Dissertations / Theses on the topic 'Zero-inflated negative binomial regression'

The classical Poisson, geometric and negative binomial regression models for count data belong to the family of generalized linear models and are available at the core of the statistics toolbox in the R system for statistical computing. After reviewing the conceptual and computational features of these methods, a new implementation of hurdle and zero-inflated regression models in the functions hurdle() and zeroinfl() from the package pscl is introduced. It re-uses design and functionality of the basic R functions just as the underlying conceptual tools extend the classical models. Both hurdle and zero-inflated model, are able to incorporate over-dispersion and excess zeros-two problems that typically occur in count data sets in economics and the social sciences-better than their classical counterparts. Using cross-section data on the demand for medical care, it is illustrated how the classical as well as the zero-augmented models can be fitted, inspected and tested in practice. (authors' abstract)

The objective of this project is to fit a sequence of increasingly complex zero-inflated censored regression models to a known data set. It is quite common to find censored count data in statistical analyses of health-related data. Modeling such data while ignoring the censoring, zero-inflation, and overdispersion often results in biased parameter estimates. This project develops various regression models that can be used to predict a count response variable that is affected by various predictor variables. The regression parameters are estimated with Bayesian analysis using a Markov chain Monte Carlo (MCMC) algorithm. The tests for model adequacy are discussed and the models are applied to an observed data set.

The classical Poisson, geometric and negative binomial regression models for count data belong to the family of generalized linear models and are available at the core of the statistics toolbox in the R system for statistical computing. After reviewing the conceptual and computational features of these methods, a new implementation of zero-inflated and hurdle regression models in the functions zeroinfl() and hurdle() from the package pscl is introduced. It re-uses design and functionality of the basic R functions just as the underlying conceptual tools extend the classical models. Both model classes are able to incorporate over-dispersion and excess zeros - two problems that typically occur in count data sets in economics and the social and political sciences - better than their classical counterparts. Using cross-section data on the demand for medical care, it is illustrated how the classical as well as the zero-augmented models can be fitted, inspected and tested in practice. (author's abstract)
Series: Research Report Series / Department of Statistics and Mathematics

“Vision Zero,” first adopted by Sweden in 1997, is a road safety policy that aims to achieve a transportation system having zero fatalities or serious injuries for all modes of transportation. It takes a proactive approach to road safety system by identifying risk and taking steps to prevent injuries. Historically, traffic related crashes have disproportionately impacted vulnerable communities and system users including people of color, low income individuals, seniors, children, and pedestrians, bicyclists, and transit users (who typically walk to and from public transport). These inequities are addressed in the Vision Zero framework by prioritizing interventions in areas that need safety improvements the most. In 2016, the Alexandria City Council voted unanimously to develop a “Vision Zero” policy and program as a part of its updated transportation master plan. It required an initial equity analysis to assess the impact of traffic crashes on the traditionally underserved communities / groups (groups from at least one of these categories: low-income; minority; elderly; children; limited English proficiency; persons with disabilities; and/or pedestrians/ bicyclists/ transit users). This study combines three different methods to investigate the equity issues regarding traffic safety: 1) descriptive analysis of the spatial pattern of crashes and their relationship with the demographic profiles of neighborhoods at census block group level (for 2010-2014 period); 2) descriptive analysis of the crash trends in Alexandria; and 3) exploratory regression analyses for two different units of analysis (an aggregate regression analysis of crashes at census block group, and a disaggregate regression analysis of the individual level crash reports of traffic crashes). The analysis found that the elderly, school aged children, rail/subway users, and pedestrians had a higher risk of fatalities and severe injuries in traffic crashes. Higher job densities, alcohol impairment, and speeding were significantly related to higher KSI, whereas, smaller block sizes (higher number of street segments per sq. mile area of census block group), higher housing density, and use of safety equipment were related to lower KSI.
Master of Urban and Regional Planning
“Vision Zero,” first adopted by Sweden in 1997, is a road safety policy that aims to achieve a transportation system having zero fatalities or serious injuries for all modes of transportation. It takes a proactive approach to road safety system by identifying risk and taking steps to prevent injuries. Historically, traffic related crashes have disproportionately impacted vulnerable communities and system users including people of color, low income individuals, seniors, children, and pedestrians, bicyclists, and transit users (who typically walk to and from public transport). These inequities are addressed in the Vision Zero framework by prioritizing interventions in areas that need safety improvements the most. In 2016, the Alexandria City Council voted unanimously to develop a “Vision Zero” policy and program as a part of its updated transportation master plan. It required an initial equity analysis to assess the impact of traffic crashes on the traditionally underserved communities / groups (groups from at least one of these categories: low-income; minority; elderly; children; limited English proficiency; persons with disabilities; and/or pedestrians/ bicyclists/ transit users). This study combines three different methods to investigate the equity issues regarding traffic safety: 1) descriptive analysis of the spatial pattern of crashes and their relationship with the demographic profiles of neighborhoods at census block group level (for 2010-2014 period); 2) descriptive analysis of the crash trends in Alexandria; and 3) exploratory regression analyses for two different units of analysis (an aggregate regression analysis of crashes at census block group, and a disaggregate regression analysis of the individual level crash reports of traffic crashes). The analysis found that the elderly, school aged children, rail/subway users, and pedestrians had a higher risk of fatalities and severe injuries in traffic crashes. Higher job densities, alcohol impairment, and speeding were significantly related to higher KSI, whereas, smaller block sizes (higher number of street segments per sq. mile area of census block group), higher housing density, and use of safety equipment were related to lower KSI.

