@article{min02, author = {Min, Yongyi and Agresti, Alan}, title = {Modeling nonnegative data with clumping at zero: A survey}, volume = {1}, URL = {http://jirss.irstat.ir/browse.php?a\underline{}code=A-10-1-27\&slc\underline{}lang=en\&sid=1}, journal = {Journal of the Iranian Statistical Society}, year = {2002}, pages={7-33}, } @article {neelon13, author = {Neelon, Brian and Ghosh, Pulak and Loebs, Patrick F.}, title = {A spatial {P}oisson hurdle model for exploring geographic variation in emergency department visits}, journal = {Journal of the Royal Statistical Society: Series A (Statistics in Society)}, volume = {176}, number = {2}, publisher = {Blackwell Publishing Ltd}, issn = {1467-985X}, url = {http://dx.doi.org/10.1111/j.1467-985X.2012.01039.x}, doi = {10.1111/j.1467-985X.2012.01039.x}, pages = {389--413}, keywords = {Bivariate conditionally auto-regressive prior, Emergency department visits, Poisson hurdle model, Spatial analysis, Zero-inflated data}, year = {2013}, } @article{mullahy86, title = "Specification and testing of some modified count data models", journal = "Journal of Econometrics", volume = "33", number = "3", pages = "341 - 365", year = "1986", note = "", issn = "0304-4076", doi = "10.1016/0304-4076(86)90002-3", url = "http://www.sciencedirect.com/science/article/pii/0304407686900023", author = "John Mullahy" } @article {heilbron94, author = {Heilbron, David C.}, title = {Zero-Altered and other regression models for count data with added zeros}, journal = {Biometrical Journal}, volume = {36}, number = {5}, publisher = {WILEY-VCH Verlag}, issn = {1521-4036}, url = {http://dx.doi.org/10.1002/bimj.4710360505}, doi = {10.1002/bimj.4710360505}, pages = {531--547}, keywords = {Generalized linear model, Maximum likelihood, Negative binomial, Overdispersion, Poisson, Two-part model}, year = {1994}, } @article{patil62, author = {Patil, G. P.}, title = {Maximum likelihood estimation for generalized power series distributions and its application to a truncated binomial distribution}, volume = {49}, number = {1-2}, pages = {227--237}, year = {1962}, doi = {10.1093/biomet/49.1-2.227}, URL = {http://biomet.oxfordjournals.org/content/49/1-2/227.short}, eprint = {http://biomet.oxfordjournals.org/content/49/1-2/227.full.pdf+html}, journal = {Biometrika} } @article{ghosh06, title = "{B}ayesian analysis of zero-inflated regression models", journal = "Journal of Statistical Planning and Inference", volume = "136", number = "4", pages = "1360 - 1375", year = "2006", note = "", issn = "0378-3758", doi = "10.1016/j.jspi.2004.10.008", url = "http://www.sciencedirect.com/science/article/pii/S0378375804004008", author = "Sujit K. Ghosh and Pabak Mukhopadhyay and Jye-Chyi(JC) Lu", keywords = "Bayesian inference", keywords = "Data augmentation", keywords = "Gibbs sampling", keywords = "Markov chain Monte Carlo", keywords = "WinBUGS", keywords = "Zero-inflated power series models" } @Book{consul89, author = {Consul, P.}, title = {Generalized Poisson distributions: Properties and Applications}, publisher = {Marcel Dekker}, address = {New York}, year = 1989 } @article{consul73, author = {Consul, P. C. and Jain, G. C.}, title = {A Generalization of the {P}oisson Distribution}, journal = {Technometrics}, volume = {15}, number = {4}, pages = {791-799}, year = {1973}, } @article{gschobl08, year={2008}, issn={0932-5026}, journal={Statistical Papers}, volume={49}, issue={3}, doi={10.1007/s00362-006-0031-6}, title={Modelling count data with overdispersion and spatial effects}, url={http://dx.doi.org/10.1007/s00362-006-0031-6}, publisher={Springer-Verlag}, keywords={Bayesian inference; Count data; Overdispersion; Spatial regression models; Zero inflated models}, author={Gschl\"{o}{\ss}l, Susanne and Czado, Claudia}, pages={531--552}, language={English} } @Unpublished{green94, author = {Green, W.}, title = {Accounting for excess zeros and sample selection in {P}oisson and negative binomial regression models}, note = {Working Paper EC-94-10, Department of Economics, New York University}, year = {1994}, note={Accessed July 16, 2015} } @article{Mwalili08, author = {Mwalili, Samuel M and Lesaffre, Emmanuel and Declerck, Dominique}, title = {The zero-inflated negative binomial regression model with correction for misclassification: an example in caries research}, volume = {17}, number = {2}, pages = {123--139}, year = {2008}, doi = {10.1177/0962280206071840}, abstract ={Zero-inflated models for count data are becoming quite popular nowadays and are found in many application areas, such as medicine, economics, biology, sociology and so on. However, in practice these counts are often prone to measurement error which in this case boils down to misclassification. Methods to deal with misclassification of counts have been suggested recently, but only for the binomial model and the Poisson model. Here we look at a more complex model, that is, the zero-inflated negative binomial, and illustrate how correction for misclassification can be achieved. Our approach is illustrated on the dmft-index which is a popular measure for caries experience in caries research. An extra problem was the fact that several dental examiners were involved in scoring caries experience. Using our example, we illustrate how a non-differential misclassification process for each examiner can lead to differential misclassification overall.}, URL = {http://smm.sagepub.com/content/17/2/123.abstract}, eprint = {http://smm.sagepub.com/content/17/2/123.full.pdf+html}, journal = {Statistical Methods in Medical Research} } @article{neelon10, author = {Neelon, B H and O'Malley, A J and Normand, S-L T}, title = {A {B}ayesian model for repeated measures zero-inflated count data with application to outpatient psychiatric service use}, volume = {10}, number = {4}, pages = {421--439}, year = {2010}, doi = {10.1177/1471082X0901000404}, abstract ={In applications involving count data, it is common to encounter an excess number of zeros. For example, in the study of outpatient service utilization, the number of utilization days will take on integer values, with many subjects having no utilization (zero values). Mixed distribution models, such as the zero-inflated Poisson and zero-inflated negative binomial, are often used to fit such data. A more general class of mixture models, called hurdle models, can be used to model zero deflation as well as zero inflation. Several authors have proposed frequentist approaches to fitting zero-inflated models for repeated measures. We describe a practical Bayesian approach which incorporates prior information, has optimal small-sample properties and allows for tractable inference. The approach can be easily implemented using standard Bayesian software. A study of psychiatric outpatient service use illustrates the methods.}, URL = {http://smj.sagepub.com/content/10/4/421.abstract}, eprint = {http://smj.sagepub.com/content/10/4/421.full.pdf+html}, journal = {Statistical Modelling} } @article {joe05, author = {Joe, Harry and Zhu, Rong}, title = {Generalized {P}oisson Distribution: the Property of Mixture of {P}oisson and Comparison with Negative Binomial Distribution}, journal = {Biometrical Journal}, volume = {47}, number = {2}, publisher = {WILEY-VCH Verlag}, issn = {1521-4036}, url = {http://dx.doi.org/10.1002/bimj.200410102}, doi = {10.1002/bimj.200410102}, pages = {219--229}, keywords = {Poisson mixture, Overdispersion, Skewness, Zero-inflated distribution}, year = {2005}, } @unpublished{ridout98, author = {Ridout, M and Dem\'{e}trio, CGB and Hinde, J}, title = {Models for count data with many zeros}, note={Proceedings from the International Biometric Conference, Cape Town. Accessed July 16, 2015}, url= {https://www.kent.ac.uk/smsas/personal/msr/webfiles/zip/ibc\underline{}fin.pdf}, year = {1998}, } @article{albert11, author = {Albert, J M and Wang, W and Nelson, S}, title = {Estimating overall exposure effects for zero-inflated regression models with application to dental caries}, year = {2011}, doi = {10.1177/0962280211407800}, abstract ={Zero-inflated (ZI) models, which may be derived as a mixture involving a degenerate distribution at value zero and a distribution such as negative binomial (ZINB), have proved useful in dental and other areas of research by accommodating �extra� zeroes in the data. Used in conjunction with generalised linear models, they allow covariate-adjusted inference of an exposure effect on the mixing probability and on the mean for the non-degenerate distribution. However, these models do not directly provide covariate-adjusted inference for the overall exposure effect. Focusing on the ZINB and ZI beta binomial models, we propose an approach that uses model-predicted values for each person under each exposure state. This �average predicted value� method allows covariate-adjusted estimation of flexible functions of exposure group means such as the difference or ratio. A second approach considers a log link for both components of the ZINB to allow a direct approach to estimation. We apply these new methods to a study of dental caries in very low birth weight adolescents. Simulation studies show good bias and robustness properties for both approaches under various scenarios. Robustness diminishes when there is exposure group imbalance for a covariate with a large effect.}, URL = {http://smm.sagepub.com/content/early/2011/09/08/0962280211407800.abstract}, eprint = {http://smm.sagepub.com/content/early/2011/09/08/0962280211407800.full.pdf+html}, journal = {Statistical Methods in Medical Research} } @article{preisser12, author = {Preisser, J S and Stamm, J W and Long, D L}, title = {Review and Recommendations for Zero-Inflated Count Regression Modeling of Dental Caries Indices in Epidemiological Studies}, year = {2012}, doi = {10.1159/000338992}, journal = {Caries Research}, pages={413--423}, volume={46} } @article{min05, author = {Min, Y and Agresti, A}, title = {Random effect models for repeated measures of zero-inflated count data}, volume = {5}, number = {1}, pages = {1--19}, year = {2005}, doi = {10.1191/1471082X05st084oa}, URL = {http://smj.sagepub.com/content/5/1/1.abstract}, eprint = {http://smj.sagepub.com/content/5/1/1.full.pdf+html}, journal = {Statistical Modelling} } @article{lambert92, jstor_articletype = {research-article}, title = {Zero-Inflated {P}oisson Regression, with an Application to Defects in Manufacturing}, author = {Lambert, Diane}, journal = {Technometrics}, jstor_issuetitle = {}, volume = {34}, number = {1}, jstor_formatteddate = {Feb., 1992}, pages = {1--14}, url = {http://www.jstor.org/stable/1269547}, ISSN = {00401706}, language = {English}, year = {1992}, publisher = {American Statistical Association and American Society for Quality}, copyright = {Copyright � 1992 American Statistical Association and American Society for Quality}, } @article {hall00, author = {Hall, Daniel B.}, title = {Zero-Inflated {P}oisson and Binomial Regression with Random Effects: A Case Study}, journal = {Biometrics}, volume = {56}, number = {4}, publisher = {Blackwell Publishing Ltd}, issn = {1541-0420}, url = {http://dx.doi.org/10.1111/j.0006-341X.2000.01030.x}, doi = {10.1111/j.0006-341X.2000.01030.x}, pages = {1030--1039}, keywords = {Excess zeros, EM algorithm, Generalized linear mixed model, Heterogeneity, Mixed effects, Overdispersion, Repeated measures}, year = {2000}, } @article {Yau01, author = {Yau, Kelvin K. W. and Lee, Andy H.}, title = {Zero-inflated {P}oisson regression with random effects to evaluate an occupational injury prevention programme}, journal = {Statistics in Medicine}, volume = {20}, number = {19}, publisher = {John Wiley & Sons, Ltd.