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Jackknifed Liu-type estimator in the Conway-Maxwell Poisson regression model | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 13، شماره 1، خرداد 2022، صفحه 3153-3168 اصل مقاله (405.13 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.6064 | ||
| نویسندگان | ||
| Husam AbdulRazzak Rasheed1؛ Nazik J. Sadik2؛ Zakariya Yahya Algamal3 | ||
| 1Mustansiriyah University, Iraq | ||
| 2Baghdad University, Iraq | ||
| 3University of Mosul, Iraq | ||
| تاریخ دریافت: 13 اردیبهشت 1400، تاریخ بازنگری: 27 تیر 1400، تاریخ پذیرش: 30 مهر 1401 | ||
| چکیده | ||
| Modelling of count data has been of extreme interest to researchers. However, in practice, count data is often identified with overdispersion or underdispersion. The Conway Maxwell Poisson regression model (CMPRE) has been proven powerful in modelling count data with a wide range of dispersion. In regression modeling, it is known that multicollinearity negatively affects the variance of the maximum likelihood estimator. To address this problem, shrinkage estimators, such as Liu and Liu-type estimators have been consistently verified to be attractive to decrease the effects of multicollinearity. However, these shrinkage estimators are considered biased estimators. In this study, the jackknife approach and its modified version are proposed for modeling count data with CMPRE. These two estimators are proposed to reduce the effects of multicollinearity and the biasedness of using the Liu-type estimator simultaneously. The results of Monte Carlo simulation and real data recommend that the proposed estimators were significant improvement relative to other competitor estimators, in terms of absolute bias and mean squared error with superiority to the modified jackknifed Liu-type estimator. | ||
| کلیدواژه‌ها | ||
| Multicollinearity؛ Liu-type estimator؛ Conway-Maxwell-Poisson regression model؛ Jackknife estimator؛ Monte Carlo simulation | ||
| مراجع | ||
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[1] A. Alkhateeb and Z. Algamal, Jackknifed liu-type estimator in Poisson regression model, J.Iran. Stat. Soc. 19(1) (2020) 21–37. [2] N.K. Rashad and Z.Y. Algamal, A new ridge estimator for the Poisson regression model, Iran. J. Technol. Trans. A: Sci. 43(6) (2019) 2921–2928. [3] L.H. Vanegas and L.M. Rondon, A data transformation to deal with constant under/over-dispersion in Poisson and binomial regression models, J. Statist. Comput Simul. 90(10) (2020) 1811–1833. [4] B. Forthmann and P. Doebler, Reliability of researcher capacity estimates and count data dispersion: A comparison of Poisson, negative binomial and conway-maxwell-poisson models, Scientometrics 126(4) (2021) 3337–3354. [5] R.A. Francis, S.R. Geedipally, S.D. Guikema, S.S. Dhavala, D. Lord and S. LaRocca, Characterizing the performance of the Conway-Maxwell Poisson generalized linear model, Risk Anal. Int. J. 32(1) (2012) 167–183. [6] G.M. Abdella, J. Kim, K.N. Al-Khalifa and A.M. Hamouda, Penalized Conway-maxwell-Poisson regression for modelling dispersed discrete data: The case study of motor vehicle crash frequency, Safety Sci. 120 (2019) 157–163. [7] A. Huang, emphMean-parametrized Conway–Maxwell–Poisson regression models for dispersed counts, J. Sagepub. Statist. Modell. 