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A Journal of Theoretical and Applied Statistics
Volume 53, 2019 - Issue 4
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Original Articles

Estimation in zero-inflated binomial regression with missing covariates

, &
Pages 839-865 | Received 13 Sep 2017, Accepted 06 May 2019, Published online: 21 May 2019

References

  • Lambert D. Zero-inflated Poisson regression, with an application to defects in manufacturing. Technometrics. 1992;34(1):1–14. doi: 10.2307/1269547
  • Dietz E, Böhning D. On estimation of the Poisson parameter in zero-modified Poisson models. Comput Stat Data Anal. 2000;34(4):441–459. doi: 10.1016/S0167-9473(99)00111-5
  • Lim HK, Li WK, Yu PLH. Zero-inflated Poisson regression mixture model. Comput Stat Data Anal. 2014;71:151–158. doi: 10.1016/j.csda.2013.06.021
  • Monod A. Random effects modeling and the zero-inflated Poisson distribution. Commun Stat Theory Methods. 2014;43(4):664–680. Technometrics 34, 1–14. doi: 10.1080/03610926.2013.814782
  • Hall DB. Zero-inflated Poisson and binomial regression with random effects: a case study. Biometrics. 2000;56(4):1030–1039. doi: 10.1111/j.0006-341X.2000.01030.x
  • Min Y, Agresti A. Random effect models for repeated measures of zero-inflated count data. Stat Model. 2005;5(1):1–19. doi: 10.1191/1471082X05st084oa
  • Zhao W, Zhang R, Liu J, et al. Semi varying coefficient zero-inflated generalized Poisson regression model. Commun Stat Theory Methods. 2015;44(1):171–185. doi: 10.1080/03610926.2012.735325
  • Feng J, Zhu Z. Semiparametric analysis of longitudinal zero-inflated count data. J Multivar Anal. 2011;102:61–72. doi: 10.1016/j.jmva.2010.08.001
  • Lam KF, Xue H, Cheung YB. Semiparametric analysis of zero-inflated count data. Biometrics. 2006;62(4):996–1003. doi: 10.1111/j.1541-0420.2006.00575.x
  • Ridout M, Hinde J, Demetrio CGB. A score test for testing a zero-inflated Poisson regression model against zero-inflated negative binomial alternatives. Biometrics. 2001;57(1):219–223. doi: 10.1111/j.0006-341X.2001.00219.x
  • Garay AM, Hashimoto EM, Ortega EMM, et al. On estimation and influence diagnostics for zero-inflated negative binomial regression models. Comput Stat Data Anal. 2011;55(3):1304–1318. doi: 10.1016/j.csda.2010.09.019
  • Moghimbeigi A, Eshraghian MR, Mohammad K, et al. Multilevel zero-inflated negative binomial regression modeling for over-dispersed count data with extra zeros. J Appl Stat. 2008;35(9):1193–1202. doi: 10.1080/02664760802273203
  • Mwalili SM, Lesaffre E, Declerck D. The zero-inflated negative binomial regression model with correction for misclassification: an example in caries research. Stat Methods Med Res. 2008;17(2):123–139. doi: 10.1177/0962280206071840
  • Vieira AMC, Hinde JP, Demetrio CGB. Zero-inflated proportion data models applied to a biological control assay. J Appl Stat. 2000;27(3):373–389. doi: 10.1080/02664760021673
  • Diop A, Diop A, Dupuy J-F. Simulation-based inference in a zero-inflated Bernoulli regression model. Commun Stat Simul Comput. 2016;45(10):3597–3614. doi: 10.1080/03610918.2014.950743
  • Gilthorpe MS, Frydenberg M, Cheng Y, et al. Modelling count data with excessive zeros: The need for class prediction in zero-inflated models and the issue of data generation in choosing between zero-inflated and generic mixture models for dental caries data. Stat Med. 2009;28:3539–3553. doi: 10.1002/sim.3699
  • Matranga D, Firenze A, Vullo A. Can Bayesian models play a role in dental caries epidemiology? Evidence from an application to the BELCAP data set. Community Dent Oral Epidemiol. 2013;41(5):473–480.
  • Diallo AO, Diop A, Dupuy J-F. Asymptotic properties of the maximum likelihood estimator in zero-inflated binomial regression. Commun Stat Theory Methods. 2017;46(20):9930–9948. doi: 10.1080/03610926.2016.1222437