}, issn = {1097-0258}, url = {http://dx.doi.org/10.1002/sim.860}, doi = {10.1002/sim.860}, pages = {2907--2920}, year = {2001}, } @article{dietz00, title = "On estimation of the {P}oisson parameter in zero-modified {P}oisson models", author = {Dietz, Ekkehart and B\"{o}hning, Dankmar}, journal = "Computational Statistics \& Data Analysis ", volume = "34", number = "4", pages = "441--459", year = "2000", note = "", issn = "0167-9473", doi = "http://dx.doi.org/10.1016/S0167-9473(99)00111-5", url = "http://www.sciencedirect.com/science/article/pii/S0167947399001115", } @Book{cameron98, author={Cameron,A. Colin and Trivedi,Pravin K.}, title={Regression Analysis of Count Data}, publisher={Cambridge University Press}, year=1998, month={December}, volume={}, number={9780521635677}, series={Cambridge Books}, edition={}, keywords={}, url={http://ideas.repec.org/b/cup/cbooks/9780521635677.html} } @book{winkelmann08, added-at = {2009-08-21T12:15:08.000+0200}, address = {Berlin}, author = {Winkelmann, {Rainer}}, biburl = {http://www.bibsonomy.org/bibtex/27362518a5a4705d18004eb4f2a25da30/fbw_hannover}, edition = {5}, interhash = {4790bfc0a2c94d901bb08966f2bc76ab}, intrahash = {7362518a5a4705d18004eb4f2a25da30}, isbn = {354040404X}, keywords = {Arbeitsmobilit�t Deutschland Econometric_models Econometrics Ereignisdatenanalyse Labor_mobility Regression Sch�tztheorie Sch�tzung Theorie Time-series_analysis Zeitreihenanalyse Z�hldatenmodell �konometrie �konometrisches_Modell}, pagetotal = {XIV, 304}, ppn_gvk = {368353176}, publisher = {Springer}, subtitle = {with 20 tables}, timestamp = {2009-08-21T12:15:08.000+0200}, title = {Econometric Analysis of Count Data}, url = {http://www.springer.com/us/book/9783540776482}, year = 2008 } @Incollection{boswell70, author={Boswell, M. T. and Patil, G. P.}, booktitle={Random Counts in Models and Structures}, editor= {G. P. Patel}, title={Chance mechanisms generating the negative binomial distributions}, pages={3--22}, publisher={Pennsylvania State University Press}, address = {University Park, PA and London}, year=1970, volume=1 } @Book{zuur12, author={Zurr, Alain F. and Saveliev, Anatoly A. and Ieno, Elena N.}, title={Zero Inflated Models and Generalized Linear Mixed Models with R.}, publisher={Highland Statistics Ltd}, address = {Newburgh}, year=2012, url={http://www.highstat.com/book4.htm} } @article{liu07, author = {Liu, Hui}, title = {Growth Curve Models for Zero-Inflated Count Data: An Application to Smoking Behavior}, journal = {Structural Equation Modeling: A Multidisciplinary Journal}, volume = {14}, number = {2}, pages = {247--279}, year = {2007}, doi = {10.1080/10705510709336746}, URL = {http://www.tandfonline.com/doi/abs/10.1080/10705510709336746}, eprint = {http://www.tandfonline.com/doi/pdf/10.1080/10705510709336746} } @article{roeder99, jstor_articletype = {research-article}, title = {Modeling Uncertainty in Latent Class Membership: A Case Study in Criminology}, author = {Roeder, Kathryn and Lynch, Kevin G. and Nagin, Daniel S.}, journal = {Journal of the American Statistical Association}, jstor_issuetitle = {}, volume = {94}, number = {447}, jstor_formatteddate = {Sep., 1999}, pages = {766--776}, url = {http://www.jstor.org/stable/2669989}, ISSN = {01621459}, language = {English}, year = {1999}, publisher = {American Statistical Association}, copyright = {Copyright � 1999 American Statistical Association}, } @article{dalrymple03, author = {Dalrymple, M. L. and Hudson, I. L. and Ford, R. P. K.}, title = {Finite mixture, zero-inflated {P}oisson and hurdle models with application to {SIDS}}, journal = {Computational Statstics \& Data Analysis}, issue_date = {28 January 2003}, volume = {41}, number = {3-4}, month = jan, year = {2003}, issn = {0167-9473}, pages = {491--504}, numpages = {14}, url = {http://dx.doi.org/10.1016/S0167-9473(02)00187-1}, doi = {10.1016/S0167-9473(02)00187-1}, acmid = {639253}, publisher = {Elsevier Science Publishers B. V.}, address = {Amsterdam, The Netherlands, The Netherlands}, keywords = {climate, excess zeros, heterogeneity, mixture models, sudden infant death syndrome}, } @article {desantis11, author = {DeSantis, Stacia M. and Bandyopadhyay, Dipankar}, title = {Hidden {M}arkov models for zero-inflated {P}oisson counts with an application to substance use}, journal = {Statistics in Medicine}, volume = {30}, number = {14}, publisher = {John Wiley & Sons, Ltd.}, issn = {1097-0258}, url = {http://dx.doi.org/10.1002/sim.4207}, doi = {10.1002/sim.4207}, pages = {1678--1694}, keywords = {Bayesian, cue-reactivity, hidden Markov model, Markov chain Monte Carlo, zero inflation}, year = {2011}, } @article {dobbie01, author = {Dobbie, Melissa J. and Welsh, A.H.}, title = {Modelling Correlated Zero-inflated Count Data}, journal = {Australian \& New Zealand Journal of Statistics}, volume = {43}, number = {4}, publisher = {Blackwell Publishers Ltd.}, issn = {1467-842X}, url = {http://dx.doi.org/10.1111/1467-842X.00191}, doi = {10.1111/1467-842X.00191}, pages = {431--444}, keywords = {correlated data, generalized estimating equation (GEE), marginal model, truncated Poisson distribution, zero-inflated counts}, year = {2001}, } @article{Dobbie01b, author = {Dobbie, Melissa J and Welsh, Alan H}, title = {Models for zero-inflated count data using the {N}eyman type {A} distribution}, journal = {Statistical Modelling}, volume = {1}, number = {1}, pages = {65-80}, year = {2001}, doi = {10.1177/1471082X0100100106},, URL = {http://smj.sagepub.com/content/1/1/65.abstract}, eprint = {http://smj.sagepub.com/content/1/1/65.full.pdf+html}, } @article{hall04, author = {Hall, Daniel B and Zhang, Zhengang}, title = {Marginal models for zero inflated clustered data}, volume = {4}, number = {3}, pages = {161--180}, year = {2004}, doi = {10.1191/1471082X04st076oa}, URL = {http://smj.sagepub.com/content/4/3/161.abstract}, eprint = {http://smj.sagepub.com/content/4/3/161.full.pdf+html}, journal = {Statistical Modelling} } @article {fahrmeir06, author = {Fahrmeir, Ludwig and Osuna Echavarr\'{i}a, Leyre}, title = {Structured additive regression for overdispersed and zero-inflated count data}, journal = {Applied Stochastic Models in Business and Industry}, volume = {22}, number = {4}, publisher = {John Wiley & Sons, Ltd.}, issn = {1526-4025}, url = {http://dx.doi.org/10.1002/asmb.631}, doi = {10.1002/asmb.631}, pages = {351--369}, keywords = {Bayesian semiparametric count data regression, overdispersion, zero inflation, MCMC, spatial models, patent data, car insurance}, year = {2006}, } @article {lam06, author = {Lam, K. F. and Xue, Hongqi and Bun Cheung, Yin}, title = {Semiparametric Analysis of Zero-Inflated Count Data}, journal = {Biometrics}, volume = {62}, number = {4}, publisher = {Blackwell Publishing Inc}, issn = {1541-0420}, url = {http://dx.doi.org/10.1111/j.1541-0420.2006.00575.x}, doi = {10.1111/j.1541-0420.2006.00575.x}, pages = {996--1003}, keywords = {Asymptotically efficient, Generalized partly linear model, Sieve maximum likelihood estimator, Zero-inflated Poisson regression model}, year = {2006}, } @article{hsu05, author = {Hsu, Chiu-Hsieh}, title = {Joint modelling of recurrence and progression of adenomas: a latent variable approach}, volume = {5}, number = {3}, pages = {201--215}, year = {2005}, doi = {10.1191/1471082X05st094oa}, URL = {http://smj.sagepub.com/content/5/3/201.abstract}, eprint = {http://smj.sagepub.com/content/5/3/201.full.pdf+html}, journal = {Statistical Modelling} } @article {buu11, author = {Buu, Anne and Johnson, Norman J. and Li, Runze and Tan, Xianming}, title = {New variable selection methods for zero-inflated count data with applications to the substance abuse field}, journal = {Statistics in Medicine}, volume = {30}, number = {18}, publisher = {John Wiley & Sons, Ltd.}, issn = {1097-0258}, url = {http://dx.doi.org/10.1002/sim.4268}, doi = {10.1002/sim.4268}, pages = {2326--2340}, keywords = {LASSO, one-step SCAD, variable selection, zero-inflated Poisson distribution}, year = {2011}, } @Article{desantis14, author = "Stacia M. DeSantis and Christos Lazaridis and Shuang Ji and Francis G. Spinale", title = "Analyzing propensity matched zero-inflated count outcomes in observational studies", journal = "Journal of Applied Statistics", volume = "41", number = "1", pages = "127--141", year = "2014", DOI = "http://dx.doi.org/10.1080/02664763.2013.834296", ISSN = "0266-4763 (print), 1360-0532 (electronic)", ISSN-L = "0266-4763", bibdate = "Wed Mar 5 08:09:17 MST 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/japplstat.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Applied Statistics", journal-URL = "http://www.tandfonline.com/loi/cjas20", } @article{williamson05, author = {Williamson, John M. and Lin, Hung-Mo and Lyles, Robert H.}, title = {Power calculations for {ZIP} and {ZINB} models}, volume = {5}, pages = {519--534}, year = {2007}, URL = {http://www.jds-online.com/v5-4}, journal = {Journal of Data Science} } @article{hasan09, author = {M. Tariqul Hasan and Gary Sneddon}, title = {Zero-Inflated {P}oisson Regression for Longitudinal Data}, journal = {Communications in Statistics - Simulation and Computation}, volume = {38}, number = {3}, year = {2009}, pages = {638--653}, ee = {http://dx.doi.org/10.1080/03610910802601332}, bibsource = {DBLP, http://dblp.uni-trier.de} } @article{silva11, title = {{Zero-inflated Poisson regression models for QTL mapping applied to tick-resistance in a Gyr x Holstein F2 population}}, journal = {{Genetics and Molecular Biology}}, author={Silva, Fabyano Fonseca AND Tunin, Karen P. AND Rosa, Guilherme J.M. AND da Silva, Marcos V.B. AND Azevedo, Ana Luisa Souza AND Verneque, Rui da Silva AND Machado, Marco Antonio AND Packer, Irineu Umberto}, ISSN = {1415-4757}, language = {en}, URL = {http://www.scielo.br/scielo.php?script=sci\underline{}arttext\&pid=S1415-47572011000400008\&nrm=iso}, volume = {34}, year = {2011}, month = {00}, pages = {575--582}, publisher = {scielo}, crossref = {10.1590/S1415-47572011005000049}, } @article {kleinke13, author = {Kleinke, Kristian and Reinecke, Jost}, title = {Multiple imputation of incomplete zero-inflated count data}, journal = {Statistica Neerlandica}, volume = {67}, number = {3}, issn = {1467-9574}, url = {http://dx.doi.org/10.1111/stan.12009}, doi = {10.1111/stan.12009}, pages = {311--336}, keywords = {missing data, multiple imputation, zero-inflated count data}, year = {2013}, } @article {agarwal02, author = "Agarwal, D.K. and Gelfand, A.E. and Citron-Pousty, S.", title = "Zero-inflated models with application to spatial count data", journal = "Environmental and Ecological Statistics", volume = "9", number = "4", year = "2002", abstract = "

Count data arises in many contexts. Here our concern is with spatial count data which exhibit an excessive number of zeros. Using the class of zero-inflated count models provides a flexible way to address this problem. Available covariate information suggests formulation of such modeling within a regression framework. We employ zero-inflated Poisson regression models. Spatial association is introduced through suitable random effects yielding a hierarchical model. We propose fitting this model within a Bayesian framework considering issues of posterior propriety, informative prior specification and well-behaved simulation based model fitting. Finally, we illustrate the model fitting with a data set involving counts of isopod nest burrows for 1649 pixels over a portion of the Negev desert in Israel.