Syftet med uppsatsen är att försöka förklara vad det är som påverkar tiden som en mamma ammar. För att undersöka vad det är som påverkar tiden som en mamma ammar, har en Zero inflated negative binomial-modell (ZINB-modell) tagits fram. Resultaten visar att det som avgör hur länge en mamma kommer att amma är: Graviditetens längd, mammans ålder, mammans rökvanor under graviditetens sista månader, mammans rökvanor samt mammans nationella ursprung.

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Financiadora de Estudos e Projetos
The chemical induction of carcinogens in chemopreventive animal experiments is becoming increasingly frequent in biological research. The purpose of these biological experiments is to evaluate the effect of a particular treatment on the rate of tumors incidence in animals. In this work, the number of promoted tumors per animal will be parametrically modeled following the suggestions given by Kokoska (1987) and Freedman et al. (1993). The study of these chemopreventive experiments will be presented in the context of the destructive model proposed by Rodrigues et al. (2010) with terminal variable that allows or censures the experiment at time of the animal death. Since the data analyzed in this field are subject to excess of zeros (Freedman et al. (1993)), we propose for the number of promoted tumors a negative binomial distribution (NB), a zero-inflated Poisson distribution (ZIP), and a zero-inflated Negative Binomial distribution (ZINB). The selection of these models will be made through the likelihood ratio test and the AIC, BIC criteria. The estimation of its parameters will be obtained by using the method of maximum likelihood, and further simulation studies will also be realized. As a future proposition to finalize this project, it is suggested the Bayesian methodology as an alternative to the method of maximum likelihood via the EM algorithm.
A indução química de substâncias cancerígenas em experimentos quimiopreventivos em animais é cada vez mais frequente em pesquisas biológicas. O objetivo destes experimentos biológicos é avaliar o efeito de um determinado tratamento na taxa de incidência de tumores em animais. Neste trabalho o número de tumores promovidos por animal será modelado parametricamente seguindo as sugestões dadas por Kokoska (1987) e por Freedman et al. (1993). O estudo desses experimentos quimiopreventivos será apresentado no contexto do modelo destrutivo proposto por Rodrigues et al. (2010) com variável terminal que condiciona ou censura o experimento no instante de morte do animal. Os dados analisados possuem uma grande quantidade de zeros, portanto será proposto para o número de tumores promovidos as seguintes distribuições: binomial negativa, a distribuição de Poisson com zeros inflacionados e a distribuição binomial negativa com zeros inflacionados. A seleção destes modelos será feita através do teste da razão de verossimilhança e os critérios AIC, BIC. As estimativas dos respectivos parâmetros serão obtidas utilizando o método de máxima verossimilhança e serão feitos estudos de simulação. Para continuar este projeto, a proposta futura é utilizar a metodologia Bayesiana como alternativa ao método de máxima verossimilhança via algoritmo EM.

