diff --git a/docs/compois.bib b/docs/compois.bib index 1420bfa59b05af7efd413753e53282f8b0376258..e01a1e985019550e40028b4bb5da916373876417 100644 --- a/docs/compois.bib +++ b/docs/compois.bib @@ -1,54 +1,47 @@ -@article{Daly2015, -abstract = {The Conway-Maxwell-Poisson (CMP) distribution is a natural two-parameter generalisation of the Poisson distribution which has received some attention in the statistics literature in recent years by offering flexible generalisations of some well-known models. In this work, we begin by establishing some properties of both the CMP distribution and an analogous generalisation of the binomial distribution, which we refer to as the CMB distribution. We also consider some convergence results and approximations, including a bound on the total variation distance between a CMB distribution and the corresponding CMP limit.}, -archivePrefix = {arXiv}, -arxivId = {1503.07012v1}, -author = {Daly, Fraser and Gaunt, Robert E.}, -eprint = {1503.07012v1}, -file = {:home/eduardojr/Dropbox/Articles/compois/ComPoisson\_theory.pdf:pdf}, -keywords = {60e05,60e15,60f05,62e10,Com-poisson,ams 2010 subject classification,and phrases,cmb distribution,conway-maxwell-poisson distribution,distributional transforms,s method,stein,stochas-,tic ordering}, -mendeley-tags = {Com-poisson}, -month = mar, -number = {March}, -pages = {1--24}, -title = {{The Conway-Maxwell-Poisson distribution: distributional theory and approximation}}, -url = {http://arxiv.org/abs/1503.07012}, -volume = {44}, -year = {2015} -} -@misc{Dunn2012, -author = {Dunn, Jeffrey}, -file = {:home/eduardojr/Dropbox/Articles/compois/Rpackage\_compoisson.pdf:pdf}, -publisher = {R package version 0.3}, -title = {{compoisson: Conway-Maxwell-Poisson Distribution}}, -url = {http://cran.r-project.org/package=compoisson}, +@phdthesis{Borges2012, +author = {Borges, Patrick}, +file = {:home/eduardo/Documents/Mendeley Desktop/4552.pdf:pdf}, +mendeley-groups = {TCC{\_}UFPR{\_}2015}, +school = {Universidade Federal de S{\~{a}}o Carlos}, +title = {{Novos modelos de sobreviv{\^{e}}ncia com fra{\c{c}}{\~{a}}o de cura baseados no processo da carcinog{\^{e}}nese}}, year = {2012} } -@article{Lord2006, -abstract = {There has been considerable research conducted on the development of statistical models for predicting crashes on highway facilities. Despite numerous advancements made for improving the estimation tools of statistical models, the most common probabilistic structure used for modeling motor vehicle crashes remains the traditional Poisson and Poisson-gamma (or Negative Binomial) distribution; when crash data exhibit over-dispersion, the Poisson-gamma model is usually the model of choice most favored by transportation safety modelers. Crash data collected for safety studies often have the unusual attributes of being characterized by low sample mean values. Studies have shown that the goodness-of-fit of statistical models produced from such datasets can be significantly affected. This issue has been defined as the "low mean problem" (LMP). Despite recent developments on methods to circumvent the LMP and test the goodness-of-fit of models developed using such datasets, no work has so far examined how the LMP affects the fixed dispersion parameter of Poisson-gamma models used for modeling motor vehicle crashes. The dispersion parameter plays an important role in many types of safety studies and should, therefore, be reliably estimated. The primary objective of this research project was to verify whether the LMP affects the estimation of the dispersion parameter and, if it is, to determine the magnitude of the problem. The secondary objective consisted of determining the effects of an unreliably estimated dispersion parameter on common analyses performed in highway safety studies. To accomplish the objectives of the study, a series of Poisson-gamma distributions were simulated using different values describing the mean, the dispersion parameter, and the sample size. Three estimators commonly used by transportation safety modelers for estimating the dispersion parameter of Poisson-gamma models were evaluated: the method of moments, the weighted regression, and the maximum likelihood method. In an attempt to complement the outcome of the simulation study, Poisson-gamma models were fitted to crash data collected in Toronto, Ont. characterized by a low sample mean and small sample size. The study shows that a low sample mean combined with a small sample size