", pages = "341--355", url = "http://www.ingentaconnect.com/content/klu/eest/2002/00000009/00000004/05102063" } @article {rathbun06, author = {Rathbun, Stephen and Fei, Songlin}, affiliation = {University of Georgia Department of Health Administration, Biostatistics and Epidemiology Athens GA 30605 USA}, title = {A spatial zero-inflated {P}oisson regression model for oak regeneration}, journal = {Environmental and Ecological Statistics}, publisher = {Springer Netherlands}, issn = {1352-8505}, keyword = {Biomedical and Life Sciences}, pages = {409--426}, volume = {13}, issue = {4}, url = {http://dx.doi.org/10.1007/s10651-006-0020-x}, note = {10.1007/s10651-006-0020-x}, year = {2006} } @article {verhoef07, author = {Ver Hoef, Jay M. and Jansen, John K.}, title = {Space-time zero-inflated count models of Harbor seals}, journal = {Environmetrics}, volume = {18}, number = {7}, publisher = {John Wiley & Sons, Ltd.}, issn = {1099-095X}, url = {http://dx.doi.org/10.1002/env.873}, doi = {10.1002/env.873}, pages = {697--712}, keywords = {spatial statistics, time series, Poisson, Bernoulli, hurdle model, linex loss function}, year = {2007}, } @article {feng12, author = {Feng, C.X. and Dean, C.B.}, title = {Joint analysis of multivariate spatial count and zero-heavy count outcomes using common spatial factor models}, journal = {Environmetrics}, volume = {23}, number = {6}, issn = {1099-095X}, url = {http://dx.doi.org/10.1002/env.2158}, doi = {10.1002/env.2158}, pages = {493--508}, keywords = {joint disease mapping, common spatial factor model, conditional autoregressive model, Markov chain Monte Carlo, zero-inflated Poisson}, year = {2012}, } @article {hasan09b, author = {Hasan, M. Tariqul and Sneddon, Gary and Ma, Renjun}, title = {Pattern-Mixture Zero-Inflated Mixed Models for Longitudinal Unbalanced Count Data with Excessive Zeros}, journal = {Biometrical Journal}, volume = {51}, number = {6}, publisher = {WILEY-VCH Verlag}, issn = {1521-4036}, url = {http://dx.doi.org/10.1002/bimj.200900093}, doi = {10.1002/bimj.200900093}, pages = {946--960}, keywords = {Compound Poisson distribution, Generalized linear mixed models, Missing data, Quasi-likelihood, Random effects}, year = {2009}, } @article {maruotti11, author = {Maruotti, Antonello}, title = {A two-part mixed-effects pattern-mixture model to handle zero-inflation and incompleteness in a longitudinal setting}, journal = {Biometrical Journal}, volume = {53}, number = {5}, publisher = {WILEY-VCH Verlag}, issn = {1521-4036}, url = {http://dx.doi.org/10.1002/bimj.201000190}, doi = {10.1002/bimj.201000190}, pages = {716--734}, keywords = {Hurdle model, Longitudinal count data, Non-ignorable dropout, Random effects models, Zero-inflated models}, year = {2011}, } @article {su11, author = {Su, X. G. and Fan, J. and Levine, R. and Tan, X. and Tripathi, A.}, title = {Multiple-Inflation {P}oisson Model with ${L}_1$ Regularization}, journal = {Statistica Sinica}, volume = {23}, url = {http://www3.stat.sinica.edu.tw/statistica/oldpdf/A23n35.pdf}, doi = {10.5705/ss.2012.187}, pages = {1071--1090}, year = {2013}, } @article {ghosh12, author = {Ghosh, Souparno and Gelfand, Alan E. and Zhu, Kai and Clark, James S.}, title = {The k-{ZIG}: Flexible Modeling for Zero-Inflated Counts}, journal = {Biometrics}, volume = {68}, number = {3}, publisher = {Blackwell Publishing Inc}, issn = {1541-0420}, url = {http://dx.doi.org/10.1111/j.1541-0420.2011.01729.x}, doi = {10.1111/j.1541-0420.2011.01729.x}, pages = {878--885}, keywords = {Abundance, Bayesian modeling, Link function, Log score loss, Poisson-Gamma, Presence/absence}, year = {2012}, } @article{angers03, title = "A {B}ayesian analysis of zero-inflated generalized {P}oisson model", journal = "Computational Statistics \& Data Analysis ", volume = "42", number = "1-2", pages = "37 - 46", year = "2003", note = "", issn = "0167-9473", doi = "http://dx.doi.org/10.1016/S0167-9473(02)00154-8", url = "http://www.sciencedirect.com/science/article/pii/S0167947302001548", author = "Jean-Fran\c{c}ois Angers and Atanu Biswas", } @ARTICLE{gupta96, title = {Analysis of zero-adjusted count data}, author = {Gupta, Pushpa L. and Gupta, Ramesh C. and Tripathi, Ram C.}, year = {1996}, journal = {Computational Statistics \& Data Analysis}, volume = {23}, number = {2}, pages = {207--218}, url = {http://EconPapers.repec.org/RePEc:eee:csdana:v:23:y:1996:i:2:p:207-218} } @article {jenkner16, author = {Jenkner, Carolin and Lorenz, Eva and Becher, Heiko and Sauerbrei, Willi}, title = {Modeling continuous covariates with a ``spike'' at zero: Bivariate approaches}, journal = {Biometrical Journal}, issn = {1521-4036}, url = {http://dx.doi.org/10.1002/bimj.201400112}, doi = {10.1002/bimj.201400112}, pages = {n/a--n/a}, keywords = {Fractional polynomials, Regression modeling, Spike at zero, Correlated predictors}, year = {2016}, } @article{li99, author = {Li, Chin-Shang and Lu, Jye-Chyi and Park, Jinho and Kim, Kyungmoo and Brinkley, Paul A. and Peterson, John P.}, title = {Multivariate zero-inflated {P}oisson models and their applications}, journal = {Technometrics}, issue_date = {Feb. 1999}, volume = {41}, number = {1}, month = feb, year = {1999}, issn = {0040-1706}, pages = {29--38}, numpages = {10}, url = {http://dx.doi.org/10.2307/1270992}, doi = {10.2307/1270992}, acmid = {310650}, publisher = {American Society for Quality Control and American Statistical Association}, address = {Alexandria, Va, USA}, keywords = {maximum likelihood, mixture distribution, multivariate Bernoulli, multivariate Poisson, quality control, zero-defect probability}, } @article {walhin01, author = {Walhin, Jean Francois}, title = {Bivariate {ZIP} Models}, journal = {Biometrical Journal}, volume = {43}, number = {2}, publisher = {WILEY-VCH Verlag Berlin GmbH}, issn = {1521--4036}, url = {http://dx.doi.org/10.1002/1521-4036(200105)43:2<147::AID-BIMJ147>3.0.CO;2-5}, doi = {10.1002/1521-4036(200105)43:2$<$147::AID-BIMJ147$>$3.0.CO;2-5}, pages = {147--160}, keywords = {Zero-Inflated Poisson, Bivariate Poisson, Bivariate mixed Poisson distribution, trivariate reduction method, recursion, maximum likelihood}, year = {2001}, } @Article{majumdar10, author={Anandamayee Majumdar and Corinna Gries}, title={Bivariate Zero-Inflated Regression for Count Data: A {B}ayesian Approach with Application to Plant Counts}, journal={The International Journal of Biostatistics}, year=2010, volume={6}, number={1}, pages={27}, month={}, keywords={Categorical Data Analysis; Multivariate Analysis; Statistical Models; Statistical Theory and Methods}, abstract={Lately, bivariate zero-inflated (BZI) regression models have been used in many instances in the medical sciences to model excess zeros. Examples include the BZI Poisson (BZIP), BZI negative binomial (BZINB) models, etc. Such formulations vary in the basic modeling aspect and use the EM algorithm (Dempster, Laird and Rubin, 1977) for parameter estimation. A different modeling formulation in the Bayesian context is given by Dagne (2004). We extend the modeling to a more general setting for multivariate ZIP models for count data with excess zeros as proposed by Li, Lu, Park, Kim, Brinkley and Peterson (1999), focusing on a particular bivariate regression formulation. For the basic formulation in the case of bivariate data, we assume that Xi are (latent) independent Poisson random variables with parameters λ i , i = 0, 1, 2. A bi-variate count vector ( Y1 , Y 2) response follows a mixture of four distributions; p 0 stands for the mixing probability of a point mass distribution at (0, 0); p 1, the mixing probability that Y 2 = 0, while Y 1 = X 0 + X 1; p 2, the mixing probability that Y 1 = 0 while Y 2 = X 0 + X 2; and finally (1 - p 0 - p 1 - p 2), the mixing probability that Y i = X i + X 0, i = 1, 2. The choice of the parameters { pi , λ i , i = 0, 1, 2} ensures that the marginal distributions of Y i are zero inflated Poisson (λ 0 + λ i ). All the parameters thus introduced are allowed to depend on co-variates through canonical link generalized linear models (McCullagh and Nelder, 1989). This flexibility allows for a range of real-life applications, especially in the medical and biological fields, where the counts are bivariate in nature (with strong association between the processes) and where there are excess of zeros in one or both processes. Our contribution in this paper is to employ a fully Bayesian approach consolidating the work of Dagne (2004) and Li et al. (1999) generalizing the modeling and sampling-based methods described by Ghosh, Mukhopadhya}, url={http://ideas.repec.org/a/bpj/ijbist/v6y2010i1n27.html} } @ARTICLE{arab11, author = {{Arab}, A. and {Holan}, S.~H. and {Wikle}, C.~K. and {Wildhaber}, M.~L. }, title = {Semiparametric Bivariate Zero-Inflated {P}oisson Models with Application to Studies of Abundance for Multiple Species}, journal = {ArXiv e-prints}, archivePrefix = "arXiv", eprint = {1105.3169}, primaryClass = "stat.ME", keywords = {Statistics - Methodology, Statistics - Applications}, year = 2011, month = May, adsurl = {http://adsabs.harvard.edu/abs/2011arXiv1105.3169A}, adsnote = {Provided by the SAO/NASA Astrophysics Data System}, url={http://arxiv.org/abs/1105.3169v1} } @article {bago06, author = {Bago d'Uva, Teresa}, title = {Latent class models for utilisation of health care}, journal = {Health Economics}, volume = {15}, number = {4}, publisher = {John Wiley & Sons, Ltd.}, issn = {1099-1050}, url = {http://dx.doi.org/10.1002/hec.1112}, doi = {10.1002/hec.1112}, pages = {329--343}, keywords = {count data, finite mixture models, hurdle model, panel data}, year = {2006}, } @article {neelon11, author = {Neelon, Brian and O'Malley, A. James and Normand, Sharon-Lise T.}, title = {A {B}ayesian Two-Part Latent Class Model for Longitudinal Medical Expenditure Data: Assessing the Impact of Mental Health and Substance Abuse Parity}, journal = {Biometrics}, volume = {67}, number = {1}, publisher = {Blackwell Publishing Inc}, issn = {1541-0420}, url = {http://dx.doi.org/10.1111/j.1541-0420.2010.01439.x}, doi = {10.1111/j.1541-0420.2010.01439.x}, pages = {280--289}, keywords = {Bayesian analysis, Growth mixture model, Latent class model, Mental health parity, Semi-continuous data, Two-part model}, year = {2011}, } @Incollection{manning81, author={Manning, WG and Morris, CN and Newhouse, JP and Orr, LL and Duan, N, and Keeler, EB and Leibowitz, A and Marquis, KH and Marquis, MS and Phelps, CE}, booktitle={ Health, Economics, and Health Economics}, editor = {van der Gaag, J and Perlman, M}, title={A two-part model of the demand for medical care: preliminary results from the health insurance study}, pages={103--123}, publisher={North-Holland}, address = {Amsterdam}, year=1981 } @article{duan83a, jstor_articletype = {research-article}, title = {A Comparison of Alternative Models for the Demand for Medical Care}, author = {Duan, Naihua and Manning, Willard G., Jr. and Morris, Carl N. and Newhouse, Joseph P.}, journal = {Journal of Business \& Economic Statistics}, jstor_issuetitle = {}, volume = {1}, number = {2}, jstor_formatteddate = {Apr., 1983}, pages = {pp. 115--126}, url = {http://www.jstor.org/stable/1391852}, ISSN = {07350015}, abstract = {We have tested alternative models of the demand for medical care using experimental data. The estimated response of demand to insurance plan is sensitive to the model used. We therefore use a split-sample analysis and find that a model that more closely approximates distributional assumptions and uses a nonparametric retransformation factor performs better in terms of mean squared forecast error. Simpler models are inferior either because they are not robust to outliers (e.g., ANOVA, ANOCOVA), or because they are inconsistent when strong distributional assumptions are violated (e.g., a two-parameter Box-Cox transformation).}, language = {English}, year = {1983}, publisher = {American Statistical Association}, copyright = {Copyright � 1983 American Statistical Association}, } @article{cooper03, author = {Cooper, Nicola J. and Sutton, Alex J. and Mugford, Miranda and Abrams, Keith R.