  • Diallo AO, Diop A, Dupuy J-F. Analysis of multinomial counts with joint zero-inflation, with an application to health economics. J Stat Planning Inference. 2018;194:85-–105. doi: 10.1016/j.jspi.2017.09.005
  • Deng D, Zhang Y. Score tests for both extra zeros and extra ones in binomial mixed regression models. Commun Stat Theory Methods. 2015;44:2881–2897. doi: 10.1080/03610926.2013.809118
  • Dupuy J-F. Inference in a generalized endpoint-inflated binomial regression model. Statistics. 2017;51(4):888–903. doi: 10.1080/02331888.2017.1316724
  • Tian G-L, Ma H, Zhou Y, et al. Generalized endpoint-inflated binomial model. Comput Stat Data Anal. 2015;89:97–114. doi: 10.1016/j.csda.2015.03.009
  • Guo X, Xu W, Zhu L. Multi-index regression models with missing covariates at random. J Multivar Anal. 2014;123:345–363. doi: 10.1016/j.jmva.2013.10.006
  • Liang H, Wang S, Robins JM, et al. Estimation in partially linear models with missing covariates. J Am Stat Assoc. 2004;99(466):357–367. doi: 10.1198/016214504000000421
  • Robins JM, Rotnitzky A, Zhao LP. Estimation of regression coefficients when some regressors are not always observed. J Am Stat Assoc. 1994;89(427):846–866. doi: 10.1080/01621459.1994.10476818
  • Schafer JL, Yucel RM. Computational strategies for multivariate linear mixed-effects models with missing values. J Comput Graph Stat. 2002;11(2):437–457. doi: 10.1198/106186002760180608
  • Yang X, Belin T, Boscardin W. Imputation and variable selection in linear regression models with missing covariates. Biometrics. 2005;61(2):498–506. doi: 10.1111/j.1541-0420.2005.00317.x
  • Davis KA, Sinha SK, Park CG. Constrained inference for generalized linear models with incomplete covariate data. J Stat Comput Simul. 2015;85(4):693–710. doi: 10.1080/00949655.2013.837907
  • Horton NJ, Laird NM. Maximum likelihood analysis of generalized linear models with missing covariates. Stat Methods Med Res. 1999;8(1):37–50. doi: 10.1177/096228029900800104
  • Ibrahim JG, Chen M-H, Lipsitz SR, et al. Missing-data methods for generalized linear models: a comparative review. J Am Stat Assoc. 2005;100(469):332–346. doi: 10.1198/016214504000001844
  • Ibrahim JG, Lipsitz SR, Chen M-H. Missing covariates in generalized linear models when the missing data mechanism is non-ignorable. J R Stat Soc Ser B. 1999;61(1):173–190. doi: 10.1111/1467-9868.00170
  • Ibrahim JG. Incomplete data in generalized linear models. J Am Stat Assoc. 1990;85(411):765–769. doi: 10.1080/01621459.1990.10474938
  • Sinha SK, Laird NM, Fitzmaurice GM. Multivariate logistic regression with incomplete covariate and auxiliary information. J Multivar Anal. 2010;101(10):2389–2397. doi: 10.1016/j.jmva.2010.06.010
  • Chen HY, Little RJA. Proportional hazards regression with missing covariates. J Am Stat Assoc. 1999;94(447):896–908. doi: 10.1080/01621459.1999.10474195
  • Hao M, Song X, Sun L. Reweighting estimators for the additive hazards model with missing covariates. Can J Stat. 2014;42(2):285–307. doi: 10.1002/cjs.11210
  • Herring AH, Ibrahim JG. Likelihood-based methods for missing covariates in the Cox proportional hazards model. J Am Stat Assoc. 2001;96(453):292–302. doi: 10.1198/016214501750332866
  • Luo XD, Tsai WY, Xu Q. Pseudo-partial likelihood estimators for the Cox regression model with missing covariates. Biometrika. 2009;96(3):617–633. doi: 10.1093/biomet/asp027
  • Paik MC. Multiple imputation for the Cox proportional hazards model with missing covariates. Lifetime Data Anal. 1997;3(3):289–298. doi: 10.1023/A:1009657116403
  • Paik MC, Tsai W-Y. On using the Cox proportional hazards model with missing covariates. Biometrika. 1997;84(3):579–593. doi: 10.1093/biomet/84.3.579
  • Qiu Z. Statistical inference under imputation for proportional hazard model with missing covariates. Commun Stat Theory Methods. 2017;46(23):11575–11590. doi: 10.1080/03610926.2016.1275696
