Test Statistics for Dispersion Parameter in Poisson Regression and Generalized Poisson Regression Models

Main Article Content

Veeranun Pongsapukdee
Pairoj Khawsittiwong
Maysiya Yamjaroenkit

Abstract

Two symmetrical distributed test statistics, called Zm and Z0_New are proposed and their goodness-of-fit tests are compared with other available five test statistics: Wald-t, Score test, Z μ, ZY, and Z0, for overdispersion in Poisson regression model versus generalized Poisson model. Five thousand data sets in each condition of overdispersion parameters and sample sizes are simulated to perform the assessment of the models’ fits using those statistics, concerning the coverage probability and power of tests. Results show that the Zm test performs closely as good a Zμ and ZYtests but it tend to be better than the others when the sample size is large. Even if the Z0_New test has the largest power; however, in consideration for coverage probability and power of tests, the Zm test probably be more reliable. The Zm test statistic is interesting not only in its simplest form, with the reasonable coverage probability and power but also in its robust property of using median that needs fewer assumptions for its parent distribution.

Downloads

Download data is not yet available.

Article Details

How to Cite
Pongsapukdee, V., Khawsittiwong, P., & Yamjaroenkit, M. (2016). Test Statistics for Dispersion Parameter in Poisson Regression and Generalized Poisson Regression Models. Science, Engineering and Health Studies, 10(2), 31–36. https://doi.org/10.14456/sustj.2016.18
Section
Research Articles

References

Agresti, A. (2013). Categorical Data Analysis, 3rd ed., New York: John Wiley & Sons.

Böhning, D. A (1994). Note on test for Poisson overdispersion. Biometrika, 81: 418-419.

Cameron, A. C. and Trivedi, P. K. (1998). Regression Analysis of Count Data, Cambridge: Cambridge University Press, pp. 87-146.

Consul, P. C. (1989). Generalized Poisson Distribution: Properties and Application, New York: Dekker, Inc., pp. 377-385.

Consul, P. C. and Jain, G. C. (1973). A generalized of the Poisson distribution. Techonometrics, 15(4): 791-799.

Dean, C. B. (1992). Testing for overdispersion in Poisson and binomial regression models. Journal of the American Statistical Association, 87: 451-457.

Dean, C. and Lawless, J. F. (1989). Test for detecting overdispersion in Poisson regression models. Journal of the American Statistical Association, 84: 467-471.

Famoye, F. (1997). Restricted generalized Poisson regression model. Communication in Statistics – Theory and Method, 22: 1335-1354.

Frome, E. L. (1983). The analysis of rates using Poisson regression models. Biometrics, 39: 665-674.

Frome, E. L., Kutner, M. H. and Beauchamp, J. J. (1973). Regression analysis of Poisson distributed data. Journal of the American Statistical Association, 68: 935-940.

Lawless, J. F. (1987a). Negative binomial regression models. Canadian Journal of Statistics, 15: 209-226.

McCulloch, C., E. and Searle, S. (2001). Generalized, linear, and mixed models, New York: John Wiley & Sons, pp. 220-238.

Nelder, J. A., and Wedderburn, R. W. M. (1972). Generalized linear models. Journal of the Royal Statistical Society A, 135(3): 370-384.

Pongsapukdee, V. (2012) Analysis of categorical data: Theories and applications with GLIM, SPSS, SAS and MTB, 3rd ed.,Nakhon Pathom: Silpakorn University Press, pp. 203-209, 406-418.

Salee, W., and Pongsapukdee, V. (2013). Odds prediction of drought category using loglinear models based on SPI in the northeast of Thailand. Silpakorn University Science and Technology Journal, 7(1): 32-40.

Wang, W., and Famoye, F. (1997). Modeling household fertility decisions with generalized Poisson regression. Journal of Population Economics, 10: 273-283.

Yamjaroenkit, M., and Pongsapukdee, V. (2012). Tests of dispersion parameter in generalized Poisson regression models. In Proceeding of Silapakorn University International Conference on Academic Research and Creative Arts: Integration of Art and Science. The Art and Culture Center Commemorating the 6th Cycle Birthday Anniversary of His Majesty The King, Silpakorn University, Nakon Pathom, Thailand.

Yamjaroenkit, M. (2012). Tests of Dispersion Parameter in Generalized Poisson Regression Models. M.Sc. thesis, Department of Statistics, Silpakorn University.

Yang, Z., Hardin, J. W. and Addy, C. L. (2009). A score test for overdispersion in Poisson regression based on the generalized Poisson-2 model. Journal of Statistical Planning and Inference, 139: 1514-1521.