can seriously affect the estimation of the dispersion parameter, no matter which estimator is used within the estimation process. The probability the dispersion parameter becomes unreliably estimated increases significantly as the sample mean and sample size decrease. Consequently, the results show that an unreliably estimated dispersion parameter can significantly undermine empirical Bayes (EB) estimates as well as the estimation of confidence intervals for the gamma mean and predicted response. The paper ends with recommendations about minimizing the likelihood of producing Poisson-gamma models with an unreliable dispersion parameter for modeling motor vehicle crashes. ?? 2006 Elsevier Ltd. All rights reserved.}, -author = {Lord, Dominique}, -doi = {10.1016/j.aap.2006.02.001}, -file = {:home/eduardojr/Dropbox/Articles/compois/PoissonGamma\_Motor.pdf:pdf}, -isbn = {0001-4575}, -issn = {00014575}, -journal = {Accident Analysis and Prevention}, -keywords = {Com-poisson,Empirical Bayes,Low sample mean values,Poisson-gamma,Small sample size,Statistical models}, -mendeley-tags = {Com-poisson}, -number = {4}, -pages = {751--766}, -pmid = {16545328}, -title = {{Modeling motor vehicle crashes using Poisson-gamma models: Examining the effects of low sample mean values and small sample size on the estimation of the fixed dispersion parameter}}, -volume = {38}, -year = {2006} +@article{Conway1962, +author = {Conway, Richard W and Maxwell, William L}, +journal = {Journal of Industrial Engineering}, +mendeley-groups = {TCC{\_}UFPR{\_}2015}, +pages = {132----136}, +title = {{A queuing model with state dependent service rates}}, +volume = {12}, +year = {1962} +} +@article{King1989, +abstract = {This paper discusses the problem of variance specification in models for event count data. Event counts are dependent variables that can take on only nonnegative integer values, such as the number of wars or coups d'etat in a year. I discuss several generalizations of the Poisson regression model, presented in King (1988), to allow for substantively interesting stochastic processes that do not fit into the Poisson framework. Individual models that cope with, and help analyze, heterogeneity, contagion, and negative contagion are each shown to lead to specific statistical models for event count data. In addition, I derive a new generalized event count (GEC) model that enables researchers to extract significant amounts of new information from existing data by estimating features of these unobserved substantive processes. Applications of this model to congressional challenges of presidential vetoes and superpower conflict demonstrate the dramatic advantages of this approach.}, +author = {King, Gary}, +doi = {10.2307/2111071}, +file = {:home/eduardo/Documents/Mendeley Desktop/King - 1989 - Variance Specification in Event Count Models From Restrictive Assumptions to a Generalized Estimator.pdf:pdf}, +isbn = {00925853}, +issn = {00925853}, +journal = {American Journal of Political Science}, +mendeley-groups = {TCC{\_}UFPR{\_}2015}, +month = {aug}, +number = {3}, +pages = {762--784}, +title = {{Variance specification in event count models: from restrictive assumptions to a generalized estimator}}, +url = {http://www.jstor.org/stable/2111071}, +volume = {33}, +year = {1989} } @article{Lord2010, abstract = {The objective of this article is to evaluate the performance of the COM-Poisson GLM for analyzing crash data exhibiting underdispersion (when conditional on the mean). The COM-Poisson distribution, originally developed in 1962, has recently been reintroduced by statisticians for analyzing count data subjected to either over- or underdispersion. Over the last year, the COM-Poisson GLM has been evaluated in the context of crash data analysis and it has been shown that the model performs as well as the Poisson-gamma model for crash data exhibiting overdispersion. To accomplish the objective of this study, several COM-Poisson models were estimated using crash data collected at 162 railway-highway crossings in South Korea between 1998 and 2002. This data set has been shown to exhibit underdispersion when models linking crash data to various explanatory variables are estimated. The modeling results were compared to those produced from the Poisson and gamma probability models documented in a previous published study. The results of this research show that the COM-Poisson GLM can handle crash data when the modeling output shows signs of underdispersion. Finally, they also show that the model proposed in this study provides better statistical performance than the gamma probability and the traditional Poisson models, at least for this data set.