Comparison of Piecewise Regression and Polynomial Regression Analyses in Health and Simulation Data Sets

Yıl 2020, Cilt: 11 Sayı: 2, 144 - 151, 15.06.2020

Buğra Varol , İmran Kurt Omurlu , Mevlüt Türe

Öz

Objective: Piecewise
regression, which one or more pieces are combined in breakpoints, is widely
used as a statistical technique. It was aimed to compare piecewise regression
analyses and polynomial regression analysis using both simulated data and real
data sets.

Material-Method: In
the application step of the study, algorithms were created by using R software
for simulation practice. Polynomial and piecewise regression analysis methods
were compared using data sets with n=100 units and 1000 times running
simulation. In addition, estimation performances of piecewise and polynomial
regression built by using the data sets which contained in the number of
tuberculosis cases according to age in 2010 year and the number of measles
cases from 1993 to 2015 years in Turkey were compared.

Results: It
was found that there was a significant difference between all of the polynomial
and piecewise regression models (p<0.001). The  values of piecewise regression models were higher than
polynomial regression models; MSE, AIC and BIC values were observed to be
lower. According to the result of both simulation and real data set
applications, piecewise regression models which were generated according to
optimal knots were found to have better estimation performance than polynomial
regression models according to , MSE, AIC
and BIC criteria.

Conclusions: This
study revealed that data analysis with piecewise regressions having optimal
knots provided statistically superiority, although polynomial regression
methods are preferred in the field of health studies mostly.

Anahtar Kelimeler

Piecewise Regression, Simulation, Tuberculosis, Measles, Polynomial Regression

Comparison of Piecewise Regression and Polynomial Regression Analyses in Health and Simulation Data Sets

Öz

Amaç:
Bir
veya daha fazla parçanın kırılma noktalarında birleştirildiği parçalı
regresyon, istatistiksel bir teknik olarak yaygın bir şekilde kullanılmaktadır.
Bu çalışmada hem simülasyon verisi hem de gerçek veri setleri kullanılarak tek
değişkenli polinom regresyon analizi ile karesel ve kübik parçalı regresyon
analizlerinin karşılaştırılması hedeflendi.

Materyal-Metot: Çalışmanın uygulama basamağında R
yazılım programı kullanılarak simülasyon uygulaması için algoritmalar yazıldı.
Polinom ve sürekli parçalı regresyon analiz yöntemlerinin karşılaştırılması
n=100 birimlik veri setleri için 1000 tekrarlı simülasyon ile gerçekleştirildi.
Ayrıca Türkiye’de 2010 yılındaki tüberküloz vaka sayılarını içeren tüberküloz
veri seti ile Türkiye’deki 1973-2010 yılları arasındaki kızamık vaka sayılarını
içeren kızamık veri setleri kullanılarak oluşturulan polinom ve parçalı
regresyon modellerinin tahmin performansları; , HKO, ABK ve BBK değerlerine göre
karşılaştırıldı.

Bulgular: Tüm polinom ve parçalı regresyon
modellerinin ,
HKO, ABK ve BBK değerleri bakımından performansları istatistiksel olarak
birbirinden farklı bulundu (p<0.001). Parçalı regresyon modellerinin  değerlerinin polinom regresyon modellerine
göre daha yüksek; HKO, ABK ve BBK değerlerinin ise daha düşük olduğu
gözlendi.  Gerçek veri setleri ile
yapılan uygulamalarda en uygun dönüm noktalarına göre oluşturulan tüm parçalı
regresyon modellerinin  değerlerinin
polinom regresyonlardan daha yüksek; HKO, ABK ve BBK değerlerinin ise daha
düşük olduğu belirlendi Oluşturulan parçalı regresyon modellerinin veri setlerini polinom
regresyonlara göre daha iyi tahmin ettiği belirlendi.

Sonuç: Sağlık alanında yapılan çalışmaların çoğunda
polinom regresyon yöntemlerinin tercih edilmesine rağmen bu çalışma ile en
uygun dönüm noktalı parçalı regresyonlarla veri analizinin istatistiksel açıdan
üstünlük sağladığı
uygulamalarla ortaya konmuştur.

Anahtar Kelimeler

Parçalı Regresyon, Simülasyon, Tüberküloz, Kızamık, Polinom Regresyon

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