This thesis develops two variant statistical models for count data based upon compound models for contexts when the counts may be viewed as derived from two generations, which may or may not be independent. Unlike standard compound models, the variants model the sum of both generations. We consider cases where both generations are negative binomial or one is Poisson and the other is negative binomial. The first variant, denoted SVA, follows a zero restriction, where a zero in the first generation will automatically be followed by a zero in the second generation. The second variant, denoted SVB, is a convolution model that does not possess this zero restriction. The main properties of the SVA and SVB models are outlined and compared with standard compound models. The results show that the SVA distributions are similar to standard compound distributions for some fixed parameters. Comparisons of SVA, Poisson hurdle, negative binomial hurdle and their zero-inflated counterpart using simulated SVA data indicate that different models can give similar results, as the generating models are not always selected as the best fitting. This thesis focuses on the use of the variant models to model citation counts. We show that the SVA models are more suitable for modelling citation data than other previously used models such as the negative binomial model. Moreover, the application of SVA and SVB models may be used to describe the citation process. This thesis also explores model selection techniques based on log-likelihood methods, Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). The suitability of the models is also assessed using two diagrammatic methods, randomised quantile residual plots and Christmas tree plots. The Christmas tree plots clearly illustrate whether the observed data are within fluctuation bounds under the fitted model, but the randomised quantile residual plots utilise the cumulative distribution, and hence are insensitive to individual data values. Both plots show the presence of citation counts that are larger than expected under the fitted model in the data sets.

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This work has as central theme the Inflated Modified Power Series Distributions, where the objective is to study its main properties and the applicability in the bayesian context. This class of models includes the generalized Poisson, binomial and negative binomial distributions. These probability distributions are very helpful to models discrete data with inflated values. As particular case the - zero inflated Poisson models (ZIP) is studied, where the main purpose was to verify the effectiveness of it when compared to the Poisson distribution. The same methodology was considered for the negative binomial inflated distribution, but comparing it with the Poisson, negative binomial and ZIP distributions. The Bayes factor and full bayesian significance test were considered for selecting models.
Este trabalho tem como tema central a classe de distribuições série de potências inflacionadas, em que o intuito é estudar suas principais propriedades e a aplicabilidade no contexto bayesiano. Esta classe de modelos engloba as distribuições de Poisson, binomial e binomial negativa simples e as generalizadas e, por isso é muito aplicada na modelagem de dados discretos com valores excessivos. Como caso particular propôs-se explorar a distribuição de Poisson zero inflacionada (ZIP), em que o objetivo principal foi verificar a eficácia de sua modelagem quando comparada à distribuição de Poisson. A mesma metodologia foi considerada para a distribuição binomial negativa inflacionada, mas comparando-a com as distribuições de Poisson, binomial negativa e ZIP. Como critérios formais para seleção de modelos foram considerados o fator de Bayes e o teste de significância completamente bayesiano.

The gravity model for international trade is one of the most successful empirical models in trade literature. There is a long tradition to log-linearise the multiplicative model and to estimate the parameters of interest by least squares. But this practice is inappropriate for several reasons. First of all, bilateral trade flows are frequently zero and disregarding countries that do not trade with each other produces biased results. Second, log-linearisation in the presence of heteroscedasticity leads to inconsistent estimates in general. In recent years, the Poisson gravity model along with pseudo maximum likelihood estimation methods have become popular as a way of dealing with such econometric issues as arise when dealing with origin-destination flows. But the standard Poisson model specification is vulnerable to problems of overdispersion and excess zero flows. To overcome these problems, this paper presents zero-inflated extensions of the Poisson and negative binomial specifications as viable alternatives to both the log-linear and the standard Poisson specifications of the gravity model. The performance of the alternative model specifications is assessed on a real world example, where more than half of country-level trade flows are zero. (authors' abstract)
Series: Working Papers in Regional Science