}, title = {Use of {B}ayesian {M}arkov Chain {M}onte {C}arlo Methods to Model Cost-of-Illness Data}, volume = {23}, number = {1}, pages = {38--53}, year = {2003}, doi = {10.1177/0272989X02239653}, abstract ={It is well known that the modeling of cost data is often problematic due to the distribution of such data. Commonly observed problems include 1) a strongly right-skewed data distribution and 2) a significant percentage of zero-cost observations. This article demonstrates how a hurdle model can be implemented from a Bayesian perspective by means of Markov Chain Monte Carlo simulation methods using the freely available software WinBUGS. Assessment of model fit is addressed through the implementation of two cross-validation methods. The relative merits of this Bayesian approach compared to the classical equivalent are discussed in detail. To illustrate the methods described, patient-specific nonhealth-care resource-use data from a prospective longitudinal study and the Norfolk Arthritis Register (NOAR) are utilized for 218 individuals with early inflammatory polyarthritis (IP). The NOAR database also includes information on various patient-level covariates.}, URL = {http://mdm.sagepub.com/content/23/1/38.abstract}, eprint = {http://mdm.sagepub.com/content/23/1/38.full.pdf+html}, journal = {Medical Decision Making} } @article {xie04, author = {Xie, Haiyi and McHugo, Gregory and Sengupta, Anjana and Clark, Robin and Drake, Robert}, title = {A Method for Analyzing Longitudinal Outcomes with Many Zeros}, journal = {Mental Health Services Research}, publisher = {Springer Netherlands}, issn = {1522-3434}, keyword = {Medicine}, pages = {239-246}, volume = {6}, issue = {4}, url = {http://dx.doi.org/10.1023/B:MHSR.0000044749.39484.1b}, note = {10.1023/B:MHSR.0000044749.39484.1b}, year = {2004} } @article{su09, author = {Su, Li and Tom, Brian D. M. and Farewell, Vernon T.}, title = {Bias in 2-part mixed models for longitudinal semicontinuous data}, volume = {10}, number = {2}, pages = {374-389}, year = {2009}, doi = {10.1093/biostatistics/kxn044}, URL = {http://biostatistics.oxfordjournals.org/content/10/2/374.abstract}, eprint = {http://biostatistics.oxfordjournals.org/content/10/2/374.full.pdf+html}, journal = {Biostatistics} } @ARTICLE{olsen01, author = {Olsen, Maren K and Schafer, Joseph L}, title = {A Two-Part Random-Effects Model for Semicontinuous Longitudinal Data}, journal = {Journal of the American Statistical Association}, volume = {96}, number = {454}, pages = {730-745}, year = {2001}, doi = {10.1198/016214501753168389}, URL = {http://amstat.tandfonline.com/doi/abs/10.1198/016214501753168389}, eprint = {http://amstat.tandfonline.com/doi/pdf/10.1198/016214501753168389} } @article {Chai08, author = {Chai, High Seng and Bailey, Kent R.}, title = {Use of log-skew-normal distribution in analysis of continuous data with a discrete component at zero}, journal = {Statistics in Medicine}, volume = {27}, number = {18}, publisher = {John Wiley & Sons, Ltd.}, issn = {1097-0258}, url = {http://dx.doi.org/10.1002/sim.3210}, doi = {10.1002/sim.3210}, pages = {3643--3655}, keywords = {censoring, skew-normal distribution, two-part model}, year = {2008}, } @article{Azzalini85, author = {Azzalini, A.}, title = {A class of distributions which includes the normal ones}, journal = {Scandinavian Journal of Statistics}, year = {1985}, pages = {171--178}, volume = {12}, } @article{manning05, title = "Generalized modeling approaches to risk adjustment of skewed outcomes data", journal = "Journal of Health Economics", volume = "24", number = "3", pages = "465--488", year = "2005", note = "", issn = "0167-6296", doi = "10.1016/j.jhealeco.2004.09.011", url = "http://www.sciencedirect.com/science/article/pii/S0167629605000056", author = "Willard G. Manning and Anirban Basu and John Mullahy", keywords = "Health econometrics", keywords = "Log models", keywords = "Generalized linear models", keywords = "Skewed outcomes" } @article{liu10, title = "A flexible two-part random effects model for correlated medical costs", journal = "Journal of Health Economics", volume = "29", number = "1", pages = "110--123", year = "2010", note = "", issn = "0167-6296", doi = "10.1016/j.jhealeco.2009.11.010", url = "http://www.sciencedirect.com/science/article/pii/S0167629609001386", author = "Lei Liu and Robert L. Strawderman and Mark E. Cowen and Ya-Chen T. Shih", keywords = "Medical cost data", keywords = "Mixed model", keywords = "Random effect", keywords = "Health econometrics", keywords = "Zero-inflated data" } @article{Stacy65, author = {Stacy, E. W. and Mihram, G. A.}, title = {{Parameter estimation for a generalized gamma distribution}}, journal = {Technometrics}, volume = {7}, pages = {349--358}, url = {http://www.tandfonline.com/doi/abs/10.1080/00401706.1965.10490268}, year = {1965} } @article{liu12, author = {Liu, Lei and Strawderman, Robert L and Johnson, Bankole A and O'Quigley, John M}, title = {Analyzing repeated measures semi-continuous data, with application to an alcohol dependence study}, year = {2012}, doi = {10.1177/0962280212443324}, URL = {http://smm.sagepub.com/content/early/2012/04/01/0962280212443324.abstract}, eprint = {http://smm.sagepub.com/content/early/2012/04/01/0962280212443324.full.pdf+html}, journal = {Statistical Methods in Medical Research} } @article{tobin58, jstor_articletype = {research-article}, title = {Estimation of Relationships for Limited Dependent Variables}, author = {Tobin, James}, journal = {Econometrica}, jstor_issuetitle = {}, volume = {26}, number = {1}, jstor_formatteddate = {Jan., 1958}, pages = {pp. 24-36}, url = {http://www.jstor.org/stable/1907382}, ISSN = {00129682}, abstract = {}, language = {English}, year = {1958}, publisher = {The Econometric Society}, copyright = {Copyright � 1958 The Econometric Society}, } @article{moulton95, jstor_articletype = {research-article}, title = {A Mixture Model with Detection Limits for Regression Analyses of Antibody Response to Vaccine}, author = {Moulton, Lawrence H. and Halsey, Neal A.}, journal = {Biometrics}, jstor_issuetitle = {}, volume = {51}, number = {4}, jstor_formatteddate = {Dec., 1995}, pages = {pp. 1570-1578}, url = {http://www.jstor.org/stable/2533289}, ISSN = {0006341X}, abstract = {Antibody concentration values as determined by quantitative assays often are left-censored due to detection limits or limits established for purposes of specificity. Standard analyses which assume the data arise from a single lognormal response distribution may not be appropriate, when more observations are censored than would be expected under such a model. Interference from maternal antibodies due to vaccination at an early age, for example, could result in a high proportion of nonresponders to vaccine. A mixture model consisting of a censored lognormal distribution and a point distribution located below the detection limit is proposed for such situations. Antibody data from a study of measles vaccine are used to illustrate the utility of this approach and the interpretation of the model parameters.}, language = {English}, year = {1995}, publisher = {International Biometric Society}, copyright = {Copyright � 1995 International Biometric Society}, } @article {chai08, author = {Chai, High Seng and Bailey, Kent R.}, title = {Use of log-skew-normal distribution in analysis of continuous data with a discrete component at zero}, journal = {Statistics in Medicine}, volume = {27}, number = {18}, publisher = {John Wiley & Sons, Ltd.}, issn = {1097-0258}, url = {http://dx.doi.org/10.1002/sim.3210}, doi = {10.1002/sim.3210}, pages = {3643--3655}, keywords = {censoring, skew-normal distribution, two-part model}, year = {2008}, } @article{duan83b, jstor_articletype = {research-article}, title = {Smearing Estimate: A Nonparametric Retransformation Method}, author = {Duan, Naihua}, journal = {Journal of the American Statistical Association}, jstor_issuetitle = {}, volume = {78}, number = {383}, jstor_formatteddate = {Sep., 1983}, pages = {pp. 605-610}, url = {http://www.jstor.org/stable/2288126}, ISSN = {01621459}, abstract = {The smearing estimate is proposed as a nonparametric estimate of the expected response on the untransformed scale after fitting a linear regression model on a transformed scale. The estimate is consistent under mild regularity conditions, and usually attains high efficiency relative to parametric estimates. It can be viewed as a low-premium insurance policy against departures from parametric distributional assumptions. A real-world example of predicting medical expenditures shows that the smearing estimate can outperform parametric estimates even when the parametric assumption is nearly satisfied.}, language = {English}, year = {1983}, publisher = {American Statistical Association}, copyright = {Copyright � 1983 American Statistical Association}, } @article{tooze02, author = {Tooze, Janet A and Grunwald, Gary K and Jones, Richard H}, title = {Analysis of repeated measures data with clumping at zero}, volume = {11}, number = {4}, pages = {341--355}, year = {2002}, doi = {10.1191/0962280202sm291ra}, URL = {http://smm.sagepub.com/content/11/4/341.abstract}, eprint = {http://smm.sagepub.com/content/11/4/341.full.pdf+html}, journal = {Statistical Methods in Medical Research} } @article {cooper07, author = {Cooper, Nicola J. and Lambert, Paul C. and Abrams, Keith R. and Sutton, Alexander J.}, title = {Predicting costs over time using {B}ayesian {M}arkov chain {M}onte {C}arlo methods: an application to early inflammatory polyarthritis}, journal = {Health Economics}, volume = {16}, number = {1}, publisher = {John Wiley & Sons, Ltd.}, issn = {1099-1050}, url = {http://dx.doi.org/10.1002/hec.1141}, doi = {10.1002/hec.1141}, pages = {37--56}, keywords = {Bayesian methods, two-part models, repeated measures, Markov chain Monte Carlo, prediction, inflammatory polyarthritis}, year = {2007}, } @article{wu88, jstor_articletype = {research-article}, title = {Estimation and Comparison of Changes in the Presence of Informative Right Censoring by Modeling the Censoring Process}, author = {Wu, Margaret C. and Carroll, Raymond J.}, journal = {Biometrics}, jstor_issuetitle = {}, volume = {44}, number = {1}, jstor_formatteddate = {Mar., 1988}, pages = {pp. 175-188}, url = {http://www.jstor.org/stable/2531905}, ISSN = {0006341X}, abstract = {In the estimation and comparison of the rates of change of a continuous variable between two groups, the unweighted averages of individual simple least squares estimates from each group are often used. Under a linear random effects model, when all individuals have complete observations at identical time points, these statistics are maximum likelihood estimates for the expected rates of change. However, with censored or missing data, these estimates are no longer efficient when compared to generalized least squares estimates. When, in addition, the right-censoring process is dependent on the individual rates of change (i.e., informative right censoring), the generalized least squares estimates will be biased. Likelihood-ratio tests for informativeness of the censoring process and maximum likelihood estimates for the expected rates of change and the parameters of the right-censoring process are developed under a linear random effects model with a probit model for the right-censoring process. In realistic situations, we illustrate that the bias in estimating group rate of change and the reduction of power in comparing group differences could be substantial when strong dependency of the right-censoring process on individual rates of change is ignored.}, language = {English}, year = {1988}, publisher = {International Biometric Society}, copyright = {Copyright � 1988 International Biometric Society}, } @Book{little02, author={Little, Roderick J A and Rubin, Donald B}, title={Statistical Analysis with Missing Data}, publisher={John Wiley \& Sons}, address = {Hoboken}, edition={2}, year=2002 } @Incollection{albert09, author={Albert, PS and Follman, DA}, booktitle={Longitudinal Data Analysis}, editor = {Fitzmaurice, G and Davidian, M and Verbeke, G and Molenberghs, G}, title={Shared-parameter models}, pages={433--452}, publisher={ Chapman \& Hall/CRC Press}, address = {Boca Raton}, year=2009 } @article {liu08, author = {Liu, Lei and Ma, Jennie Z. and Johnson, Bankole A.