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

Abstract

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).

Keywords

• Negative Binomial Regression
• Overdispersion
• Poisson Regression
• Zero-Inflated Negative Binomial regression
• Zero-Inflated Poisson Regression

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

Abstract

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).

Keywords

• Aşırı Yayılım
• Negatif Binom Regresyonu
• Poisson Regresyonu
• Sıfır Ağırlıklı Negatif Binom Regresyonu
• Sıfır Ağırlıklı Poisson Regresyonu

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