Changes in the abundance and distribution of free (drinking) water can influence wildlife in arid regions. In the western USA, free water is considered by wildlife managers to be important for bighorn sheep (Ovis canadensis), elk (Cervus elaphus), mule deer (Odocoileus hemionus), and pronghorn (Antilocapra americana). Nonetheless, we lack information on the influence of habitat and landscape features surrounding water sources, including wildlife water developments, and how these features may influence use of water by sexes differently. Consequently, a better understanding of differential use of water by the sexes could influence the conservation and management of those ungulates and water resources in their habitats. We deployed remote cameras at water sources to document water source use. For mule deer specifically, we monitored all known water sources on one mountain range in western Utah, during summer from 2007 to 2011 to document frequency and timing of water use, number of water sources used by males and females, and to estimate population size from individually identified mule deer. Male and female mule deer used different water sources but visited that resource at similar frequencies. On average, mule deer used 1.4 water sources and changed water sources once per summer. Additionally, most wildlife water developments were used by both sexes. We also randomly sampled 231 water sources with remote cameras in a clustered-sampling design throughout Utah in 2006 and from 2009 to 2011. In association with camera sampling at water sources, we measured several site and landscape scale features around each water source to identify patterns in ungulate use informative for managers. We used model selection to identify features surrounding water sources that were related to visitation rates for male and female bighorn sheep, elk, mule deer, and pronghorn. Top models for each species were different, but supported models for males and females of the same species generally included similar covariates, although with varying strengths. Our results highlight the differing use of water sources by the sexes. This information will help guide managers when siting and reprovisioning wildlife water developments meant to benefit those species, and when prioritizing natural water sources for preservation or enhancement.

Este trabajo presenta dos líneas de investigación desarrolladas en los últimos años en torno a la etapa de evaluación en datos de recuento. Los campos de estudio han sido: los datos de recuento, concretamente el estudio del modelo de regresión de Poisson y sus extensiones y la etapa de evaluación como punto de inflexión en el proceso de modelado estadístico. Los resultados obtenidos ponen de manifiesto la importancia de aplicar el modelo adecuado a las características de los datos así como de evaluar el ajuste del mismo. Por otra parte la comparación de pruebas, índices, estimadores y modelos intentan señalar la adecuación o la preferencia de unos sobre otros en determinadas circunstancias y en función de los objetivos del investigador.
This paper presents two lines of research that have been developed in recent years on the evaluation stage in count data. The areas of study have been both count data, specifically the study of Poisson regression modelling and its extension, and the evaluation stage as a point of reflection in the statistical modelling process. The results obtained demonstrate the importance of applying appropriate models to the characteristics of data as well as evaluating their fit. On the other hand, comparisons of trials, indices, estimators and models attempt to indicate the suitability or preference for one over the others in certain circumstances and according to research objectives.

This dissertation examines the ways international research collaboration affects the ability of Colombian research teams to produce bibliographic outputs, and to contribute to local knowledge. Research hypotheses are tested using Zero Inflated Negative Binomial Regression models to account for the effects of international research collaboration on team output while controlling for team characteristics, partner characteristics, scientific discipline, sector, the characteristics of the teams' home institution, and team location. The study uses control groups and the Propensity Score Matching approach to assess the overall impact of international research collaboration on research team performance while controlling for the effects of endogeneity and selection bias. Results show that international research collaboration is positively associated with both team output and teams' ability to contribute to local knowledge. The study shows that such effects depend on the type of collaboration chosen and the type of partner involved. Particularly, it shows that while co-authoring with colleagues located overseas or receiving foreign funding positively affects team performance, hosting foreign researchers does not seem to affect a team's productivity or its ability to contribute to local knowledge once all other variables are held constant. It also finds that collaborating with partners from the South yields greater productivity counts than collaborating with partners from the North, but that collaboration with partners from northern countries is strongly associated with a team's ability to contribute to local knowledge, while collaboration with partners from southern countries is not. Theoretical and policy implications of these and other counterintuitive findings are discussed.