}, author = {Lord, Dominique and Geedipally, Srinivas Reddy and Guikema, Seth D.}, doi = {10.1111/j.1539-6924.2010.01417.x}, -file = {:home/eduardojr/Dropbox/Articles/compois/ComPoisson\_traffic.pdf:pdf}, +file = {:home/eduardo/Documents/Mendeley Desktop/Lord, Geedipally, Guikema - 2010 - Extension of the application of conway-maxwell-poisson models Analyzing traffic crash data exhibiting.pdf:pdf}, isbn = {1539-6924 (Electronic) 0272-4332 (Linking)}, issn = {02724332}, journal = {Risk Analysis}, keywords = {Com-poisson,Conway-Maxwell-Poisson,gamma models,negative binomial models,regression models,underdispersion}, +mendeley-groups = {TCC{\_}UFPR{\_}2015}, mendeley-tags = {Com-poisson}, number = {8}, pages = {1268--1276}, @@ -57,31 +50,25 @@ title = {{Extension of the application of conway-maxwell-poisson models: Analyzi volume = {30}, year = {2010} } -@article{Lord2008, -abstract = {This paper documents the application of the Conway-Maxwell-Poisson (COM-Poisson) generalized linear model (GLM) for modeling motor vehicle crashes. The COM-Poisson distribution, originally developed in 1962, has recently been re-introduced by statisticians for analyzing count data subjected to over- and under-dispersion. This innovative distribution is an extension of the Poisson distribution. The objectives of this study were to evaluate the application of the COM-Poisson GLM for analyzing motor vehicle crashes and compare the results with the traditional negative binomial (NB) model. The comparison analysis was carried out using the most common functional forms employed by transportation safety analysts, which link crashes to the entering flows at intersections or on segments. To accomplish the objectives of the study, several NB and COM-Poisson GLMs were developed and compared using two datasets. The first dataset contained crash data collected at signalized four-legged intersections in Toronto, Ont. The second dataset included data collected for rural four-lane divided and undivided highways in Texas. Several methods were used to assess the statistical fit and predictive performance of the models. The results of this study show that COM-Poisson GLMs perform as well as NB models in terms of GOF statistics and predictive performance. Given the fact the COM-Poisson distribution can also handle under-dispersed data (while the NB distribution cannot or has difficulties converging), which have sometimes been observed in crash databases, the COM-Poisson GLM offers a better alternative over the NB model for modeling motor vehicle crashes, especially given the important limitations recently documented in the safety literature about the latter type of model. ?? 2007 Elsevier Ltd. All rights reserved.}, -author = {Lord, Dominique and Guikema, Seth D. and Geedipally, Srinivas Reddy}, -doi = {10.1016/j.aap.2007.12.003}, -file = {:home/eduardojr/Dropbox/Articles/compois/ComPoisson\_Motor.pdf:pdf}, -isbn = {0001-4575}, -issn = {00014575}, -journal = {Accident Analysis and Prevention}, -keywords = {Bayesian models,Com-poisson,Conway-Maxwell-Poisson distribution,Negative binomial,Regression models,Statistical models}, -mendeley-tags = {Com-poisson}, -number = {3}, -pages = {1123--1134}, -pmid = {18460381}, -title = {{Application of the Conway-Maxwell-Poisson generalized linear model for analyzing motor vehicle crashes}}, -volume = {40}, -year = {2008} +@article{Nelder1972, +author = {Nelder, John Ashworth and Wedderburn, Robert William Maclagan}, +file = {:home/eduardo/Documents/Mendeley Desktop/Nelder, Wedderburn - 1972 - Generalized Linear Models.pdf:pdf}, +journal = {Journal of the Royal Statistical Society. Series A (General)}, +mendeley-groups = {TCC{\_}UFPR{\_}2015}, +pages = {370--384}, +title = {{Generalized Linear Models}}, +volume = {135}, +year = {1972} } @article{Park2009, abstract = {Developing sound or reliable statistical models for analyzing motor vehicle crashes is very important in highway safety studies. However, a significant difficulty associated with the model development is related to the fact that crash data often exhibit over-dispersion. Sources of dispersion can be varied and are usually unknown to the transportation analysts. These sources could potentially affect the development of negative binomial (NB) regression models, which