modelleri, bağımlı değişkenin aykırı değerlerine duyarlı olabilir ya da diğer koşullu dağılım özellikleri hakkında hiçbir bilgi sağlamayabilir. Bu durumda sayma verileri için sağlam yöntemlerden olan kantil regresyon kullanılabilir. Kantil regresyon aykırı değerlerin varlığında sağlam tahmin avantajlarına sahiptir. Bu makalede bağımlı değişken sayma verilerinden oluşan makale sayısıdır. Bağımsız değişkenler cinsiyet, evli olup olmadığı, 5 yaşının altında çocuk sayısı, doktora prestiji ve danışmanın son 3 yıldaki makale sayısı değişkenlerinden oluşmaktadır. Çalışmada Poisson ve negatif binom dağılım uygulandıktan sonra %25, %50, %75 ve %90 kantil regresyon tahminleri elde edilmiştir.