Network screening and countermeasure selection are two crucial steps in the highway improvement process. In network screening, potential improvement locations are ranked and prioritized based on a specific method with a set of criteria. The most common practice by transportation agencies has been to use a simple scoring method, which, in general, weighs and scores each criterion and then ranks the locations based on their relative overall scoring. The method does not deal well with criteria that are qualitative in nature, nor does it account for the impacts of correlation among the criteria. The introduction of Analytic Hierarchy Process (AHP) provides agencies with a method to include both quantitative and qualitative criteria. However, it does not address the issue on correlation. This dissertation explores the use of both Analytic Network Process (ANP) and Fuzzy Analytic Network Process (FANP) for their potential capabilities to address both issues. Using urban four-lane divided highways in Florida for bicycle safety improvements, both ANP and FANP were shown to provide more reasonable rankings than AHP, with FANP providing the best results among the methods. After the locations are ranked and prioritized for improvements, the next step is to evaluate the potential countermeasures for improvements at the selected top-ranked locations. In this step, the standard practice has been to use Crash Modification Factors (CMFs) to quantify the potential impacts from implementing specific countermeasures. In this research, CMFs for bicycle crashes on urban facilities in Florida were developed using the Generalized Linear Model approach with a Zero-Inflated Negative Binomial (ZINB) distribution. The CMFs were tested for their spatial and temporal transferability and the results show only limited transferability both spatially and temporally. The CMFs show that, in general, wider lanes, lower speed limits, and presence of vegetation in the median reduce bicycle crashes, while presence of sidewalk and sidewalk barrier increase bicycle crashes. The research further considered bicycle exposure using the bicycle activity data from the Strava smartphone application. It was found that increased bicycle activity reduces bicycle crash probabilities on segments but increases bicycle crash probabilities at signalized intersections. Also, presence of bus stops and use of permissive signal phasing at intersections were found to increase bicycle crash probabilities.

Dissertação de mestrado em Estatística
Os modelos de regressão para dados de contagem são muito utilizados nas mais variadas áreas de estudo para a modelação de fenómenos. Estes modelos integram um quadro especial de metodologias devido ao facto de a variável resposta tomar apenas valores inteiros não negativos. A distribuição de Poisson é a mais conhecida, e a mais utilizada para modelar dados de contagem, no entanto sempre que existe sobredispersão, torna-se necessário recorrer a outras distribuições, nomeadamente à distribuição Binomial Negativa. Outro problema comum nos dados de contagem é o excesso de zeros na variável resposta. Os modelos de regressão de zeros inflacionados são amplamente usados para modelar esse tipo de dados. Estes modelos modelam as contagens como uma mistura de duas distribuições com dois processos subjacentes, um que trata do excesso de zeros modelado por uma massa pontual, e um outro que trata das contagens sendo modelado por uma distribuição de Poisson ou Binomial Negativa. Neste trabalho pretendeu-se estudar os modelos de regressão para dados de contagem e a sua aplicação a dados bancários relativos a clientes a quem foi garantido crédito de consumo por um banco. Tem como principal objetivo estudar a relação do número de não pagamento da prestação do empréstimo de um cliente em função das caracteristicas do cliente e do contrato. Em particular, foram ajustados os modelos de regressão de Poisson, modelos de regressão Binomial Negativa, modelos de regressão de Poisson de zeros inflacionados e modelos de regressão binomial negativa de zeros inflacionados utilizando o algoritmo EM para obter as estimativas de máxima verosimilhança dos parâmetros. Os resultados obtidos mostraram que os modelos de regressão de zeros inflacionados apresentam um melhor ajustamento, quando comparados com os modelos que não têm em consideração o excesso de zeros. Mostraram ainda que os modelos baseados na distribuição Binomial Negativa, são os mais adequados para modelar estes dados, em vez dos modelos baseados na distribuição de Poisson.
Regression models for count data are highly used in several areas of study for modelation of phenomena. These models feature a special methodological board that comes from the fact that the response variable just takes non-negative integer values. The Poisson distribution is the most recognized and most widely used to model count data, however when there is overdispersion, it becomes necessary the use other distributions, as so, including negative binomial distribution. Another common problem in count data, is the excess of zeros in the response variable. Zero inflated regression models are widely used to model this type of data. These models model the counts as a mixture of two distributions with two underlying processes, one that deals with excess of zeros modeled by a pontual mass, and another one that handles the counts by being modelated by a Poisson or Negative Binomial distributions. In this work we intended to study regression models for count data and its application on bank data clients to whom it was granted consumption credit by a bank. Its main objective is to study the relationship of the number of non payment of the installment of a client depending on the characteristics of client and the contract. In particular, we fit the Poisson regression models, negative binomial regression models, zero inflated Poisson regression models and negative binomial regression models for zero inflated using the EM algorithm to obtain maximum likelihood estimates of the parameters. The results showed that zero inflated regression models have a better fit compared with models that do not take into account the extra zeros. Also showed that models based on the negative binomial distribution, are more suitable for modeling this data instead of models based on Poisson distribution.