are often the model of choice in highway safety. To help in this endeavor, this paper documents an alternative formulation that could be used for capturing heterogeneity in crash count models through the use of finite mixture regression models. The finite mixtures of Poisson or NB regression models are especially useful where count data were drawn from heterogeneous populations. These models can help determine sub-populations or groups in the data among others. To evaluate these models, Poisson and NB mixture models were estimated using data collected in Toronto, Ontario. These models were compared to standard NB regression model estimated using the same data. The results of this study show that the dataset seemed to be generated from two distinct sub-populations, each having different regression coefficients and degrees of over-dispersion. Although over-dispersion in crash data can be dealt with in a variety of ways, the mixture model can help provide the nature of the over-dispersion in the data. It is therefore recommended that transportation safety analysts use this type of model before the traditional NB model, especially when the data are suspected to belong to different groups.}, author = {Park, Byung-Jung and Lord, Dominique}, doi = {10.1016/j.aap.2009.03.007}, -file = {:home/eduardojr/Dropbox/Articles/compois/PARK-DISSERTATION-article.pdf:pdf;:home/eduardojr/Dropbox/Articles/compois/PARK-DISSERTATION.pdf:pdf}, +file = {:home/eduardo/Documents/Mendeley Desktop/Park, Lord - 2009 - Application of finite mixture models for vehicle crash data analysis.pdf:pdf;:home/eduardo/Documents/Mendeley Desktop/Park, Lord - 2009 - Application of finite mixture models for vehicle crash data analysis(2).pdf:pdf}, issn = {1879-2057}, journal = {Accident; analysis and prevention}, keywords = {Com-poisson}, +mendeley-groups = {TCC{\_}UFPR{\_}2015}, mendeley-tags = {Com-poisson}, number = {4}, pages = {683--691}, @@ -91,39 +78,67 @@ volume = {41}, year = {2009} } @book{Paula2013, -abstract = {A \'{a}rea de modelagem estat\'{\i}stica de regress\~{a}o recebeu um grande impulso desde a cria\c{c}\~{a}o dos modelos lineares generalizados (MLGs) no in\'{\i}cio da d\'{e}- cada de 70. O crescente interesse pela \'{a}rea motivou a realiza\c{c}\~{a}o de v\'{a}rios encontros informais no in\'{\i}cio dos anos 80, a maioria deles na Inglaterra, at\'{e} que em 1986 foi realizado na cidade de Innsbruck na \'{A}ustria o “1st Internati- onalWorkshop on Statistical Modelling”(1st IWSM). Esse encontro tem sido realizado anualmente sendo que o \'{u}ltimo (25th IWSM) aconteceu em julho de 2010 na Universidade de Glasgow, Esc\'{o}cia. O 26th IWSM ser\'{a} realizado em julho de 2011 em Val\^{e}ncia, Espanha. No Brasil a \'{a}rea come\c{c}ou efetiva- mente a se desenvolver a partir de meados da d\'{e}cada de 80 e em particular ap\'{o}s a 1a Escola de Modelos de Regress\~{a}o (1EMR) realizada na Universi- dade de S\~{a}o Paulo em 1989. As demais escolas ocorreram desde ent\~{a}o a cada dois anos sendo que a \'{u}ltima (11EMR) foi realizada em mar\c{c}o de 2009 na cidade de Recife, PE. A 12EMR ser\'{a} realizada em mar\c{c}o de 2011 na cidade de Fortaleza, CE.}, +abstract = {A {\'{a}}rea de modelagem estat{\'{i}}stica de regress{\~{a}}o recebeu um grande impulso desde a cria{\c{c}}{\~{a}}o dos modelos lineares generalizados (MLGs) no in{\'{i}}cio da d{\'{e}}- cada de 70. O crescente interesse pela {\'{a}}rea motivou a realiza{\c{c}}{\~{a}}o de v{\'{a}}rios encontros informais no in{\'{i}}cio dos anos 80, a maioria deles na Inglaterra, at{\'{e}} que em 1986 foi realizado na cidade de Innsbruck na {\'{A}}ustria o “1st Internati- onalWorkshop on Statistical Modelling”(1st IWSM). Esse encontro tem sido realizado anualmente sendo que o {\'{u}}ltimo (25th IWSM) aconteceu em julho de 2010 na Universidade de Glasgow, Esc{\'{o}}cia. O 26th IWSM ser{\'{a}} realizado em julho de 2011 em Val{\^{e}}ncia, Espanha. No Brasil a {\'{a}}rea come{\c{c}}ou efetiva- mente a se desenvolver a partir de meados da d{\'{e}}cada de 80 e em particular ap{\'{o}}s a 1a Escola de Modelos de Regress{\~{a}}o (1EMR) realizada na Universi- dade de S{\~{a}}o Paulo em 1989. As demais escolas ocorreram desde ent{\~{a}}o a cada dois anos sendo que a {\'{u}}ltima (11EMR) foi realizada em mar{\c{c}}o de 2009 na cidade de Recife, PE. A 12EMR ser{\'{a}} realizada em mar{\c{c}}o de 2011 na cidade de Fortaleza, CE.