Proposed methods in estimating the ridge regression parameter in Poisson regression model


The Poisson regression model is considered as an important model among the
linear logarithm models. It is usually used to model the count dependent variable. However, as in linear regression model, the multicollinearity problem
may be present leading to negatively affect the model parameter estimation.
In this study, several methods are proposed to estimate the ridge parameter. Monte-Carlo simulation studies with different factors were conducted to
evaluate the performance of the used estimators. The results demonstrate
the better performance of the proposed estimator compared to other used
estimators in terms of mean squared error (MSE).

DOI Code: 10.1285/i20705948v11n2p506

Keywords: Multicollinearity; ridge estimator; Poisson regression model.


Algamal, Z. Y. (2012). Diagnostic in poisson regression models. Electronic Journal of

Applied Statistical Analysis, 5(2):178–186.

Algamal, Z. Y. and Lee, M. H. (2015). Penalized poisson regression model using adaptive modified elastic net penalty. Electronic Journal of Applied Statistical Analysis,


Asar, Y. and Gen¸c, A. (2017). A new two-parameter estimator for the poisson regression

model. Iranian Journal of Science and Technology, Transactions A: Science.

Asar, Y., Karaibrahimo˘glu, A., and Gen¸c, A. (2014). Modified ridge regression parameters: A comparative monte carlo study. Hacettepe Journal of Mathematics and

Statistics, 43(5):827–841.

Bhat, S. S. (2016). A comparative study on the performance of new ridge estimators.

Pakistan Journal of Statistics and Operation Research, 12(2):317–325.

Cameron, A. C. and Trivedi, P. K. (2013). Regression analysis of count data, volume 53.

Cambridge university press.

De Jong, P. and Heller, G. Z. (2008). Generalized linear models for insurance data,

volume 10. Cambridge University Press Cambridge.

Hoerl, A. E. and Kennard, R. W. (1970). Ridge regression: Biased estimation for

nonorthogonal problems. Technometrics, 12(1):55–67.

KaC¸ iranlar, S. and Dawoud, I. (2017). On the performance of the poisson and the

negative binomial ridge predictors. Communications in Statistics - Simulation and

Computation, pages 0–0.

Kibria, B. M. G. (2003). Performance of some new ridge regression estimators. Communications in Statistics - Simulation and Computation, 32(2):419–435.

Kibria, B. M. G., M˚ansson, K., and Shukur, G. (2015). A simulation study of some biasing parameters for the ridge type estimation of poisson regression. Communications

in Statistics - Simulation and Computation, 44(4):943–957.

M˚ansson, K. and Shukur, G. (2011). A poisson ridge regression estimator. Economic

Modelling, 28(4):1475–1481.

Full Text: pdf

Creative Commons License
This work is licensed under a Creative Commons Attribuzione - Non commerciale - Non opere derivate 3.0 Italia License.