  • Song X, Wang C-Y. Time-varying coefficient proportional hazards model with missing covariates. Stat Med. 2013;32(12):2013–2030. doi: 10.1002/sim.5652
  • White IR, Royston P. Imputing missing covariate values for the Cox model. Stat Med. 2009;28(15):1982–1998. doi: 10.1002/sim.3618
  • Chen X-D, Fu Y-Z. Model selection for zero-inflated regression with missing covariates. Comput Stat Data Anal. 2011;55(1):765–773. doi: 10.1016/j.csda.2010.06.023
  • Lukusa TM, Lee S-M, Li C-S. Semiparametric estimation of a zero-inflated Poisson regression model with missing covariates. Metrika. 2016;79(4):457–483. doi: 10.1007/s00184-015-0563-7
  • Lukusa TM, Lee S-M, Li C-S. Review of zero-inflated models with missing data. Current Res Biostat. 2017;7(1):1–12. doi: 10.3844/amjbsp.2017.1.12
  • Boucher J-P, Denuit M, Guillen M. Number of accidents or number of claims? An approach with zero-inflated Poisson models for panel data. J Risk Insur. 2009;76(4):821–846. doi: 10.1111/j.1539-6975.2009.01321.x
  • Yip KCH, Yau KKW. On modeling claim frequency data in general insurance with extra zeros. Insurance Math Econom. 2005;36(2):153–163. doi: 10.1016/j.insmatheco.2004.11.002
  • Horvitz DG, Thompson DJ. A generalization of sampling without replacement from a finite universe. J Am Stat Assoc. 1952;47:663–685. doi: 10.1080/01621459.1952.10483446
  • Zhao LP, Lipsitz S. Designs and analysis of two-stage studies. Stat Med. 1992;11(6):769–782. doi: 10.1002/sim.4780110608
  • Seaman SR, White IR. Review of inverse probability weighting for dealing with missing data. Stat Methods Med Res. 2013;22(3):278–295. doi: 10.1177/0962280210395740
  • Hsieh SH, Lee SM, Shen PS. Logistic regression analysis of randomized response data with missing covariates. J Stat Plan Inference. 2010;140(4):927–940. doi: 10.1016/j.jspi.2009.09.020
  • Qi L, Wang CY, Prentice RL. Weighted estimators for proportional hazards regression with missing covariates. J Am Stat Assoc. 2005;100(472):1250–1263. doi: 10.1198/016214505000000295
  • Li T, Hu Y. Inverse probability weighted estimators for single-index models with missing covariates. Commun Stat Theory Methods. 2010;45(5):1199–1214. doi: 10.1080/03610926.2012.705208
  • Diop A, Diop A, Dupuy J-F. Maximum likelihood estimation in the logistic regression model with a cure fraction. Electron J Stat. 2011;5:460–483. doi: 10.1214/11-EJS616
  • Tsiatis A. Semiparametric theory and missing data. New York: Springer; 2007. (Springer Series in Statistics)
  • Rubin DB. Inference and missing data. Biometrika. 1976;63(3):581–592. doi: 10.1093/biomet/63.3.581
  • Gouriéroux C, Monfort A. Asymptotic properties of the maximum likelihood estimator in dichotomous logit models. J Econom. 1981;17(102):83–97. doi: 10.1016/0304-4076(81)90060-9
  • Foutz RV. On the unique consistent solution to the likelihood equations. J Am Stat Assoc. 1977;72:147–148. doi: 10.1080/01621459.1977.10479926
  • Jiang J. Large sample techniques for statistics. New York: Springer; 2010.
  • Eicker F. A multivariate central limit theorem for random linear vector forms. Ann Math Stat. 1966;37(6):1825–1828. doi: 10.1214/aoms/1177699175
  • R Core Team, 2013. R Foundation for Statistical Computing, Vienna, Austria. http://www.R-project.org/.
  • Henningsen A, Toomet O. maxLik: a package for maximum likelihood estimation in R. Comput Stat. 2011;26(3):443–458. doi: 10.1007/s00180-010-0217-1
  • Rubin DB. Multiple imputation for nonresponse in surveys. New York: John Wiley and Sons; 1987.
  • van Buuren S, Groothuis-Oudshoorn K. Mice: multivariate imputation by chained equations in R. J Stat Softw. 2011;45(3):1–67.
  • Sun B, Tchetgen Tchetgen EJ. On Inverse Probability Weighting for nonmonotone missing at random data. J Am Stat Assoc. 2018;113(521):369–379. doi: 10.1080/01621459.2016.1256814

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