The Reanalysis of the Donation Data Using the Zero-Inflated Possion Regression

Title & Authors
The Reanalysis of the Donation Data Using the Zero-Inflated Possion Regression
Kim, In-Young; Park, Tae-Kyu; Kim, Byung-Soo;

Abstract
Kim et al. (2006) analyzed the donation data surveyed by Voluneteer 21 in year 2002 at South Korea using a Poisson regression based on the mixture of two Poissons and detected significant variables for affecting the number of donations. However, noting the large deviation between the predicted and the actual frequencies of zero, we developed in this note a Poisson regression model based on a distribution in which zero inflated Poisson was added to the mixture of two Poissons. Thus the population distribution is now a mixture of three Poissons in which one component is concentrated on zero mass. We used the EM algorithm for estimating the regression parameters and detected the same variables with Kim et al`s for significantly affecting the response. However, we could estimate the proportion of the fixed zero group to be 0.201, which was the characteristic of this model. We also noted that among two significant variables, the income and the volunteer experience(yes, no), the second variable could be utilized as a strategric variable for promoting the donation.
Keywords
EM algorithm;mixture of Poisson distributions;number of donations;zero inflated Poisson(ZIP);
Language
Korean
Cited by
1.
2002년 기부횟수 자료의 재분석: 수정 및 보완,김병수;이주형;김인영;박수범;박태규;

응용통계연구, 2014. vol.27. 5, pp.743-753
1.
Reanalysis of 2002 Donation Frequency Data: Corrections and Supplements, Korean Journal of Applied Statistics, 2014, 27, 5, 743
References
1.
김인영, 박수범, 강병수, 박태규 (2006). 포아송 분포의 혼합모형을 이용한 기부 횟수 자료 분석, <응용통계연구>, 19, 1-12

2.
Bohning, D., Dietz, E., Schlattmann, P., Mendonca, L. and Kirchner, U. (1999). The zero-inflated Poisson model and the decayed, missing and filled teeth index in dental epidemiology, Journal of the Royal Statistical Society: Series A (Statistics in Society), 162, 195-209

3.
Dempster, A. P., Laird, N. M. and Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm (with discussion), Journal of the Royal Statistical Society: Series B, 39, 1-38

4.
Efron, B. and Tibshirani, R. J. (1993). An Introduction to the Bootstrap, Chapman & Hall, New York

5.
Hurvich, C. M. and Tasi, C. L. (1989). Regression and time series model selection in small samples, Biometrika, 76, 297-307

6.
Johnson, N. L., Kotz, S. and Kemp, A. W. (1992). Univariate Discrete Distributions, Second Ed. Wiley, New York

7.
Jung, B. C., Juhn, M. and Lee, J. W. (2005). Bootstrap tests for overdispersion in a zero-inflated Poisson regression model, Biometrics, 61, 626-629

8.
Lam, K. F., Xue, H. and Cheung, Y. B. (2006). Semiparametric analysis of zero-inflated count data, Biometrics, 62, 996-1003

9.
Lambert, D. (1992). Zero-inflated Poisson regression, with an application to defects in manufacturing, Technometrics, 34, 1-14

10.
Wang, P., Puterman, M. L., Cockburn, I. and Le, N. (1996). Mixed Poisson regression models with covariate dependent rates, Biometrics, 52, 381-400