Araştırma Makalesi
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Regression Methods Used in Modelling of Dependent Variable Obtained Based on Zero-Inflated Count Data

Yıl 2007, Cilt: 5 Sayı: 1, 1 - 9, 13.07.2007

Öz

In this study, Poisson regression, negative binomial regression, zero-inflated Poisson regression, and zero-inflated negative binomial regression were investigated to analyze dependent variable obtained based on zero-inflated counting. It was determined that overdispersion had a significant effect because there were many zero values in data set and there were great difference among the observations. Akaiki and Bayesian information criteria were used to choose the most appropriate model. In conclusion, zero-inflated negative binomial regression was chosen as the most appropriate model. It was determined that zero-inflated Poisson regression could be preferred to Poisson regression, and zero-inflated negative binomial regression could be preferred to negative binomial regression. In zero-inflated negative binomial regression, it was determined that predator acar (Zetzellia mali), temperature, and spraying in the model had significant effects (p<0.01) on all stages of the
harmful pest acar (Panonychus ulmi Koch).

Kaynakça

  • Agresti, A., 1997. Categorical Data Analysis. New Jersey, Canada; John and Wiley & Sons, Incorporation.
  • Böhning, D., 1994. A Note on a Test for Poisson Overdispersion. Biometrika, 81, 418-419.
  • Böhning, D., 1998. Zero- Inflated Poisson Models and C.A.MAN: A Tutorial Collection of Evidence. Biometrical Journal, 40(7), 833-843.
  • Böhning, D., Dietz, E ve Schlattmann, P., 1999. The Zero-Inflated Poisson Model and the Decayed, Missing and Filled Teeth Index in Dental Epidemiology. Journal of Royal Statistical Society, A, 162, 195–209.
  • Breslow, N., 1990. Tests of Hypotheses in Overdispersed Poisson Regression and Other Quasi-Likelihood Models. Journal of American Statistical Association, 85(410), 565-571.
  • Cameron, A.C ve Trivedi, P.K., 1998. Regression Analysis of Count Data. New York: Cambridge University Pres.
  • Cheung, Y.B., 2002. Zero-Inflated Models for Regression Analysis of Count Data: A Study of Growth and Development. Statistics in Medicine, 21, 1461-1469.
  • Cox, R., 1983. Some Remarks on Overdispersion. Biometrika,70, 269-274.
  • Dalrymple, M.L., Hudson, I.L ve Ford, R.P.K., 2003. Finite Mixture, Zero-Inflated Poisson and Hurdle Models with Application to SIDS. Computational Statistics & Data Analysis 41, 491-504.
  • Frome, E.D., Kutner, M.H ve Beauchamp, J.J., 1973. Regression Analysis of Poisson-Distributed Data. Journal of American Statistical Association, 68(344), 935-940.
  • Hall, D.A., 2000. Zero-Inflated Poisson and Negative Binomial Regression with Random Effects: A Case Study. Biometrics, 56, 1030-1039.
  • Kasap, İ., 2004. Effect of Different Apple Cultivars and of Temperatures on Biology and Life Table Parameters of TwoSpotted Spider Mite, Tetranychus Urticae Koch (Acarina: Tetranychidae). Phytoparasitica, 32(1): 73-82.
  • Lambert, D., 1992. Zero-Inflated Poisson Regression, with an Application to Defects in Mnaufacturin. Technometrics, 34(1), 1-13.
  • Lawles, J.F., 1987. Negative Binomial and Mixed Poisson Regression. The Canadian Journal of Statistcs, 15(3), 209-225.
  • Lee, A.H ve Wang, K., 2001. Analysis of Zero-Inflated Poisson Data Incorporating Extent of Exposure. Biometrical Journal, 43(8), 963-975.
  • McCullagh, P ve Nelder, J.A., 1989. Generalized Linear Models. Second Edition, London, UK, Chapmann and Hall.
  • Muthen, L.K ve Muthen, B., 2002. MPlus: User’s Guide. Los Angeles, CA: Muthén & Muthén.
  • Nelder, J.A ve Wedderburn, R.W.M., 1972. Generalized Linear Models. Journal of Royal Statistical Society A, 135(3), 370- 384.
  • Ridout, M., Hinde, J ve Demetrio, C.G.B., 2001. A Score Test for a Zero-Inflated Poisson Regression Model Against Zero-Inflated Negative Binomial Alteratves. Biometrics, 57, 219-233.
  • SAS., 2007. SAS/Stat. Software. Hangen and Enhanced, USA: SAS, Institute. Incorporation.
  • Stokes, M.E., Davis, C.S ve Koch, G.G., 2000. Categorical Data Analysis Using the SAS System. USA; John and Wiley & Sons, Incorporation.
  • Yau, K.K.W ve Lee, A.H., 2001. Zero-Inflated Poisson Regression with Random Effects to Evaluate an Occupational Injury Prevention Programme. Statistics in Medicine, 20, 2907-2920.

