319
Views
2
CrossRef citations to date
0
Altmetric
Article

Poisson regression diagnostics with ridge estimation

, & ORCID Icon
Pages 4174-4192 | Received 26 Oct 2020, Accepted 09 Jul 2021, Published online: 06 Aug 2021

References

  • Algamal, Z. Y. 2018. Biased estimators in Poisson regression model in the presence of multicollinearity: A subject review. Al-Qadisiyah Journal for Administrative and Economic Sciences 20 (1):37–43.
  • Algamal, Z. Y., and M. M. Alanaz. 2018. Proposed methods in estimating the ridge regression parameter in Poisson regression model. Electronic Journal of Applied Statistical Analysis 11 (2):506–15.
  • Amin, M., M. N. Akram, and M. Amanullah. 2020. On the James-Stein estimator for the Poisson regression model. Communications in Statistics - Simulation and Computation. Advance online publication. doi: 10.1080/03610918.2020.1775851.
  • Amin, M., M. N. Akram, and B. M. G. Kibria. 2021. A new adjusted Liu estimator for the Poisson regression model. Concurrency and Computation: Practice and Experience. Advance online publication. doi: 10.1002/cpe.6340.
  • Amin, M., M. N. Akram, and A. Majid. 2021. On the estimation of Bell regression model using ridge estimator. Communications in Statistics - Simulation and Computation. Advance online publication. doi: 10.1080/03610918.2020.1870694.
  • Amin, M., M. Amanullah, M. Aslam, and M. Qasim. 2019. Influence diagnostics in gamma ridge regression model. Journal of Statistical Computation and Simulation 89 (3):536–56. doi: 10.1080/00949655.2018.1558226.
  • Amin, M., M. Amanullah, and M. Qasim. 2020. Diagnostic techniques for the inverse Gaussian regression model. Communications in Statistics - Theory and Methods. Advance online publication. doi: 10.1080/03610926.2020.1777308.
  • Amin, M., M. Faisal, and M. N. Akram. 2021. Influence diagnostics in the inverse Gaussian ridge regression model: Applications in chemometrics. Journal of Chemometrics 35 (6):1–20. doi: 10.1002/cem.3342.
  • Amin, M., M. Amanullah, and M. Aslam. 2016. Empirical evaluation of the inverse Gaussian regression residuals for the assessment of influential points. Journal of Chemometrics 30 (7):394–404. doi: 10.1002/cem.2805.
  • Amin, M., M. Amanullah, and G. M. Cordeiro. 2017. Influence diagnostics in the gamma regression model with adjusted deviance residuals. Communications in Statistics - Simulation and Computation 46 (9):6959–73. doi: 10.1080/03610918.2016.1222420.
  • Asar, Y., and A. Genc. 2018. A new two-parameter estimator for the Poisson regression model. Iranian Journal of Science and Technology, Transactions A: Science 42 (2):793–803. doi: 10.1007/s40995-017-0174-4.
  • Belsley, D. A., E. Kuh, and R. Welsch. 1980. Regression diagnostics: Identifying influential data and sources of collinearity. New York: Wiley.
  • Chau, A. M. H., E. C. M. Lo, M. C. M. Wong, and C. H. Chu. 2018. Interpreting Poisson regression models in dental caries studies. Caries Research 52 (4):339–45. doi: 10.1159/000486970.
  • Chowdhury, K. K., E. V. Gijo, and R. Raghavan. 2000. Quality improvement through design of experiments: A case study. Quality Engineering 12 (3):407–16. doi: 10.1080/08982110008962604.
  • Cook, R. D. 1977. Detection of influential observation in linear regression. Technometrics 19 (1):15–18.
  • Davison, A. C., and C. L. Tsai. 1992. Regression model diagnostics. International Statistical Review/Revue Internationale de Statistique 60 (3):337–53. doi: 10.2307/1403682.
  • Dobson, A. J. 2002. An introduction to generalized linear models. 2nd ed. London: Chapman & Hall/CRC Press.
  • Draper, N. R., and J. A. John. 1981. Influential observations and outliers in regression. Technometrics 23 (1):21–26. doi: 10.1080/00401706.1981.10486232.
  • Frome, E. L. 1983. The analysis of rates using Poisson regression models. Biometrics 39 (3):665–74. doi: 10.2307/2531094.
  • Hardin, J. W., and J. M. Hilbe. 2012. Generalized estimating equations. USA: Chapman and Hall/CRC.
