Analyzing clustered count data with a cluster-specific random effect zero-inflated Conway–Maxwell–Poisson distribution

References

• G.D.C. Barriga and F. Louzada, The zero-inflated Conway–Maxwell–Poisson distribution: Bayesian inference, regression modeling and influence diagnostic, Stat. Methodol. 21 (2014), pp. 23–34. doi: 10.1016/j.stamet.2013.11.003
   Web of Science ®Google Scholar
• A.W. Blocker, fastGHQuad: Fast Rcpp implementation of Gauss-Hermite quadrature, preprint (2014). Available at https://cran.rproject.org/web/packages/fastGHQuad/fastGHQuad.pdf.
   Google Scholar
• H. Choo-Wosoba, S.M. Levy, and S. Datta, Marginal regression models for clustered count data based on zero-inflated Conway–Maxwell–Poisson distribution with applications, Biometrics 72 (2016), pp. 606–618. doi: 10.1111/biom.12436
   PubMed Web of Science ®Google Scholar
• R.W. Conway and W.L. Maxwell, A queuing model with state dependent service rates, J. Ind. Eng. 12 (1962), pp. 132–136.
   Google Scholar
• K.A. Fulton, D. Liu, D.L. Haynie, and P.S. Albert, Mixed model and estimating equation approaches for zero inflation in clustered binary response data with application to a dating violence study, Ann. Appl. Statist. 9 (2015), pp. 275–299. doi: 10.1214/14-AOAS791
   PubMed Web of Science ®Google Scholar
• D.B. Hall, Zero-inflated Poisson and binomial regression with random effects: A case study, Biometrics 56 (2000), pp. 1030–1039. doi: 10.1111/j.0006-341X.2000.01030.x
   PubMed Web of Science ®Google Scholar
• M.T. Hasan, G. Sneddon, and R. Ma, Pattern-mixture zero-inflated mixed models for longitudinal unbalanced count data with excessive zeros, Biometrics 51 (2009), pp. 946–960. doi: 10.1002/bimj.200900093
   Web of Science ®Google Scholar
• N. Jansakul and J.P. Hinde, Score tests for zero-inflated Poisson models, Comput. Statist. Data Anal. 40 (2002), pp. 75–96. doi: 10.1016/S0167-9473(01)00104-9
   Web of Science ®Google Scholar
• M.H. Kutner, C.J. Nachtsheim, and J. Neter, Applied Linear Regression Models, 4th ed., McGraw-Hill, New York, 2003.
   Google Scholar
• E. Lesaffre and B. Spiessens, On the effect of the number of quadrature points in a logistic random-effects model: An example, Appl. Stat. 50 (2001), pp. 325–335.
   Web of Science ®Google Scholar
• D. Lord, S.D. Guikema, and S.R. Geedipally, Application of the Conway-Maxwell-Poisson generalized linear model for analyzing motor vehicle crashes, Accid. Anal. Prev. 40 (2008), pp. 1123–1134. doi: 10.1016/j.aap.2007.12.003
   PubMed Web of Science ®Google Scholar
• Y. Min and A. Agresti, Random effect models for repeated measures of zero-inflated count data, Stat. Model. 5 (2005), pp. 1–19. doi: 10.1191/1471082X05st084oa
   Web of Science ®Google Scholar
• A. Paschold, N.B. Larson, C. Marcon, J.C. Schnable, C.-T. Yeh, C. Lanz, D. Nettleton, H.-P. Piepho, P.S. Schnable, and F. Hochholdinger, Nonsyntenic genes drive highly dynamic complementation of gene expression in mazie hybrids, Plant Cell 26 (2014), pp. 3939–3948. doi: 10.1105/tpc.114.130948
   PubMed Web of Science ®Google Scholar
• M. Rodrigue-Motta, D. Gianola, and B. Heringstad, A mixed effects model for overdispersed zero inflated Poisson data with an application in animal breeding, J. Data Sci. 8 (2010), pp. 379–396.
   Google Scholar
• K.F. Sellers and A. Raim, A flexible zero-inflated model to address data dispersion, Comput. Statist. Data Anal. 99 (2016), pp. 68–80. doi: 10.1016/j.csda.2016.01.007
   Web of Science ®Google Scholar
• K.F. Sellers and G. Shmueli, A flexible regression model for count data, Ann. Appl. Statist. 4 (2010), pp. 943–961. doi: 10.1214/09-AOAS306
   Web of Science ®Google Scholar
• G. Shmueli, T.P. Minka, J.B. Kadane, S. Borle, and P. Boatwright, A useful distribution for fitting discrete data: Revival of the Conway-Maxwell-Poisson distribution, Ann. Appl. Statist. 54 (2005), pp. 127–142.
   Google Scholar
• P. Sur, G. Shmueli, S. Bose, and P. Dubey, Modeling bimodal discrete data using Conway–Maxwell–Poisson mixture models, J. Bus. Econ. Stat. 33 (2015), pp. 352–365. doi: 10.1080/07350015.2014.949343
   Web of Science ®Google Scholar
• K.K.W. Yau, K. Wang, and A.H. Lee, Zero-inflated negative binomial mixed regression modeling of over-dispersed count data with extra zeros, Biometrics 45 (2003), pp. 437–452. doi: 10.1002/bimj.200390024
   Web of Science ®Google Scholar