Turkiye Klinikleri Journal of Biostatistics

.: ORIGINAL RESEARCH
Conway-Maxwell-Poisson (COM-Poisson) Regresyon Modeli: Aşırı ve Az Yayılımlı Verilere Uygulaması
Conway-Maxwell-Poisson (COM-Poisson) Regression Model: Application to Over- and Under Dispersed Data
Bahar ÇELİKa, Esin AVCIa
aİstatistik Bölümü, Giresun Üniversitesi Fen Edebiyat Fakültesi, Giresun, TÜRKİYE
Turkiye Klinikleri J Biostat. 2019;11(3):213-23
doi: 10.5336/biostatic.2019-70440
Article Language: TR
Full Text
ÖZET
 Amaç: Bağımlı değişkenin sayma/kesikli olma durumuyla birçok araştırmada karşılaşılmaktadır. Her ne kadar Poisson regresyon modeli sayma verilerinin analizinde sıklıkla kullanılsa da ortalama ile varyans eşitliği varsayımı birçok deneysel veri için sağlanmamaktadır. Aşırı/az yayılım olarak tanımlanan bu durumlarda alternatif regresyon modelleriyle analiz edilmesi daha uygun olmaktadır. Hem aşırı hem de az yayılım durumu için uygun analiz olanağı veren Conway-Maxwell-Poisson Regresyon modeli ayrıntılı olarak tanıtmaktır. Gereç ve Yöntemler: Poisson, negatif binom ve COM-Poisson regresyon modelleri önce aşırı yayılım gösteren 2011-2014 yılları arasında Giresun ili Toplum Ruh Sağlığı Merkezine (TRSM) kayıtlı olan hastaların, merkeze gelme sayılarına etki eden sosyo-demografik faktörlerin modellenmesinde, daha sonra az yayılım gösteren öğretmenlerin sosyal medya hesap sayılarına etki eden okul türü, cinsiyet ve yaş grubu faktörlerinin modellenmesinde uygulanmıştır. Her iki veri seti için değişken seçim yöntemi olarak tüm olası alt kümeler yöntemi kullanılmıştır. En küçük AIC değerli model en iyi model olarak seçilmiştir. Bulgular: TRSM'ye geliş sayılarına cinsiyet, eğitim düzeyi, medeni durum ile sosyal güvence durumunun, sosyal medya hesabına ise okul türü ve yaş grubunun etkili olduğu saptanmıştır. Sonuç: Her iki veri setinde de COM-Poisson regresyon en iyi modeli oluşturmuştur.

Anahtar Kelimeler: Aşırı-az yayılım; Conway-Maxwell-Poisson; sayma veri; negatif binom regresyon; Poisson regresyon
ABSTRACT
 Objective: Counting/discrete dependent variable is encountered in many studies. Although the Poisson regression model is frequently used in the analysis of counting data, the assumption of the equality of mean and variance is not provided for many experimental data. It is more appropriate to analyze with alternative regression models in case of over-under dispersion. The Conway-Maxwell-Poisson Regression model which is suitable for analysis of both over-under dispersed data is presenting in detail. Material and Methods: Poisson, negative binomial and COM-Poisson regression models were used to determine the effect of socio-demographic factors on the number of visits Giresun Community Mental Health Center (TRSM) between 2011 and 2014. Then, three regression models applied to model school type, gender, and age group factors with the number of social media accounts of the teachers. All possible subset regression approach was used as a variable selection method for both data sets. The smallest AIC-valued model was selected as the best model. Results: It was determined that gender, education level, marital status and social security status were effective on the number of arrivals to TRSM and the type of school and age group on social media account. Conclusion: COM-Poisson regression was the best model in both datasets.

Keywords: Over-under dispersion; Conway-Maxwell-Poisson; count data; negative binomial regression; Poisson regression.
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