Sıfır Değer Ağırlıklı Sayıma Dayalı Olarak Elde Edilen Bağımlı Değişkenin Modellenmesinde Kullanılan Regresyon Yöntemleri

Yıl 2007, Cilt: 5 Sayı: 1, 1 - 9, 13.07.2007

Öz

Çalışmada, sıfır değer ağırlıklı sayıma dayalı olarak elde edilen bağımlı değişkenin analizi için Poisson regresyonu, negatif Binom regresyonu, sıfır ağırlıklı Poisson regresyonu ve sıfır ağırlıklı negatif Binom regresyonu incelenmiştir. Veri kümesinde sıfır değerlerinin çok olması ve gözlemler arasındaki büyük farklılıktan dolayı aşırı yayılımın önemli bir etkiye sahip olduğu saptanmıştır. Uygun model seçiminde Akaiki ve Bayesçi bilgi ölçütleri kullanılmıştır. Bunun sonucunda, sıfır ağırlıklı negatif Binom regresyon modeli en uygun model olarak seçilmiştir. Uyum ölçütleri sonucunda, sıfır ağırlıklı Poisson regresyonun, Poisson regresyonuna ve sıfır ağırlıklı negatif Binom regresyonun da, negatif Binom regresyona tercih edilebileceği saptanmıştır. Sıfır ağırlıklı negatif Binom regresyonunda, modele alınan avcı akarın (Zetzellia mali), sıcaklığın ve ilaçlamanın zararlı akar Panonychus ulmi Koch’un tüm dönemleri toplamı üzerine etkileri önemli bulunmuştur (p<0.01).

Kaynakça

  • Agresti, A., 1997. Categorical Data Analysis. New Jersey, Canada; John and Wiley & Sons, Incorporation.
  • Böhning, D., 1994. A Note on a Test for Poisson Overdispersion. Biometrika, 81, 418-419.
  • Böhning, D., 1998. Zero- Inflated Poisson Models and C.A.MAN: A Tutorial Collection of Evidence. Biometrical Journal, 40(7), 833-843.
  • Böhning, D., Dietz, E ve Schlattmann, P., 1999. The Zero-Inflated Poisson Model and the Decayed, Missing and Filled Teeth Index in Dental Epidemiology. Journal of Royal Statistical Society, A, 162, 195–209.
  • Breslow, N., 1990. Tests of Hypotheses in Overdispersed Poisson Regression and Other Quasi-Likelihood Models. Journal of American Statistical Association, 85(410), 565-571.
  • Cameron, A.C ve Trivedi, P.K., 1998. Regression Analysis of Count Data. New York: Cambridge University Pres.
  • Cheung, Y.B., 2002. Zero-Inflated Models for Regression Analysis of Count Data: A Study of Growth and Development. Statistics in Medicine, 21, 1461-1469.
  • Cox, R., 1983. Some Remarks on Overdispersion. Biometrika,70, 269-274.
  • Dalrymple, M.L., Hudson, I.L ve Ford, R.P.K., 2003. Finite Mixture, Zero-Inflated Poisson and Hurdle Models with Application to SIDS. Computational Statistics & Data Analysis 41, 491-504.
  • Frome, E.D., Kutner, M.H ve Beauchamp, J.J., 1973. Regression Analysis of Poisson-Distributed Data. Journal of American Statistical Association, 68(344), 935-940.
  • Hall, D.A., 2000. Zero-Inflated Poisson and Negative Binomial Regression with Random Effects: A Case Study. Biometrics, 56, 1030-1039.
  • Kasap, İ., 2004. Effect of Different Apple Cultivars and of Temperatures on Biology and Life Table Parameters of TwoSpotted Spider Mite, Tetranychus Urticae Koch (Acarina: Tetranychidae). Phytoparasitica, 32(1): 73-82.
  • Lambert, D., 1992. Zero-Inflated Poisson Regression, with an Application to Defects in Mnaufacturin. Technometrics, 34(1), 1-13.
  • Lawles, J.F., 1987. Negative Binomial and Mixed Poisson Regression. The Canadian Journal of Statistcs, 15(3), 209-225.
  • Lee, A.H ve Wang, K., 2001. Analysis of Zero-Inflated Poisson Data Incorporating Extent of Exposure. Biometrical Journal, 43(8), 963-975.
  • McCullagh, P ve Nelder, J.A., 1989. Generalized Linear Models. Second Edition, London, UK, Chapmann and Hall.
  • Muthen, L.K ve Muthen, B., 2002. MPlus: User’s Guide. Los Angeles, CA: Muthén & Muthén.
  • Nelder, J.A ve Wedderburn, R.W.M., 1972. Generalized Linear Models. Journal of Royal Statistical Society A, 135(3), 370- 384.
  • Ridout, M., Hinde, J ve Demetrio, C.G.B., 2001. A Score Test for a Zero-Inflated Poisson Regression Model Against Zero-Inflated Negative Binomial Alteratves. Biometrics, 57, 219-233.
  • SAS., 2007. SAS/Stat. Software. Hangen and Enhanced, USA: SAS, Institute. Incorporation.
  • Stokes, M.E., Davis, C.S ve Koch, G.G., 2000. Categorical Data Analysis Using the SAS System. USA; John and Wiley & Sons, Incorporation.
  • Yau, K.K.W ve Lee, A.H., 2001. Zero-Inflated Poisson Regression with Random Effects to Evaluate an Occupational Injury Prevention Programme. Statistics in Medicine, 20, 2907-2920.
Toplam 22 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular İstatistik
Bölüm Araştırma Makaleleri
Yazarlar

Abdullah Yeşilova

Barış Kaki Bu kişi benim

İsmail Kasap Bu kişi benim

Yayımlanma Tarihi 13 Temmuz 2007
Yayımlandığı Sayı Yıl 2007 Cilt: 5 Sayı: 1

Kaynak Göster

APA Yeşilova, A., Kaki, B., & Kasap, İ. (2007). Sıfır Değer Ağırlıklı Sayıma Dayalı Olarak Elde Edilen Bağımlı Değişkenin Modellenmesinde Kullanılan Regresyon Yöntemleri. İstatistik Araştırma Dergisi, 5(1), 1-9.