}, author = {Paula, Gilberto Alvarenga}, -doi = {10.1590/S1415-790X2001000300007}, -file = {:home/eduardojr/Dropbox/Books/giapaula\_2013.pdf:pdf}, -keywords = {GLM,Regress\~{a}o}, -mendeley-tags = {GLM,Regress\~{a}o}, -publisher = {IME-USP S\~{a}o Paulo}, -title = {{Modelos de regress\~{a}o com apoio computacional}}, -url = {https://www.ime.usp.br/~giapaula/textoregressao.htm}, +file = {:home/eduardo/Documents/Mendeley Desktop/Paula - 2013 - Modelos de regress{\~{a}}o com apoio computacional.pdf:pdf}, +keywords = {GLM,Regress{\~{a}}o}, +mendeley-groups = {TCC{\_}UFPR{\_}2015}, +mendeley-tags = {GLM,Regress{\~{a}}o}, +publisher = {IME-USP S{\~{a}}o Paulo}, +title = {{Modelos de regress{\~{a}}o com apoio computacional}}, +url = {https://www.ime.usp.br/{~}giapaula/textoregressao.htm}, year = {2013} } @inproceedings{RibeiroJr2012, author = {{Ribeiro Jr}, Paulo Justiniano and Bonat, Wagner Hugo and Krainski, Elias Teixeira and Zeviani, Walmes Marques}, -booktitle = {20º Simp\'{o}sio Nacional de Probabilidade e Estat\'{\i}stica}, -file = {:home/eduardojr/Dropbox/Books/MCIE\_LEG.pdf:pdf}, -keywords = {Infer\^{e}ncia,M\'{e}todos Computacionais,Verossimilhan\c{c}a}, -mendeley-tags = {Infer\^{e}ncia,M\'{e}todos Computacionais,Verossimilhan\c{c}a}, +booktitle = {20{\textordmasculine} Simp{\'{o}}sio Nacional de Probabilidade e Estat{\'{i}}stica}, +file = {:home/eduardo/Documents/Mendeley Desktop/Ribeiro Jr et al. - 2012 - M{\'{e}}todos computacionais para infer{\^{e}}ncia com aplica{\c{c}}{\~{o}}es em R.pdf:pdf}, +keywords = {Infer{\^{e}}ncia,M{\'{e}}todos Computacionais,Verossimilhan{\c{c}}a}, +mendeley-groups = {TCC{\_}UFPR{\_}2015}, +mendeley-tags = {Infer{\^{e}}ncia,M{\'{e}}todos Computacionais,Verossimilhan{\c{c}}a}, pages = {282}, -title = {{M\'{e}todos computacionais para infer\^{e}ncia com aplica\c{c}\~{o}es em R}}, +title = {{M{\'{e}}todos computacionais para infer{\^{e}}ncia com aplica{\c{c}}{\~{o}}es em R}}, url = {http://leg.ufpr.br/doku.php/cursos:mcie}, year = {2012} } +@phdthesis{Ribeiro2012, +author = {Ribeiro, Ang{\'{e}}lica Maria Tortola}, +file = {:home/eduardo/Documents/Mendeley Desktop/4336.pdf:pdf}, +mendeley-groups = {TCC{\_}UFPR{\_}2015}, +school = {Universidade Federal de S{\~{a}}o Carlos}, +title = {{Distribui{\c{c}}{\~{a}}o COM-Poisson na an{\'{a}}lise de dados de experimentos de quimiopreven{\c{c}}{\~{a}}o do c{\^{a}}ncer em animais}}, +year = {2012} +} +@article{Sellers2016, +abstract = {Excess zeroes are often thought of as a cause of data over-dispersion (i.e. when the variance exceeds the mean); this claim is not entirely accurate. In actuality, excess zeroes reduce the mean of a dataset, thus inflating the dispersion index (i.e. the variance divided by the mean). While this results in an increased chance for data over-dispersion, the implication is not guaranteed. Thus, one should consider a flexible distribution that not only can account for excess zeroes, but can also address potential over- or under-dispersion. A zero-inflated Conway-Maxwell-Poisson (ZICMP) regression allows for modeling the relationship between explanatory and response variables, while capturing the effects due to excess zeroes and dispersion. This work derives the ZICMP model and illustrates its flexibility, extrapolates the corresponding likelihood ratio test for the presence of significant data dispersion, and highlights various statistical properties and model fit through several examples.}, +author = {Sellers, Kimberly F. and Raim, Andrew}, +doi = {10.1016/j.csda.2016.01.007}, +file = {:home/eduardo/Documents/Mendeley Desktop/compoissonzeroinflated.pdf:pdf}, +issn = {01679473}, +journal = {Computational Statistics {\&} Data Analysis}, +keywords = {Conway-Maxwell-Poisson,Excess zeroes,Over-dispersion,Under-dispersion}, +mendeley-groups = {TCC{\_}UFPR{\_}2015}, +month = {jul}, +pages = {68--80}, +publisher = {Elsevier B.V.}, +title = {{A flexible zero-inflated model to address data dispersion}}, +url = {http://dx.doi.org/10.1016/j.csda.2016.01.007 http://linkinghub.elsevier.com/retrieve/pii/S0167947316000165}, +volume = {99}, +year = {2016} +} @article{Sellers2010, abstract = {Poisson regression is a popular tool for modeling count data and is applied in a vast array of applications from the social to the physical sciences and beyond. Real data, however, are often over- or under-dispersed and, thus, not conducive to Poisson regression. We propose a regression model based on the Conway--Maxwell-Poisson (COM-Poisson) distribution to address this problem. The COM-Poisson regression generalizes the well-known Poisson and logistic regression models, and is suitable for fitting count data with a wide range of dispersion levels. With a GLM approach that takes advantage of exponential family properties, we discuss model estimation, inference, diagnostics, and interpretation, and present a test for determining the need for a COM-Poisson regression over a standard Poisson regression. We compare the COM-Poisson to several alternatives and illustrate its advantages and usefulness using three data sets with varying dispersion.