}, title = {A multi-level two-part random effects model, with application to an alcohol-dependence study}, journal = {Statistics in Medicine}, volume = {27}, number = {18}, publisher = {John Wiley & Sons, Ltd.}, issn = {1097-0258}, url = {http://dx.doi.org/10.1002/sim.3205}, doi = {10.1002/sim.3205}, pages = {3528--3539}, keywords = {hierarchical model, longitudinal data analysis, mixed model, logistic model, nested random effects, generalized linear mixed model}, year = {2008}, } @Unpublished{muthen01, author = {Muth\'{e}n, Bengt O.}, title = {Two-part Growth Mixture Modeling}, note ={Unpublished Manuscript}, year = {2001}, url={http://pages.gseis.ucla.edu/faculty/muthen/articles/Article\underline{}094.pdf} } @article{brown15, title = "Modelling household finances: A {B}ayesian approach to a multivariate two-part model", journal = "Journal of Empirical Finance ", volume = "33", number = "", pages = "190--207", year = "2015", note = "", issn = "0927-5398", doi = "http://dx.doi.org/10.1016/j.jempfin.2015.03.017", url = "http://www.sciencedirect.com/science/article/pii/S0927539815000353", author = "Sarah Brown and Pulak Ghosh and Li Su and Karl Taylor", } @article {liu09, author = {Liu, Lei}, title = {Joint modeling longitudinal semi-continuous data and survival, with application to longitudinal medical cost data}, journal = {Statistics in Medicine}, volume = {28}, number = {6}, publisher = {John Wiley & Sons, Ltd.}, issn = {1097-0258}, url = {http://dx.doi.org/10.1002/sim.3497}, doi = {10.1002/sim.3497}, pages = {972--986}, keywords = {health economics, proportional hazards model, frailty model, dependent censoring, health service research, survival analysis}, year = {2009}, } @article{hatfield11, author = {Hatfield, Laura A. and Boye, Mark E. and Carlin, Bradley P.}, title = {Joint Modeling of Multiple Longitudinal Patient-Reported Outcomes and Survival}, journal = {Journal of Biopharmaceutical Statistics}, volume = {21}, number = {5}, pages = {971-991}, year = {2011}, doi = {10.1080/10543406.2011.590922}, URL = {http://www.tandfonline.com/doi/abs/10.1080/10543406.2011.590922}, eprint = {http://www.tandfonline.com/doi/pdf/10.1080/10543406.2011.590922} } @article {swallow15, author = {Swallow, Ben and Buckland, Stephen T. and King, Ruth and Toms, Mike P.}, title = {Bayesian hierarchical modelling of continuous non-negative longitudinal data with a spike at zero: An application to a study of birds visiting gardens in winter}, journal = {Biometrical Journal}, issn = {1521-4036}, url = {http://dx.doi.org/10.1002/bimj.201400081}, doi = {10.1002/bimj.201400081}, pages = {n/a--n/a}, keywords = {Bayesian hierarchical model, Continuous nonnegative data, Excess zeros, Tweedie distributions}, year = {2015}, } @article{mahmud10, abstract = {{A positive association was observed between viral infection status and both the probability of experiencing any respiratory symptoms, and their severity during the year. For DAVIS data the random effects probit -log skew normal model fits significantly better than the random effects probit -log normal model, endorsing our parametric choice for the model. The simulation study indicates that our proposed model seems to be robust to misspecification of the distribution of the positive skewed response.}}, author = {Mahmud, Sadia and Lou, Wy Wendy W. and Johnston, Neil W.}, citeulike-article-id = {7385335}, citeulike-linkout-0 = {http://dx.doi.org/10.1186/1471-2288-10-55}, citeulike-linkout-1 = {http://view.ncbi.nlm.nih.gov/pubmed/20540810}, citeulike-linkout-2 = {http://www.hubmed.org/display.cgi?uids=20540810}, day = {14}, doi = {10.1186/1471-2288-10-55}, issn = {1471-2288}, journal = {BMC medical research methodology}, keywords = {log-normal, longitudinal, mis-specification, probit, repeated, sas, skew, skew-normal, stats, zero}, month = jun, pages = {55+}, pmid = {20540810}, posted-at = {2010-08-22 04:23:27}, priority = {2}, title = {{A probit- log- skew-normal mixture model for repeated measures data with excess zeros, with application to a cohort study of paediatric respiratory symptoms.}}, url = {http://dx.doi.org/10.1186/1471-2288-10-55}, volume = {10}, year = {2010} } @article {basu10, author = {Basu, Anirban and Manning, Willard G.}, title = {Estimating lifetime or episode-of-illness costs under censoring}, journal = {Health Economics}, volume = {19}, number = {9}, publisher = {John Wiley & Sons, Ltd.}, issn = {1099-1050}, url = {http://dx.doi.org/10.1002/hec.1640}, doi = {10.1002/hec.1640}, pages = {1010--1028}, keywords = {censored costs, inverse probability weighting, episode of illness}, year = {2010}, } @article{zhang06, jstor_articletype = {research-article}, title = {Bayesian Inference for a Two-Part Hierarchical Model: An Application to Profiling Providers in Managed Health Care}, author = {Zhang, Min and Strawderman, Robert L. and Cowen, Mark E. and Wells, Martin T.}, journal = {Journal of the American Statistical Association}, jstor_issuetitle = {}, volume = {101}, number = {475}, jstor_formatteddate = {Sep., 2006}, pages = {pp. 934-945}, url = {http://www.jstor.org/stable/27590773}, ISSN = {01621459}, abstract = {Profiling is currently an important, and hotly debated, topic in health care and other industries looking for ways to control costs, increase profitability, and increase service quality. Managed care in particular has seen a proliferation in the use of statistical profiling methodology, particularly with regard to monitoring expenditure data. This article focuses on the specific problem of developing statistical methods appropriate for profiling physician contributions to patient pharmacy expenditures incurred in managed care setting. The two-part hierarchical model with a correlated random-effects structure considered here accounts for both the skewed, zero-inflated nature of pharmacy expenditure data and the fact that patient pharmacy expenditures are correlated within physicians. The random-effects structure has an attractive interpretation in terms of a conceptual model for physician prescribing patterns. Using this model, we propose to rank physicians based on an appropriately constructed provider-level performance measure. This information is subsequently used to develop a novel financial incentive scheme. Inference is conducted in a Bayesian framework using Markov chain Monte Carlo.}, language = {English}, year = {2006}, publisher = {American Statistical Association}, copyright = {Copyright � 2006 American Statistical Association}, } @article{vuong89, jstor_articletype = {research-article}, title = {Likelihood Ratio Tests for Model Selection and Non-Nested Hypotheses}, author = {Vuong, Quang H.}, journal = {Econometrica}, jstor_issuetitle = {}, volume = {57}, number = {2}, jstor_formatteddate = {Mar., 1989}, pages = {pp. 307-333}, url = {http://www.jstor.org/stable/1912557}, ISSN = {00129682}, abstract = {In this paper, we develop a classical approach to model selection. Using the Kullback-Leibler Information Criterion to measure the closeness of a model to the truth, we propose simple likelihood-ratio based statistics for testing the null hypothesis that the competing models are equally close to the true data generating process against the alternative hypothesis that one model is closer. The tests are directional and are derived successively for the cases where the competing models are non-nested, overlapping, or nested and whether both, one, or neither is misspecified. As a prerequisite, we fully characterize the asymptotic distribution of the likelihood ratio statistic under the most general conditions. We show that it is a weighted sum of chi-square distribution or a normal distribution depending on whether the distributions in the competing models closest to the truth are observationally identical. We also propose a test of this latter condition.}, language = {English}, year = {1989}, publisher = {The Econometric Society}, copyright = {Copyright � 1989 The Econometric Society}, } @article{desmarais13, author = {Desmarais, B. A. and Harden, J. J.}, title = "Testing for zero inflation in count models: Bias correction for the Vuong test", journal = "Stata Journal", publisher = "Stata Press", address = "College Station, TX", volume = "13", number = "4", year = "2013", pages = "810-835(26)", url = "http://www.stata-journal.com/article.html?article=st0319" } @article{Wilson15, title = "The misuse of the {V}uong test for non-nested models to test for zero-inflation ", journal = "Economics Letters ", volume = "127", number = "0", pages = "51 - 53", year = "2015", note = "", issn = "0165-1765", doi = "http://dx.doi.org/10.1016/j.econlet.2014.12.029", url = "http://www.sciencedirect.com/science/article/pii/S016517651400490X", author = "Paul Wilson", } @article{chernoff54, title = {On the distribution of the likelihood ratio}, author = {Chernoff, Herman}, journal = {The Annals of Mathematical Statistics}, volume = {25}, number = {3}, pages = {pp. 573-578}, url = {http://www.jstor.org/stable/2236839}, year = {1954}, } @article{molenberghs07, author = {Molenberghs, Geert and Verbeke, Geert}, title = {Likelihood Ratio, Score, and {W}ald Tests in a Constrained Parameter Space}, journal = {The American Statistician}, volume = {61}, number = {1}, pages = {pp. 22-27}, url = {http://www.jstor.org/stable/27643833}, year = {2007}, } @article {todem12, author = {Todem, David and Hsu, Wei-Wen and Kim, KyungMann}, title = {On the Efficiency of Score Tests for Homogeneity in Two-Component Parametric Models for Discrete Data}, journal = {Biometrics}, volume = {68}, number = {3}, url = {http://dx.doi.org/10.1111/j.1541-0420.2011.01737.x}, pages = {975--982}, year = {2012}, } @article {cao14, author = {Cao, Guanqun and Hsu, Wei-Wen and Todem, David}, title = {A score-type test for heterogeneity in zero-inflated models in a stratified population}, journal = {Statistics in Medicine}, volume = {33}, number = {12}, url = {http://dx.doi.org/10.1002/sim.6092}, doi = {10.1002/sim.6092}, pages = {2103--2114}, year = {2014}, } @article {ridout01, author = {Ridout, Martin and Hinde, John and Dem\'{e}Atrio, Clarice G. B.}, title = {A Score Test for Testing a Zero-Inflated {P}oisson Regression Model Against Zero-Inflated Negative Binomial Alternatives}, journal = {Biometrics}, volume = {57}, number = {1}, publisher = {Blackwell Publishing Ltd}, issn = {1541-0420}, url = {http://dx.doi.org/10.1111/j.0006-341X.2001.00219.x}, doi = {10.1111/j.0006-341X.2001.00219.x}, pages = {219--223}, keywords = {Count data, Negative binomial, Poisson regression model, Score test, Zero inflation}, year = {2001}, } @article {xiang07, author = {Xiang, Liming and Lee, Andy H. and Yau, Kelvin K. W. and McLachlan, Geoffrey J.}, title = {A score test for overdispersion in zero-inflated {P}oisson mixed regression model}, journal = {Statistics in Medicine}, volume = {26}, number = {7}, publisher = {John Wiley & Sons, Ltd.}, issn = {1097-0258}, url = {http://dx.doi.org/10.1002/sim.2616}, doi = {10.1002/sim.2616}, pages = {1608--1622}, keywords = {count data, negative binomial, overdispersion, random effects, score test, zero-inflation}, year = {2007}, } @article{liang86, author = {Liang, Kung-Yee and Zeger, Scott L.}, title = {Longitudinal data analysis using generalized linear models}, volume = {73}, number = {1}, pages = {13-22}, year = {1986}, doi = {10.1093/biomet/73.1.13}, abstract ={This paper proposes an extension of generalized linear models to the analysis of longitudinal data. We introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence. The estimating equations are derived without specifying the joint distribution of a subject's observations yet they reduce to the score equations for niultivariate Gaussian outcomes. Asymptotic theory is presented for the general class of estimators. Specific cases in which we assume independence, m-dependence and exchangeable correlation structures from each subject are discussed. Efficiency of the pioposecl estimators in two simple situations is considered. The approach is closely related to quasi-likelihood.