References
- del Castillo J, Pérez-Casany M. Overdispersed and underdispersed Poisson generalizations. J Stat Plan Inference. 2005;134:486–500. doi: 10.1016/j.jspi.2004.04.019
- Yang Z, Hardin JW, Addy CL, et al. Testing approaches for overdispersion in poisson regression versus the generalized poisson model. Biom J. 2007;49:565–584. doi: 10.1002/bimj.200610340
- Patil M, Shirke D. Testing parameter of the power series distribution of a zero inflated power series model. Stat Methodol. 2007;4:393–406. doi: 10.1016/j.stamet.2006.12.001
- Choo-Wosoba H, Levy SM, Datta S. Marginal regression models for clustered count data based on zero-inflated Conway–Maxwell–Poisson distribution with applications. Biometrics. 2015;72:606–618. doi: 10.1111/biom.12436
- Barriga GD, Louzada F. The zero-inflated Conway–Maxwell–Poisson distribution: bayesian inference, regression modeling and influence diagnostic. Stat Methodol. 2014;21:23–34. doi: 10.1016/j.stamet.2013.11.003
- Samani EB, Amirian Y, Ganjali M. Likelihood estimation for longitudinal zero-inflated power series regression models. J Appl Stat. 2012;39:1965–1974. doi: 10.1080/02664763.2012.699951
- 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
- Lee S, Lee Y, Chen CW. Parameter change test for zero-inflated generalized poisson autoregressive models. Statistics. 2016;50:540–557. doi: 10.1080/02331888.2015.1083020
- Conceição K, Louzada F, Andrade M, Helou E. Zero-modified power series distribution and its hurdle distribution version. J Stat Comput Simul. 2017;87:1842–1862. doi: 10.1080/00949655.2017.1289529
- Lambert D. Zero-inflated Poisson regression, with an application to defects in manufacturing. Technometrics. 1992;34:1–14. doi: 10.2307/1269547
- Cameron AC, Trivedi PK. Regression Analysis of Count Data. Cambridge: Cambridge University Press; 1998.
- Zeileis A, Kleiber C, Jackman S. Regression models for count data in R. J Stat Softw, Articles. 2008;27:1–25.
- Pandya M, Pandya H, Pandya S. Bayesian inference on mixture of geometric with degenerate distribution: zero inflated geometric distribution. Int J Res Rev Appl Sci. 2012;13:53–65.
- Zipkin EF, Leirness JB, Kinlan BP, et al. Fitting statistical distributions to sea duck count data: implications for survey design and abundance estimation. Stat Methodol. 2014;17:67–81. doi: 10.1016/j.stamet.2012.10.002
- Edwin TK. Power series distributions and zero-inflated models. Doctoral Dissertation, University of Nairobi; 2014.
- van den Broek J.. A score test for zero inflation in a Poisson distribution. Biometrics. 1995;51:738–743. doi: 10.2307/2532959
- Ridout M, Hinde J, Demétrio C. A score test for testing a zero-inflated Poisson regression model against zero-inflated negative binomial alternatives. Biometrics. 2001;57:219–223. doi: 10.1111/j.0006-341X.2001.00219.x
- Gupta PL, Gupta RC, Tripathi RC. Score test for zero inflated generalized Poisson regression model. Commun Stat-Theory Methods. 2005;33:47–64. doi: 10.1081/STA-120026576
- Xiang L, Lee AH, Yau KK, et al. A score test for zero-inflation in correlated count data. Stat Med. 2006;25:1660–1671. doi: 10.1002/sim.2308
- Todem D, Hsu W-W, Kim K. On the efficiency of score tests for homogeneity in two-component parametric models for discrete data. Biometrics. 2012;68:975–982. doi: 10.1111/j.1541-0420.2011.01737.x
- Hsu W-W, Todem D, Kim K, et al. A Wald test for zero inflation and deflation for correlated count data from dental caries research. Stat Model. 2014;14:471–488. doi: 10.1177/1471082X14535480
- Terrell GR. The gradient statistic. Comput Sci Stat. 2002;34:206–215.
- Lemonte AJ, Ferrari SLP. The local power of the gradient test. Ann Inst Stat Math. 2012;64:373–381. doi: 10.1007/s10463-010-0315-4
- Rao CR. Score test: historical review and recent developments. In Balakrishnan N., Kannan N., and Nagaraja H. N., editors. Advances in ranking and selection, multiple comparisons, and reliability. Birkhuser: Boston; 2005.
- Lemonte A. The Gradient Test: Another Likelihood-Based Test. London: Academic Press; 2016.
- Corless RM, Gonnet GH, Hare DEG, et al. On the Lambert W function. Adv Comput Math. 1996;5:329–359. doi: 10.1007/BF02124750
- R Core Team. R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing; 2016.
- Goerg GM. LambertW: Probabilistic Models to Analyze and Gaussianize Heavy-Tailed, Skewed Data. R library version 0.6.42016.
- Cox DR, Reid N. Parameter orthogonality and approximate conditional inference. J R Stat Soc B. 1987;49:1–39.
- Rao CR. Linear Statistical Inference and its Applications. 2nd ed. New York: Wiley; 1973.