}, +annote = {Refer{\^{e}}ncia para COMPoissonReg package}, archivePrefix = {arXiv}, arxivId = {1011.2077}, author = {Sellers, Kimberly F. and Shmueli, Galit}, doi = {10.1214/09-AOAS306}, eprint = {1011.2077}, -file = {:home/eduardojr/Dropbox/Articles/compois/ComPoisson\_theory2 .pdf:pdf;:home/eduardojr/Dropbox/Articles/compois/ComPoisson\_theory2.pdf:pdf}, +file = {:home/eduardo/Documents/Mendeley Desktop/Sellers, Shmueli - 2010 - A flexible regression model for count data.pdf:pdf;:home/eduardo/Documents/Mendeley Desktop/Sellers, Shmueli - 2010 - A flexible regression model for count data(2).pdf:pdf}, issn = {19326157}, journal = {Annals of Applied Statistics}, keywords = {Com-poisson,Conway-Maxwell-Poisson (COM-Poisson) distribution,Dispersion,Generalized Poisson,Generalized linear models (GLM)}, +mendeley-groups = {TCC{\_}UFPR{\_}2015}, mendeley-tags = {Com-poisson}, number = {2}, pages = {943--961}, @@ -133,13 +148,15 @@ year = {2010} } @article{Shmueli2005, abstract = {A useful discrete distribution (the Conway2013Maxwell2013Poisson distribution) is revived and its statistical and probabilistic properties are introduced and explored. This distribution is a two-parameter extension of the Poisson distribution that generalizes some well-known discrete distributions (Poisson, Bernoulli and geometric). It also leads to the generalization of distributions derived from these discrete distributions (i.e. the binomial and negative binomial distributions). We describe three methods for estimating the parameters of the Conway2013Maxwell2013Poisson distribution. The first is a fast simple weighted least squares method, which leads to estimates that are sufficiently accurate for practical purposes. The second method, using maximum likelihood, can be used to refine the initial estimates. This method requires iterations and is more computationally intensive. The third estimation method is Bayesian. Using the conjugate prior, the posterior density of the parameters of the Conway2013Maxwell2013Poisson distribution is easily computed. It is a flexible distribution that can account for overdispersion or underdispersion that is commonly encountered in count data. We also explore two sets of real world data demonstrating the flexibility and elegance of the Conway2013Maxwell2013Poisson distribution in fitting count data which do not seem to follow the Poisson distribution.}, +annote = {Refer{\^{e}}ncia para compoisson package}, author = {Shmueli, Galit and Minka, Thomas P. and Kadane, Joseph B. and Borle, Sharad and Boatwright, Peter}, doi = {10.1111/j.1467-9876.2005.00474.x}, -file = {:home/eduardojr/Dropbox/Articles/compois/ComPoisson\_theory3.pdf:pdf}, +file = {:home/eduardo/Documents/Mendeley Desktop/Shmueli et al. - 2005 - A useful distribution for fitting discrete data Revival of the Conway-Maxwell-Poisson distribution.pdf:pdf}, isbn = {1467-9876}, issn = {00359254}, journal = {Journal of the Royal Statistical Society. Series C: Applied Statistics}, keywords = {Com-poisson,Conjugate family,Conway-Maxwell-Poisson distribution,Estimation,Exponential family,Overdispersion,Underdispersion}, +mendeley-groups = {TCC{\_}UFPR{\_}2015}, mendeley-tags = {Com-poisson}, number = {1}, pages = {127--142}, @@ -147,76 +164,81 @@ title = {{A useful distribution for fitting discrete data: Revival of the Conway volume = {54}, year = {2005} } +@misc{Winkelmann1994, +abstract = {"This paper deals with the estimation of single equation models in which the counts are regressed on a set of observed individual characteristics such as age, gender, or nationality.... We propose a generalized event count model to simultaneously allow for a wide class of count data models and account for over- and underdispersion. This model is successfully applied to German data on fertility, divorces and mobility." (SUMMARY IN FRE)}, +author = {Winkelmann, R and Zimmermann, K F}, +booktitle = {Mathematical population studies}, +doi = {10.1080/08898489409525374}, +file = {:home/eduardo/Documents/Mendeley Desktop/41{\_}CountDataModel{\_}MathematicalPopulationStudies{\_}1993.pdf:pdf}, +isbn = {9780470510247}, +issn = {0889-8480}, +keywords = {Demographic Factors,Developed Countries,Divorce,Estimation Technics,Europe,Fertility,Germany,Mathematical Model,Migration,Models,Nuptiality,Population,Population Dynamics,Research Methodology,Theoretical,Western Europe}, +mendeley-groups = {TCC{\_}UFPR{\_}2015}, +number = {3}, +pages = {205--221, 223}, +pmid = {12287090}, +title = {{Count data models for demographic data}}, +volume = {4}, +year = {1994} +} +@article{Winkelmann1995, +author = {Winkelmann, Rainer}, +doi = {10.1080/07350015.1995.10524620}, +file = {:home/eduardo/Documents/Mendeley Desktop/winkelmann1995.pdf:pdf}, +issn = {0735-0015}, +journal = {Journal of Business {\&} Economic Statistics}, +mendeley-groups = {TCC{\_}UFPR{\_}2015}, +month = {oct}, +number = {4}, +pages = {467--474}, +title = {{Duration Dependence and Dispersion in Count-Data Models}}, +url = {http://www.tandfonline.com/doi/abs/10.1080/07350015.1995.10524620}, +volume = {13}, +year = {1995} +} +@book{Winkelmann2008, +address = {Berlin, Heidelberg}, +author = {Winkelmann, Rainer}, +booktitle = {Vasa}, +doi = {10.1007/978-3-540-78389-3}, +file = {:home/eduardo/Documents/Mendeley Desktop/Winkelmann - 2008 - Econometric Analysis of Count Data.pdf:pdf}, +isbn = {978-3-540-77648-2}, +mendeley-groups = {TCC{\_}UFPR{\_}2015}, +pages = {342}, +publisher = {Springer Berlin Heidelberg}, +title = {{Econometric Analysis of Count Data}}, +url = {http://medcontent.metapress.com/index/A65RM03P4874243N.pdf http://link.springer.com/10.1007/978-3-540-78389-3}, +year = {2008} +} +@article{Zeileis2007, +abstract = {To offer a practical demonstration of regression models recommended for count outcomes using longitudinal predictors of children's medically attended injuries.}, +author = {Zeileis, Achim and Kleiber, Christian and Jackman, Simon}, +doi = {10.1093/jpepsy/jsn055}, +file = {:home/eduardo/Documents/Mendeley Desktop/Zeileis, Kleiber, Jackman - 2007 - Regression Models for Count Data in R.pdf:pdf}, +isbn = {1548-7660}, +issn = {1465735X}, +journal = {Journal Of Statistical Software}, +keywords = {glm,hurdle model,negative binomial model,poisson model,zero inflated model}, +mendeley-groups = {TCC{\_}UFPR{\_}2015}, +number = {8}, +pages = {1076--84}, +pmid = {18522994}, +title = {{Regression Models for Count Data in R}}, +url = {http://www.ncbi.nlm.nih.gov/pubmed/21518631}, +volume = {27}, +year = {2007} +} @article{Zeviani2014, abstract = {Event counts are response variables with non-negative integer values representing the number of times that an event occurs within a fixed domain such as a time interval, a geographical area or a cell of a contingency table. Analysis of counts by Gaussian regression models ignores the discreteness, asymmetry and heteroscedasticity and is inefficient, providing unrealistic standard errors or possibly negative predictions of the expected number of events. The Poisson regression is the standard model for count data with underlying assumptions on the generating process which may be implausible in many applications. Statisticians have long recognized the limitation of imposing equidispersion under the Poisson regression model. A typical situation is when the conditional variance exceeds the conditional mean, in which case models allowing for overdispersion are routinely used. Less reported is the case of underdispersion with fewer modeling alternatives and assessments available in the literature. One of such alternatives, the Gamma-count model, is adopted here in the analysis of an agronomic experiment designed to investigate the effect of levels of defoliation on different phenological states upon the number of cotton bolls. Data set and code for analysis are available as online supplements. Results show improvements over the Poisson model and the semi-parametric quasi-Poisson model in capturing the observed variability in the data. Estimating rather than assuming the underlying variance process leads to important insights into the process. Event counts are response variables with non-negative integer values representing the number of times that an event occurs within a fixed domain such as a time interval, a geographical area or a cell of a contingency table. Analysis of counts by Gaussian regression models ignores the discreteness, asymmetry and heteroscedasticity