}, URL = {http://biomet.oxfordjournals.org/content/73/1/13.abstract}, eprint = {http://biomet.oxfordjournals.org/content/73/1/13.full.pdf+html}, journal = {Biometrika} } @article{rosen00, author = {Rosen, O and Jiang, W and Tanner, MA}, title = {Mixtures of marginal models}, volume = {87}, number = {2}, pages = {391-404}, year = {2000}, doi = {10.1093/biomet/87.2.391}, abstract ={In this paper, we adapt a mixture model originally developed for regression models with independent data for the more general case of correlated outcome data, which includes longitudinal data as a special case. The estimation is performed by a generalisation of the EM algorithm which we call the Expectation-Solution (ES) algorithm. In this ES algorithm the M-step of the EM algorithm is replaced by a step requiring the solution of a series of generalised estimating equations. The ES algorithm, a general algorithm for solving generalised estimating equations with incomplete data, is then applied to the present problem of mixtures of marginal models. In addition to allowing for correlation inherent in correlated outcome data, the systematic component of this mixture of marginal models is more flexible than the conventional linear function. The methodology is applied in the contexts of normal and Poisson response data. Some theory regarding the ES algorithm is presented.}, URL = {http://biomet.oxfordjournals.org/content/87/2/391.abstract}, eprint = {http://biomet.oxfordjournals.org/content/87/2/391.full.pdf+html}, journal = {Biometrika} } @article {kim12, author = {Kim, Sung and Chang, Chung-Chou and Kim, Kevin and Fine, Michael and Stone, Roslyn}, affiliation = {Duke Clinical Research Institute, Duke University Medical Center, Durham, NC 27705, USA}, title = {{BLUP (REMQL)} estimation of a correlated random effects negative binomial hurdle model}, journal = {Health Services and Outcomes Research Methodology}, publisher = {Springer Netherlands}, issn = {1387-3741}, volume={12}, pages = {302--319}, year={2012}, url = {http://dx.doi.org/10.1007/s10742-012-0083-0}, note = {10.1007/s10742-012-0083-0}, } @article{gelfand90, jstor_articletype = {research-article}, title = {Sampling-Based Approaches to Calculating Marginal Densities}, author = {Gelfand, Alan E. and Smith, Adrian F. M.}, journal = {Journal of the American Statistical Association}, jstor_issuetitle = {}, volume = {85}, number = {410}, jstor_formatteddate = {Jun., 1990}, pages = {pp. 398-409}, url = {http://www.jstor.org/stable/2289776}, ISSN = {01621459}, abstract = {Stochastic substitution, the Gibbs sampler, and the sampling-importance-resampling algorithm can be viewed as three alternative sampling- (or Monte Carlo-) based approaches to the calculation of numerical estimates of marginal probability distributions. The three approaches will be reviewed, compared, and contrasted in relation to various joint probability structures frequently encountered in applications. In particular, the relevance of the approaches to calculating Bayesian posterior densities for a variety of structured models will be discussed and illustrated.}, language = {English}, year = {1990}, publisher = {American Statistical Association}, copyright = {Copyright � 1990 American Statistical Association}, } @article{rodrigues03, author = {Rodrigues, Josemar}, title = {Bayesian Analysis of Zero-Inflated Distributions}, journal = {Communications in Statistics - Theory and Methods}, volume = {32}, number = {2}, pages = {281-289}, year = {2003}, doi = {10.1081/STA-120018186}, URL = {http://www.tandfonline.com/doi/abs/10.1081/STA-120018186}, eprint = {http://www.tandfonline.com/doi/pdf/10.1081/STA-120018186} } @article {deb06, author = {Deb, Partha and Munkin, Murat K. and Trivedi, Pravin K.}, title = {Bayesian analysis of the two-part model with endogeneity: application to health care expenditure}, journal = {Journal of Applied Econometrics}, volume = {21}, number = {7}, publisher = {John Wiley & Sons, Ltd.}, issn = {1099-1255}, url = {http://dx.doi.org/10.1002/jae.891}, doi = {10.1002/jae.891}, pages = {1081--1099}, year = {2006}, } @article{ghosh09, author = {Ghosh, Pulak and Albert, Paul S.}, title = {A {B}ayesian analysis for longitudinal semicontinuous data with an application to an acupuncture clinical trial}, journal = {Computational Statistics \& Data Analysis}, issue_date = {January, 2009}, volume = {53}, number = {3}, month = jan, year = {2009}, issn = {0167-9473}, pages = {699--706}, numpages = {8}, url = {http://dx.doi.org/10.1016/j.csda.2008.09.011}, doi = {10.1016/j.csda.2008.09.011}, acmid = {1465332}, publisher = {Elsevier Science Publishers B. V.}, address = {Amsterdam, The Netherlands, The Netherlands}, } @article{manning98, title = "The logged dependent variable, heteroscedasticity, and the retransformation problem", journal = "Journal of Health Economics", volume = "17", number = "3", pages = "283 - 295", year = "1998", note = "", issn = "0167-6296", doi = "10.1016/S0167-6296(98)00025-3", url = "http://www.sciencedirect.com/science/article/pii/S0167629698000253", author = "Willard G. Manning", keywords = "Heteroscedasticity", keywords = "Retransformation", keywords = "Logged dependent variable" } @article{manning01, title = "Estimating log models: to transform or not to transform?", journal = "Journal of Health Economics", volume = "20", number = "4", pages = "461 - 494", year = "2001", note = "", issn = "0167-6296", doi = "10.1016/S0167-6296(01)00086-8", url = "http://www.sciencedirect.com/science/article/pii/S0167629601000868", author = "Willard G Manning and John Mullahy", keywords = "Health econometrics", keywords = "Transformation", keywords = "Retransformation", keywords = "Log models" } @article{buntin04, title = "Too much ado about two-part models and transformation?: Comparing methods of modeling Medicare expenditures", journal = "Journal of Health Economics", volume = "23", number = "3", pages = "525 - 542", year = "2004", note = "", issn = "0167-6296", doi = "10.1016/j.jhealeco.2003.10.005", url = "http://www.sciencedirect.com/science/article/pii/S0167629604000220", author = "Melinda Beeuwkes Buntin and Alan M. Zaslavsky", keywords = "Health care cost modeling" } @Incollection{jones11, author={Jones, A.M.}, booktitle={Oxford Handbook of Economic Forecasting}, title={Models for health care}, editor={Hendry, D. and Clements, M.}, pages={625--654}, publisher={Oxford University Press}, address = {Oxford}, year=2011 } @article{welsh06, title = "Estimating the retransformed mean in a heteroscedastic two-part model", journal = "Journal of Statistical Planning and Inference", volume = "136", number = "3", pages = "860 - 881", year = "2006", note = "", issn = "0378-3758", doi = "10.1016/j.jspi.2004.07.009", url = "http://www.sciencedirect.com/science/article/pii/S0378375804003337", author = "A.H. Welsh and X.H. Zhou", keywords = "Extra zeros", keywords = "Health care costs", keywords = "Heteroscedastic regression model", keywords = "Retransformation", keywords = "Skewed data", keywords = "Smearing", keywords = "Two-part model" } @article{ferguson73, jstor_articletype = {research-article}, title = {A Bayesian Analysis of Some Nonparametric Problems}, author = {Ferguson, Thomas S.}, journal = {The Annals of Statistics}, jstor_issuetitle = {}, volume = {1}, number = {2}, jstor_formatteddate = {Mar., 1973}, pages = {pp. 209-230}, url = {http://www.jstor.org/stable/2958008}, ISSN = {00905364}, abstract = {The Bayesian approach to statistical problems, though fruitful in many ways, has been rather unsuccessful in treating nonparametric problems. This is due primarily to the difficulty in finding workable prior distributions on the parameter space, which in nonparametric ploblems is taken to be a set of probability distributions on a given sample space. There are two desirable properties of a prior distribution for nonparametric problems. (I) The support of the prior distribution should be large--with respect to some suitable topology on the space of probability distributions on the sample space. (II) Posterior distributions given a sample of observations from the true probability distribution should be manageable analytically. These properties are antagonistic in the sense that one may be obtained at the expense of the other. This paper presents a class of prior distributions, called Dirichlet process priors, broad in the sense of (I), for which (II) is realized, and for which treatment of many nonparametric statistical problems may be carried out, yielding results that are comparable to the classical theory. In Section 2, we review the properties of the Dirichlet distribution needed for the description of the Dirichlet process given in Section 3. Briefly, this process may be described as follows. Let X be a space and A a ?-field of subsets, and let ? be a finite non-null measure on (X, A). Then a stochastic process P indexed by elements A of A, is said to be a Dirichlet process on (X, A) with parameter ? if for any measurable partition (A1, ?, Ak) of X, the random vector (P(A1), ?, P(Ak)) has a Dirichlet distribution with parameter (?(A1), ?, ?(Ak)). P may be considered a random probability measure on (X, A), The main theorem states that if P is a Dirichlet process on (X, A) with parameter ?, and if X1, ?, Xn is a sample from P, then the posterior distribution of P given X1, ?, Xn is also a Dirichlet process on (X, A) with a parameter ? + ?n 1 ?xi , where ?x denotes the measure giving mass one to the point x. In Section 4, an alternative definition of the Dirichlet process is given. This definition exhibits a version of the Dirichlet process that gives probability one to the set of discrete probability measures on (X, A). This is in contrast to Dubins and Freedman [2], whose methods for choosing a distribution function on the interval [0, 1] lead with probability one to singular continuous distributions. Methods of choosing a distribution function on [0, 1] that with probability one is absolutely continuous have been described by Kraft [7]. The general method of choosing a distribution function on [0, 1], described in Section 2 of Kraft and van Eeden [10], can of course be used to define the Dirichlet process on [0, 1]. Special mention must be made of the papers of Freedman and Fabius. Freedman [5] defines a notion of tailfree for a distribution on the set of all probability measures on a countable space X. For a tailfree prior, posterior distribution given a sample from the true probability measure may be fairly easily computed. Fabius [3] extends the notion of tailfree to the case where X is the unit interval [0, 1], but it is clear his extension may be made to cover quite general X. With such an extension, the Dirichlet process would be a special case of a tailfree distribution for which the posterior distribution has a particularly simple form. There are disadvantages to the fact that P chosen by a Dirichlet process is discrete with probability one. These appear mainly because in sampling from a P chosen by a Dirichlet process, we expect eventually to see one observation exactly equal to another. For example, consider the goodness-of-fit problem of testing the hypothesis H0 that a distribution on the interval [0, 1] is uniform. If on the alternative hypothesis we place a Dirichlet process prior with parameter ? itself a uniform measure on [0, 1], and if we are given a sample of size n ? 