  • Hilbe, J. M. 2011. Negative binomial regression. New York: Cambridge University Press.
  • Hoerl, A. E., and R. W. Kennard. 1970. Ridge regression: Biased estimation for non-orthogonal problems. Technometrics 12 (1):55–67. doi: 10.1080/00401706.1970.10488634.
  • Jahufer, A. 2013. Detecting global influential observations in Liu regression model. Open Journal of Statistics 03 (01):5–11. doi: 10.4236/ojs.2013.31002.
  • Kibria, B. M. G. 2003. Performance of some new ridge regression estimators. Communications in Statistics - Simulation and Computation 32 (2):419–35. doi: 10.1081/SAC-120017499.
  • Kibria, B. M. G., K. Månsson, and G. Shukur. 2015. A simulation study of some biasing parameters for the ridge type estimation of Poisson regression. Communications in Statistics - Simulation and Computation 44 (4):943–57. doi: 10.1080/03610918.2013.796981.
  • Krasker, W. S., and R. E. Welsch. 1982. Efficient bounded-influence regression estimation. Journal of the American Statistical Association 77 (379):595–604. doi: 10.1080/01621459.1982.10477855.
  • Månsson, K., and G. Shukur. 2011. A Poisson ridge regression estimator. Economic Modelling 28 (4):1475–81. doi: 10.1016/j.econmod.2011.02.030.
  • Mittlböck, M., and H. Heinzl. 2002. Measures of explained variation in gamma regression models. Communications in Statistics - Simulation and Computation 31 (1):61–73. doi: 10.1081/SAC-9687282.
  • Muniz, G., and B. M. G. Kibria. 2009. On some ridge regression estimators: An Empirical Comparisons. Communications in Statistics - Simulation and Computation 38 (3):621–30. doi: 10.1080/03610910802592838.
  • Pickford, M., and S. Haslett. 1999. A statistical test of single firm market power. New Zealand Economic Papers 33 (2):39–58. doi: 10.1080/00779959909544307.
  • Pregibon, D. 1981. Logistic regression diagnostics. The Annals of Statistics 9 (4):705–24. doi: 10.1214/aos/1176345513.
  • Qasim, M., B. M. G. Kibria, K. Månsson, and P. Sjölander. 2020. A new Poisson Liu regression estimator: Method and application. Journal of Applied Statistics 47 (12):2258–71. doi: 10.1080/02664763.2019.1707485.
  • Rashad, N. K., and Z. Y. Algamal. 2019. A new ridge estimator for the Poisson regression model. Iranian Journal of Science and Technology, Transactions A: Science 43 (6):2921–8. doi: 10.1007/s40995-019-00769-3.
  • Sami, F., M. Amin, and M. M. Butt. 2021. On the ridge estimation of the conway-maxwell Poisson regression model with multicollinearity: Methods and applications. Concurrency and Computation: Practice and Experience. Advance online publication. doi: 10.1002/cpe.6477.
  • Segerstedt, B. 1992. On ordinary ridge regression in generalized linear models. Communications in Statistics - Theory and Methods 21 (8):2227–46. doi: 10.1080/03610929208830909.
  • Sohn, B. Y., and G. B. Kim. 1997. Detection of outliers in weighted least squares regression. Korean Journal of Computational & Applied Mathematics 4 (2):441–52. doi: 10.1007/BF03014491.
  • Tan, F. E., M. J. Ouwens, and M. P. Berger. 2001. Detection of influential observations in longitudinal mixed effects regression models. Journal of the Royal Statistical Society: Series D (the Statistician) 50 (3):271–84. doi: 10.1111/1467-9884.00277.
  • Türkan, S., and G. Özel. 2016. A new modified Jackknifed estimator for the Poisson regression model. Journal of Applied Statistics 43 (10):1892–905. doi: 10.1080/02664763.2015.1125861.
  • Walker, E., and J. B. Birch. 1988. Influence measures in ridge regression. Technometrics 30 (2):221–7. doi: 10.1080/00401706.1988.10488370.
  • Williams, D. A. 1987. Generalized linear model diagnostics using the deviance and single case deletions. Journal of the Royal Statistical Society 36 (2):741–9.
  • Zewotir, T., and J. S. Galpin. 2005. Influence diagnostics for linear mixed models. Journal of Data Science 3 (2):153–77.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.