and is inefficient, providing unrealistic standard errors or possibly negative predictions of the expected number of events. The Poisson regression is the standard model for count data with underlying assumptions on the generating process which may be implausible in many applications. Statisticians have long recognized the limitation of imposing equidispersion under the Poisson regression model. A typical situation is when the conditional variance exceeds the conditional mean, in which case models allowing for overdispersion are routinely used. Less reported is the case of underdispersion with fewer modeling alternatives and assessments available in the literature. One of such alternatives, the Gamma-count model, is adopted here in the analysis of an agronomic experiment designed to investigate the effect of levels of defoliation on different phenological states upon the number of cotton bolls. Data set and code for analysis are available as online supplements. Results show improvements over the Poisson model and the semi-parametric quasi-Poisson model in capturing the observed variability in the data. Estimating rather than assuming the underlying variance process leads to important insights into the process.}, -author = {Zeviani, Walmes Marques and Ribeiro, Paulo Justiniano and Bonat, Wagner Hugo and Shimakura, Silvia Emiko and Muniz, Joel Augusto}, +author = {Zeviani, Walmes Marques and {Ribeiro Jr}, Paulo Justiniano and Bonat, Wagner Hugo and Shimakura, Silvia Emiko and Muniz, Joel Augusto}, doi = {10.1080/02664763.2014.922168}, -file = {:home/eduardojr/Dropbox/Articles/compois/GammaCount.pdf:pdf;:home/eduardojr/Dropbox/Articles/compois/GammaCount2.pdf:pdf}, +file = {:home/eduardo/Documents/Mendeley Desktop/Zeviani et al. - 2014 - The Gamma-count distribution in the analysis of experimental underdispersed data.pdf:pdf;:home/eduardo/Documents/Mendeley Desktop/Zeviani et al. - 2014 - The Gamma-count distribution in the analysis of experimental underdispersed data(2).pdf:pdf}, issn = {0266-4763}, journal = {Journal of Applied Statistics}, +mendeley-groups = {TCC{\_}UFPR{\_}2015}, number = {October}, pages = {1--11}, title = {{The Gamma-count distribution in the analysis of experimental underdispersed data}}, url = {http://dx.doi.org/10.1080/02664763.2014.922168}, year = {2014} } -@article{Conway1962, -author = {Conway, Richard W and Maxwell, William L}, -journal = {Journal of Industrial Engineering}, -pages = {132----136}, -title = {{A queuing model with state dependent service rates}}, -volume = {12}, -year = {1962} -} -@misc{Rcore2015, - title = {R: A Language and Environment for Statistical Computing}, - author = {{R Core Team}}, - organization = {R Foundation for Statistical Computing}, - address = {Vienna, Austria}, - year = {2015}, - url = {http://www.R-project.org/}, -} -@Manual{CompGLM, - title = {CompGLM: Conway-Maxwell-Poisson GLM and distribution functions}, - author = {Jeffrey Pollock}, - year = {2014}, - note = {R package version 1.0}, - url = {http://CRAN.R-project.org/package=CompGLM}, -} -@Manual{COMPoissonReg, - title = {COMPoissonReg: Conway-Maxwell Poisson (COM-Poisson) Regression}, - author = {Kimberly Sellers and Thomas Lotze}, - year = {2011}, - note = {R package version 0.3.4}, - url = {http://CRAN.R-project.org/package=COMPoissonReg}, -} -@Manual{compoisson, - title = {compoisson: Conway-Maxwell-Poisson Distribution}, - author = {Jeffrey Dunn}, - year = {2012}, - note = {R package version 0.3}, - url = {http://CRAN.R-project.org/package=compoisson}, -} -@article{Nelder1972, -author = {Nelder, John Ashworth and Wedderburn, Robert William Maclagan}, -file = {:home/eduardojr/Documents/MendeleyLibrary/Artigo GLM - Nelder e Weddenburn.pdf:pdf}, -journal = {Journal of the Royal Statistical Society. Series A (General)}, -pages = {370--384}, -title = {{Generalized Linear Models}}, -volume = {135}, -year = {1972} -} -@article{King1989, -author = {King, Gary}, -doi = {10.2307/2111071}, -file = {:home/eduardojr/Documents/MendeleyLibrary/King - 1989 - Variance Specification in Event Count Models From Restrictive Assumptions to a Generalized Estimator.pdf:pdf}, -issn = {00925853}, -journal = {American Journal of Political Science}, -month = {aug}, -number = {3}, -pages = {762----784}, -title = {{Variance Specification in Event Count Models: From Restrictive Assumptions to a Generalized Estimator}}, -url = {http://www.jstor.org/stable/2111071?origin=crossref}, -volume = {33}, -year = {1989} -}