2, the only nontrivial nonrandomized Bayes rule is to reject H0 if and only if two or more of the observations are exactly equal. This is really a test of the hypothesis that a distribution is continuous against the hypothesis that it is discrete. Thus, there is still a need for a prior that chooses a continuous distribution with probability one and yet satisfies properties (I) and (II). Some applications in which the possible doubling up of the values of the observations plays no essential role are presented in Section 5. These include the estimation of a distribution function, of a mean, of quantiles, of a variance and of a covariance. A two-sample problem is considered in which the Mann-Whitney statistic, equivalent to the rank-sum statistic, appears naturally. A decision theoretic upper tolerance limit for a quantile is also treated. Finally, a hypothesis testing problem concerning a quantile is shown to yield the sign test. In each of these problems, useful ways of combining prior information with the statistical observations appear. Other applications exist. In his Ph. D. dissertation [1], Charles Antoniak finds a need to consider mixtures of Dirichlet processes. He treats several problems, including the estimation of a mixing distribution, bio-assay, empirical Bayes problems, and discrimination problems.}, language = {English}, year = {1973}, publisher = {Institute of Mathematical Statistics}, copyright = {Copyright � 1973 Institute of Mathematical Statistics}, } @article{blough99, title = "Modeling risk using generalized linear models", journal = "Journal of Health Economics", volume = "18", number = "2", pages = "153 - 171", year = "1999", note = "", issn = "0167-6296", doi = "10.1016/S0167-6296(98)00032-0", url = "http://www.sciencedirect.com/science/article/pii/S0167629698000320", author = "David K. Blough and Carolyn W. Madden and Mark C. Hornbrook", keywords = "Medical risk", keywords = "Two-part model", keywords = "Generalized linear model", keywords = "Quasi-likelihood", keywords = "Model calibration" } @article {omalley08, author = {O'Malley, A. James and Smith, Murray H. and Sadler, William A.}, title = {A RESTRICTED MAXIMUM LIKELIHOOD PROCEDURE FOR ESTIMATING THE VARIANCE FUNCTION OF AN IMMUNOASSAY}, journal = {Australian \& New Zealand Journal of Statistics}, volume = {50}, number = {2}, publisher = {Blackwell Publishing Asia}, issn = {1467-842X}, url = {http://dx.doi.org/10.1111/j.1467-842X.2008.00506.x}, doi = {10.1111/j.1467-842X.2008.00506.x}, pages = {161--177}, year = {2008}, } @article{park66, jstor_articletype = {research-article}, title = {Estimation with Heteroscedastic Error Terms}, author = {Park, R. E.}, journal = {Econometrica}, jstor_issuetitle = {}, volume = {34}, number = {4}, jstor_formatteddate = {Oct., 1966}, pages = {p. 888}, url = {http://www.jstor.org/stable/1910108}, ISSN = {00129682}, abstract = {}, language = {English}, year = {1966}, publisher = {The Econometric Society}, copyright = {Copyright � 1966 The Econometric Society}, } @article {chen13, author = {Chen, Jinsong and Liu, Lei and Johnson, Bankole A. and O'Quigley, John}, title = {Penalized likelihood estimation for semiparametric mixed models, with application to alcohol treatment research}, journal = {Statistics in Medicine}, volume = {32}, number = {2}, issn = {1097-0258}, url = {http://dx.doi.org/10.1002/sim.5528}, doi = {10.1002/sim.5528}, pages = {335--346}, keywords = {generalized linear mixed models (GLMMs), Laplace approximation, logistic models, longitudinal data analysis, non-normal random effects}, year = {2013}, } @article{basu05, author = {Basu, Anirban and Rathouz, Paul J.}, title = {Estimating marginal and incremental effects on health outcomes using flexible link and variance function models}, volume = {6}, number = {1}, pages = {93-109}, year = {2005}, doi = {10.1093/biostatistics/kxh020}, abstract ={We propose an extension to the estimating equations in generalized linear models to estimate parameters in the link function and variance structure simultaneously with regression coefficients. Rather than focusing on the regression coefficients, the purpose of these models is inference about the mean of the outcome as a function of a set of covariates, and various functionals of the mean function used to measure the effects of the covariates. A commonly used functional in econometrics, referred to as the marginal effect, is the partial derivative of the mean function with respect to any covariate, averaged over the empirical distribution of covariates in the model. We define an analogous parameter for discrete covariates. The proposed estimation method not only helps to identify an appropriate link function and to suggest an underlying distribution for a specific application but also serves as a robust estimator when no specific distribution for the outcome measure can be identified. Using Monte Carlo simulations, we show that the resulting parameter estimators are consistent. The method is illustrated with an analysis of inpatient expenditure data from a study of hospitalists.}, URL = {http://biostatistics.oxfordjournals.org/content/6/1/93.abstract}, eprint = {http://biostatistics.oxfordjournals.org/content/6/1/93.full.pdf+html}, journal = {Biostatistics} } @article{akaike74, author = {Akaike, Hirotugu}, citeulike-article-id = {3245939}, journal = {{IEEE} Transactions on Automatic Control}, key = {Pattern Classification A02}, keywords = {file-import-08-09-12}, number = {6}, pages = {716--723}, posted-at = {2008-09-12 14:30:37}, priority = {2}, publisher = {IEEE Press}, title = {A New Look at the Statistical Model Identification}, volume = {19}, year = {1974} } @article{sugiura78, author = { Nariaki Sugiura }, title = {Further analysts of the data by {A}kaike' s information criterion and the finite corrections}, journal = {Communications in Statistics - Theory and Methods}, volume = {7}, number = {1}, pages = {13-26}, year = {1978}, } @article{schwartz78, jstor_articletype = {research-article}, title = {Estimating the Dimension of a Model}, author = {Gideon Schwarz}, journal = {The Annals of Statistics}, jstor_issuetitle = {}, volume = {6}, number = {2}, jstor_formatteddate = {Mar., 1978}, pages = {pp. 461-464}, url = {http://www.jstor.org/stable/2958889}, ISSN = {00905364}, language = {English}, year = {1978}, publisher = {Institute of Mathematical Statistics}, copyright = {Copyright � 1978 Institute of Mathematical Statistics}, } @article{burnham04, author = {Burnham, Kenneth P. and Anderson, David R.}, title = {Multimodel Inference: Understanding {AIC and BIC} in Model Selection}, volume = {33}, number = {2}, pages = {261-304}, year = {2004}, doi = {10.1177/0049124104268644}, URL = {http://smr.sagepub.com/content/33/2/261.abstract}, eprint = {http://smr.sagepub.com/content/33/2/261.full.pdf+html}, journal = {Sociological Methods \& Research} } @Article{diebold95, author={Diebold, Francis X and Mariano, Roberto S}, title={Comparing Predictive Accuracy}, journal={Journal of Business \& Economic Statistics}, year=1995, volume={13}, number={3}, pages={253-263}, month={July}, url={http://ideas.repec.org/a/bes/jnlbes/v13y1995i3p253-63.html} } @book{harrell01, author = {Harrell,Jr., Frank E.}, title = {Regression Modeling Strategies}, year = {2006}, isbn = {0387952322}, publisher = {Springer}, series = {Springer Series in Statistics}, address = {Secaucus, NJ, USA}, } @book{hastie11, author={Hastie, T. and Tibshirani, R. and Friedman, J.H.}, title = {The Elements of Statistical Learning: Data Mining, Inference, and Prediction}, edition = {2nd}, publisher = {Springer}, series = {Springer Series in Statistics}, url = {http://www-stat.stanford.edu/\~{}tibs/ElemStatLearn/main.html}, year = {2011}, address = {Secaucus, NJ, USA} } @article{pan01, jstor_articletype = {research-article}, title = {Akaike's Information Criterion in Generalized Estimating Equations}, author = {Pan, Wei}, journal = {Biometrics}, jstor_issuetitle = {}, volume = {57}, number = {1}, jstor_formatteddate = {Mar., 2001}, pages = {pp. 120-125}, url = {http://www.jstor.org/stable/2676849}, ISSN = {0006341X}, language = {English}, year = {2001}, publisher = {International Biometric Society}, copyright = {Copyright � 2001 International Biometric Society}, } @article {spiegelhalter02, author = {Spiegelhalter, David J. and Best, Nicola G. and Carlin, Bradley P. and Van Der Linde, Angelika}, title = {Bayesian measures of model complexity and fit}, journal = {Journal of the Royal Statistical Society: Series B (Statistical Methodology)}, volume = {64}, number = {4}, publisher = {Blackwell Publishers}, issn = {1467-9868}, url = {http://dx.doi.org/10.1111/1467-9868.00353}, doi = {10.1111/1467-9868.00353}, pages = {583--639}, keywords = {Bayesian model comparison, Decision theory, Deviance information criterion, Effective number of parameters, Hierarchical models, Information theory, Leverage, Markov chain Monte Carlo methods, Model dimension}, year = {2002}, } @article{celeux06, author = {G. Celeux and F. Forbes and C. P. Robert and D. M. Titterington}, title = {Deviance information criteria for missing data models}, journal = {Bayesian Analysis}, volume={1}, number={4}, pages={651--674}, year = {2006} } @article{watanabe10, author = {Watanabe, Sumio}, title = {Asymptotic Equivalence of {B}ayes Cross Validation and Widely Applicable Information Criterion in Singular Learning Theory}, journal = {Journal of Machine Learning Research}, issue_date = {3/1/2010}, volume = {11}, month = dec, year = {2010}, issn = {1532-4435}, pages = {3571--3594}, numpages = {24}, url = {http://dl.acm.org/citation.cfm?id=1756006.1953045}, acmid = {1953045}, publisher = {JMLR.org}, } @article{kass95, jstor_articletype = {research-article}, title = {Bayes Factors}, author = {Kass, Robert E. and Raftery, Adrian E.}, journal = {Journal of the American Statistical Association}, jstor_issuetitle = {}, volume = {90}, number = {430}, jstor_formatteddate = {Jun., 1995}, pages = {pp. 773-795}, url = {http://www.jstor.org/stable/2291091}, ISSN = {01621459}, language = {English}, year = {1995}, publisher = {American Statistical Association}, copyright = {Copyright � 1995 American Statistical Association}, } @article{berger96, jstor_articletype = {research-article}, title = {The Intrinsic {B}ayes Factor for Model Selection and Prediction}, author = {Berger, James O. and Pericchi, Luis R.}, journal = {Journal of the American Statistical Association}, jstor_issuetitle = {}, volume = {91}, number = {433}, jstor_formatteddate = {Mar., 1996}, pages = {pp. 109-122}, url = {http://www.jstor.org/stable/2291387}, ISSN = {01621459}, language = {English}, year = {1996}, publisher = {American Statistical Association}, copyright = {Copyright � 1996 American Statistical Association}, } @article{gelfand94, jstor_articletype = {research-article}, title = {Bayesian Model Choice: Asymptotics and Exact Calculations}, author = {Gelfand, A. E. and Dey, D. K.}, journal = {Journal of the Royal Statistical Society. Series B (Statistical Methodology)}, jstor_issuetitle = {}, volume = {56}, number = {3}, jstor_formatteddate = {1994}, pages = {pp. 501-514}, url = {http://www.jstor.org/stable/2346123}, ISSN = {00359246}, abstract = {Model determination is a fundamental data analytic task. Here we consider the problem of choosing among a finite (without loss of generality we assume two) set of models. After briefly reviewing classical and Bayesian model choice strategies we present a general predictive density which includes all proposed Bayesian approaches that we are aware of. Using Laplace approximations we can conveniently assess and compare the asymptotic behaviour of these approaches. Concern regarding the accuracy of these approximations for small to moderate sample sizes encourages the use of Monte Carlo techniques to carry out exact calculations. A data set fitted with nested non-linear models enables comparisons between proposals and between exact and asymptotic values.}, language = {English}, year = {1994}, publisher = {Wiley-Blackwell for the Royal Statistical Society}, copyright = {Copyright � 1994 Royal Statistical Society}, } @article {millar09, author = {Millar, Russell B.