17(6) (2017) 359–380. [8] R.W. Conway and W.L. Maxwell, A queuing model with state-dependent service rates, J. Ind. Eng. 12(2) (1962) 132–136. [9] 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, J. Biometrics 72(2) (2016) 606–618. [10] A.E. Hoerl and R.W. Kennard, Ridge regression: Biased estimation for nonorthogonal problems, Technometrics 12(1) (1970) 55–67. [11] D. Lord, S.R. Geedipally and S.D. Guikema, Extension of the application of Conway-Maxwell-Poisson models: Analyzing traffic crash data exhibiting underdispersion, Risk Anal. 30(8) (2010) 1268–1276. [12] D. Lord, S.D. Guikema and S.R. Geedipally, Application of the Conway-Maxwell-Poisson generalized linear model [13] M.F. Santarelli, D. Della Latta, M. Scipioni, V. Positano and L. Landini, A Conway-Maxwell-Poisson (cmp) model to address data dispersion on positron emission tomography, Comput. Biol. Med. 77 (2016) 90–101. [14] S.B. Chatla and G. Shmueli, Efficient estimation of com–poisson regression and a generalized additive model, Comput. Statist. Data Anal. 121 (2018) 71–88. [15] G. Shmueli, T.P. Minka, J.B. Kadane, S. Borle and P.J. Boatwright, A useful distribution for fitting discrete data: Revival of the Conway-Maxwell-Poisson distribution, J. R. Statist. Soc. 54(1) (2005) 127–142. [16] S.D. Guikema and J.P. Coffelt, A flexible count data regression model for risk analysis, Risk Anal. 28(1) (2008) 213–223. [17] B. Singh, Y. Chaubey and T. Dwivedi, An almost unbiased ridge estimator, Indian J. Statist. Series B 13 (1986) 342–346. [18] E. Akdeniz Duran and F. Akdeniz, Efficiency of the modified jackknifed liu-type estimator, Statist. Pap. 53(2) (2012) 265–280. [19] M.H. Gruber, The efficiency of jack-knifed and usual ridge type estimators: A comparison, Statist. Probab. Lett. 11(1) (1991) 49–51. [20] M. Khurana, Y. P. Chaubey and S. Chandra, Jackknifing the ridge regression estimator: A revisit, Comm. Statist. Theory Methods 43 (24) (2014) 5249–5262. [21] H. Nyquist, Applications of the jackknife procedure in ridge regression, Comput. Statist. Data Anal. 6(2) (1988) 177–183. [22] S. Turkan and G. Ozel, A new modified jackknifed estimator for the Poisson regression model, J. Appl. Stat. 43(10) (2015) 1892–1905. [23] N. Yildiz, On the performance of the jackknifed liu-type estimator in linear regression model, Comm. Staistt. Theory Methods (2017) 0-0. [24] Z.Y. Algamal, Developing a ridge estimator for the gamma regression model, J. Chemometrics 32(10) (2018). [25] Z.Y. Algamal, Biased estimators in Poisson regression model in the presence of multicollinearity: A subject review, Al-Qadisiyah J. Administrative Econ. Sci. 20(1) (2018) 37–43. [26] B.G. Kibria, K. M˚ansson and G. Shukur, A simulation study of some biasing parameters for the ridge type estimation of Poisson regression, Commun. Stat. Simul. Comput. 44(4) (2015) 943–957. [27] K. Mansson, B.G. Kibria, P. Sjolander and G. Shukur, Improved liu estimators for the Poisson regression model, Int. J. Stat. Probab. 1(1) (2012). [28] K. Liu, Using liu-type estimator to combat collinearity, Comm. Statist. Theory Methods 32(5) (2003) 1009–1020. [29] D.V. Hinkley, Jackknifing in unbalanced situations, Technometrics 19(3) (1977) 285–292. [30] B. Singh, Y. Chaubey and T. Dwivedi, An almost unbiased ridge estimator, Indian. J. Stat. Series B (1986) 342–346. [31] F.S.M. Batah, T.V. Ramanathan and S.D. Gore, The efficiency of modified jackknife and ridge type regression estimators: A comparison, Surv. Math. Appl. 3 (2008). [32] M.H. Quenouille, Notes on bias in estimation, Biometrika 43(3-4) (1956) 353–360. [33] J. Tukey, Bias and confidence in not quite large samples, Ann. Math. Stat. 29 (1958) 614. [34] B.M.G. Kibria, Performance of some new ridge regression estimators, Commun. Stat. Simul. Comput. 32(2) (2003) 419–435. [35] A. E. Hoerl, R. W. Kannard and K. F. Baldwin, Ridge regression: Some simulations, Comm. Statist. Theory Methods 4(2) (1975) 105–123. [36] D. Marcondes Filho and A.M.O.T. Sant’Anna, Principal component regression-based control charts for monitoring count data, Int. J. Adv. Manuf. Technol. 85(5) (2016) 1565–1574. [37] U. Mammadova and M.R. Ozkale, ¨ Profile monitoring for count data using Poisson and Conway-Maxwell-Poisson regression-based control charts under multicollinearity problem, J. Comput. Appl. Math. 388 (2021) 113275. | ||
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