We assessed how estimates of need-expected inpatient hospital use differ depending on whether need-expected use was estimated for a population of all Canadians, Canadian health regions, or a subpopulation of higher income Canadians, who likely had minimal healthcare access problems. Data came from the 2009/2010 Canadian Community Health Survey, a national cross-sectional survey. Using zero-inflated negative binomial regression, we modeled inpatient hospital use separately based on the three aforementioned choices of population. We adjusted for demographic, health behaviour, health status, socioeconomic, and health care supply factors. We then estimated need-expected inpatient hospital use and compared the estimates across individuals and by income and province. The three choices of population that we used in this study had similar results. Our estimates of the average need-expected use by province or income group were not sensitive to the choice of population used to estimate need-expected use.

碩士
國立臺灣科技大學
工業管理系
105
Microbiological testing is an important task in the food industry. Pathogenic microorganism contaminates the food material as clusters or group of individuals cells. The bacteria follows a zero-inflated Negative Binomial (ZINB) distribution in the entire food material. A double sampling plan (DSP) is developed for an ZINB distribution. We also provide R-code to determine the plan parameters such as the number of sample size, the acceptance number, and the rejection number on the first stage (n1, c1, and r1), and the number of the sample size and the acceptance number on the second stage (n2 and c2). Under given value of (acceptable quality level (AQL), lot tolerance percent defects (LTPD) two risk α and β. Simulated data with various of parameters (φ,p_1,α,p_2,β) are used to illustrate the applications.

Les données comptées (count data) possèdent des distributions ayant des caractéristiques particulières comme la non-normalité, l’hétérogénéité des variances ainsi qu’un nombre important de zéros. Il est donc nécessaire d’utiliser les modèles appropriés afin d’obtenir des résultats non biaisés. Ce mémoire compare quatre modèles d’analyse pouvant être utilisés pour les données comptées : le modèle de Poisson, le modèle binomial négatif, le modèle de Poisson avec inflation du zéro et le modèle binomial négatif avec inflation du zéro. À des fins de comparaisons, la prédiction de la proportion du zéro, la confirmation ou l’infirmation des différentes hypothèses ainsi que la prédiction des moyennes furent utilisées afin de déterminer l’adéquation des différents modèles. Pour ce faire, le nombre d’arrestations des membres de gangs de rue sur le territoire de Montréal fut utilisé pour la période de 2005 à 2007. L’échantillon est composé de 470 hommes, âgés de 18 à 59 ans. Au terme des analyses, le modèle le plus adéquat est le modèle binomial négatif puisque celui-ci produit des résultats significatifs, s’adapte bien aux données observées et produit une proportion de zéro très similaire à celle observée.
Count data have distributions with specific characteristics such as non-normality, heterogeneity of variances and a large number of zeros. It is necessary to use appropriate models to obtain unbiased results. This memoir compares four models of analysis that can be used for count data: the Poisson model, the negative binomial model, the Poisson model with zero inflation and the negative binomial model with zero inflation. For purposes of comparison, the prediction of the proportion of zero, the confirmation or refutation of the various assumptions and the prediction of average number of arrrests were used to determine the adequacy of the different models. To do this, the number of arrests of members of street gangs in the Montreal area was used for the period 2005 to 2007. The sample consisted of 470 men, aged 18 to 59 years. After the analysis, the most suitable model is the negative binomial model since it produced significant results, adapts well to the observed data and produces a zero proportion very similar to that observed.