}, title = {Comparison of Hierarchical {B}ayesian Models for Overdispersed Count Data using {DIC} and {B}ayes' Factors}, journal = {Biometrics}, volume = {65}, number = {3}, publisher = {Blackwell Publishing Inc}, issn = {1541-0420}, url = {http://dx.doi.org/10.1111/j.1541-0420.2008.01162.x}, doi = {10.1111/j.1541-0420.2008.01162.x}, pages = {962--969}, keywords = {Bayes' factors, Count data, DIC, Hierarchical model, Marginal likelihood, Negative binomial, Overdispersion, Poisson gamma, Poisson lognormal, WinBUGS, Zero inflation}, year = {2009}, } @Incollection{raftery07, author={Raftery, A.M. and Newton, M.A. and Satagopan, J.M. and Krivitsky, P.N.}, booktitle={Bayesian Statistics 8}, editor = {Bernardo,J. M. and Bayarri, M. J. and Berger, J. O. and Dawid,A. P. and Heckerman, D. and Smith, A. F. M. and West M. }, title={Estimating the Integrated Likelihood via Posterior Simulation Using the Harmonic Mean Identity}, pages={1--45}, publisher={Oxford University Press}, address = {Oxford}, year=2007 } @article{hoeting99, author = "Hoeting, Jennifer A. and Madigan, David and Raftery, Adrian E. and Volinsky, Chris T.", doi = "10.1214/ss/1009212519", fjournal = "Statistical Science", journal = "Statistical Science", number = "4", pages = "382--417", publisher = "The Institute of Mathematical Statistics", title = "Bayesian model averaging: a tutorial", url = "http://dx.doi.org/10.1214/ss/1009212519", volume = "14", year = "1999" } @ARTICLE{gelman96, author = {Andrew Gelman and Xiao-li Meng and Hal Stern}, title = {Posterior Predictive Assessment of Model Fitness via Realized Discrepancies}, journal = {Statistica Sinica}, year = {1996}, volume = {6}, pages = {733--807} } @Book{ando10, author={Ando, Tomohiro}, title={Bayesian Model Selection and Statistical Modeling}, publisher={Chapman Hall/CRC Press}, address = {Boca Raton}, year=2010 } @Manual{rdevelop15, 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{jackman12, title = {{pscl}: Classes and Methods for {R} Developed in the Political Science Computational Laboratory, Stanford University}, author = {Simon Jackman}, organization = {Department of Political Science, Stanford University}, address = {Stanford, California}, year = {2012}, note = {R package version 1.04.4}, url = {http://pscl.stanford.edu/}, } @Article{zeileis08, title = {Regression Models for Count Data in {R}}, author = {Achim Zeileis and Christian Kleiber and Simon Jackman}, journal = {Journal of Statistical Software}, year = {2008}, volume = {27}, number = {8}, url = {http://www.jstatsoft.org/v27/i08/}, } @article{fournier12, author = {Fournier, David A. and Skaug, Hans J. and Ancheta, Johnoel and Ianelli, James and Magnusson, Arni and Maunder, Mark N. and Nielsen, Anders and Sibert, John}, title = {{AD} Model Builder: using automatic differentiation for statistical inference of highly parameterized complex nonlinear models}, journal = {Optimization Methods and Software}, volume = {27}, number = {2}, pages = {233-249}, year = {2012}, doi = {10.1080/10556788.2011.597854}, URL = {http://www.tandfonline.com/doi/abs/10.1080/10556788.2011.597854}, eprint = {http://www.tandfonline.com/doi/pdf/10.1080/10556788.2011.597854} } @Manual{skaug12, title = {{glmmADMB}: generalized linear mixed models using AD Model Builder}, author = {Skaug, H. and Fournier, D. and Nielsen, A. and Magnusson, A. and Bolker, B.}, year = {2012}, note = {R package version 0.7.2.12.}, url = {http://glmmadmb.r-forge.r-project.org}, } @Article{hadfield10, title = {{MCMC} Methods for Multi-Response Generalized Linear Mixed Models: The {MCMCglmm} {R} Package}, author = {Jarrod D Hadfield}, journal = {Journal of Statistical Software}, year = {2010}, volume = {33}, number = {2}, pages = {1--22}, url = {http://www.jstatsoft.org/v33/i02/}, } @Manual{shabenberger09, title = {spatcounts: Spatial count regression}, author = {Holger Schabenberger}, year = {2009}, note = {R package version 1.1}, url = {http://CRAN.R-project.org/package=spatcounts}, } @Manual{sas04, author={{SAS Institute}}, title = {{SAS} 9.1.3 Help and Documentation}, institution = {SAS Institute Inc.}, year = {2000--2004}, address={Cary, NC}, url = {http://www.sas.com/}, } @Manual{stata11, title = {Stata Statistical Software: Release 12}, institution = {StataCorp LP}, year = {2011}, address={College Station, TX}, url = {http://stata.com/}, } @Misc{hilbe1, author={Joseph Hilbe}, title={{HNBLOGIT}: Stata module to estimate negative binomial-logit hurdle regression}, year=2005, month=Oct, howpublished={Statistical Software Components, Boston College Department of Economics}, abstract={hnblogit fits a negative binomial-logit maximum-likelihood hurdle model of depvar on indepvars, where depvar is a non-negative count variable.}, keywords={hurdle; negative binomial; logit}, url={http://ideas.repec.org/c/boc/bocode/s456401.html}, } @Misc{hilbe2, author={Joseph Hilbe}, title={{HPLOGIT}: Stata module to estimate {P}oisson-logit hurdle regression}, year=2005, month=Oct, howpublished={Statistical Software Components, Boston College Department of Economics}, abstract={hplogit fits a Poisson-logit maximum-likelihood hurdle model of depvar on indepvars, where depvar is a non-negative count variable.}, keywords={hurdle; Poisson; logit}, url={http://ideas.repec.org/c/boc/bocode/s456405.html}, } @article{rabe05, title = "Maximum likelihood estimation of limited and discrete dependent variable models with nested random effects", journal = "Journal of Econometrics", volume = "128", number = "2", pages = "301--323", year = "2005", note = "", issn = "0304-4076", doi = "10.1016/j.jeconom.2004.08.017", url = "http://www.sciencedirect.com/science/article/pii/S0304407604001599", author = "Sophia Rabe-Hesketh and Anders Skrondal and Andrew Pickles", keywords = "Random effects", keywords = "Random coefficients", keywords = "Multilevel models", keywords = "Hierarchical models", keywords = "Numerical integration", keywords = "Adaptive quadrature", keywords = "Spherical quadrature rules", keywords = "GLLAMM" } @manual{lillard03, author = {L. A. Lillard and C. W. A. Panis}, title = {Multiprocess Multilevel Modelling, version 2, User's Guide and Reference Manual}, year = {1998--2003}, address = {Los Angeles}, publisher = {EconoWare} } @article{lunn00, author = {Lunn, David J. and Thomas, Andrew and Best, Nicky and Spiegelhalter, David}, title = {{WinBUGS} -- A {B}ayesian modelling framework: Concepts, structure, and extensibility}, journal = {Statistics and Computing}, issue_date = {October 2000}, volume = {10}, number = {4}, month = oct, year = {2000}, issn = {0960-3174}, pages = {325--337}, numpages = {13}, url = {http://dx.doi.org/10.1023/A:1008929526011}, doi = {10.1023/A:1008929526011}, acmid = {599385}, publisher = {Kluwer Academic Publishers}, address = {Hingham, MA, USA}, keywords = {BUGS, Markov chain Monte Carlo, WinBUGS, directed acyclic graphs, object-orientation, run-time linking, type extension}, } @manual{stan15, author ={{Stan Development Team}}, year = {2015}, title = {Stan Modeling Language Users Guide and Reference Manual, Version 2.7.0}, url = {http://mc-stan.org/} } @manual{muthen12, author = {Muth\'{e}n, B. 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K.}, keywords = {software}, address = {Los Angeles, CA}, priority = {2}, publisher = {Muth\'{e}n \& Muth\'{e}n}, title = {{Mplus (Version 7)}}, year = {1998-2012}, url={https://www.statmodel.com/} } @article{Ritz04, author = {Ritz, John and Spiegelman, Donna}, title = {Equivalence of conditional and marginal regression models for clustered and longitudinal data}, volume = {13}, number = {4}, pages = {309-323}, year = {2004}, doi = {10.1191/0962280204sm368ra}, URL = {http://smm.sagepub.com/content/13/4/309.abstract}, eprint = {http://smm.sagepub.com/content/13/4/309.full.pdf+html}, journal = {Statistical Methods in Medical Research} } @article{Neelon14, author = {Neelon, Brian and Chang, Howard H and Ling, Qiang and Hastings, Nicole S}, title = {Spatiotemporal hurdle models for zero-inflated count data: Exploring trends in emergency department visits}, year = {2014}, doi = {10.1177/0962280214527079}, URL = {http://smm.sagepub.com/content/early/2014/03/27/0962280214527079.abstract}, eprint = {http://smm.sagepub.com/content/early/2014/03/27/0962280214527079.full.pdf+html}, note= {e-publication ahead of print}, journal = {Statistical Methods in Medical Research} } @article {Dreassi14, author = {Dreassi, Emanuela and Petrucci, Alessandra and Rocco, Emilia}, title = {Small area estimation for semicontinuous skewed spatial data: An application to the grape wine production in Tuscany}, journal = {Biometrical Journal}, volume = {56}, number = {1}, issn = {1521-4036}, url = {http://dx.doi.org/10.1002/bimj.201200271}, doi = {10.1002/bimj.201200271}, pages = {141--156}, keywords = {Gamma-mixed model, Geostatistical models, Hierarchical Bayesian models, Penalized splines, Two-part random effects models}, year = {2014}, } @article {arcuti16, author = {Arcuti, Simona and Pollice, Alessio and Ribecco, Nunziata and D'Onghia, Gianfranco}, title = {Bayesian spatiotemporal analysis of zero-inflated biological population density data by a delta-normal spatiotemporal additive model}, journal = {Biometrical Journal}, volume = {58}, number = {2}, issn = {1521-4036}, url = {http://dx.doi.org/10.1002/bimj.201400123}, doi = {10.1002/bimj.201400123}, pages = {372--386}, keywords = {Bayesian analysis, Biological population dynamics, Generalized additive models, MCMC, Zero-inflated data}, year = {2016}, } @ARTICLE{dempster77, author = {A. 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Norton", } @article {long14, author = {Long, D. Leann and Preisser, John S. and Herring, Amy H. and Golin, Carol E.}, title = {A marginalized zero-inflated {P}oisson regression model with overall exposure effects}, journal = {Statistics in Medicine}, volume = {33}, number = {29}, issn = {1097-0258}, url = {http://dx.doi.org/10.1002/sim.6293}, doi = {10.1002/sim.6293}, pages = {5151--5165}, keywords = {incidence, marginalized models, unprotected intercourse, zero inflation}, year = {2014}, } @article {long15, author = {Leann Long, D. and Preisser, John S. and Herring, Amy H. and Golin, Carol E.}, title = {A marginalized zero-inflated {P}oisson regression model with random effects}, journal = {Journal of the Royal Statistical Society: Series C (Applied Statistics)}, volume = {64}, number = {5}, issn = {1467-9876}, url = {http://dx.doi.org/10.1111/rssc.12104}, doi = {10.1111/rssc.12104}, pages = {815--830}, keywords = {Marginalized models, Repeated measures, Unprotected intercourse, Zero inflation}, year = {2015}, } @article {preisser16, author = {Preisser, John S. and Das, Kalyan and Long, D. Leann and Divaris, Kimon}, title = {Marginalized zero-inflated negative binomial regression with application to dental caries}, journal = {Statistics in Medicine}, volume = {35}, number = {10}, issn = {1097-0258}, url = {http://dx.doi.org/10.1002/sim.6804}, doi = {10.1002/sim.6804}, pages = {1722--1735}, keywords = {caries prevention, count data, excess zeros, marginal models, overdispersion}, year = {2016}, note = {sim.6804}, } @article{aitchison55, author = {John Aitchison}, title = {On the distribution of a positive random variable having a discrete probability mass at the origin}, journal = {Journal of The American Statistical Association}, volume = {50}, year = {1955}, pages = {901--908}, issue = {271}, doi = {10.1080/01621459.1955.10501976}, url = {http://www.jstor.org/stable/2281175} } @article{cragg71, title = {Some statistical models for limited dependent variables with application to the demand for durable goods}, author = {Cragg, John G.}, journal = {Econometrica}, volume = {39}, number = {5}, pages = {pp. 829--844}, url = {http://www.jstor.org/stable/1909582}, year = {1971}, } @article {neelon15, author = {Neelon, Brian and Zhu, Li and Neelon, Sara E. 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