Mevlüt TÜRE, İmran KURT ÖMÜRLÜ, Buğra VAROL

Simülasyon ve Sağlık Veri Setlerinde Parçalı Regresyon ile Polinom Regresyon Analizlerinin Karşılaştırılması

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 1970-2015 yılları arasındaki kızamık vaka sayılarını içeren kızamık veri setleri kullanılarak oluşturulan polinom ve parçalı regresyon modellerinin tahmin performansları; belirtme katsayısı (R2), hata kareler ortalaması (HKO), Akaike bilgi kriteri (ABK) ve Bayes bilgi kriteri (BBK) değerlerine göre karşılaştırıldı. Bulgular: Tüm polinom ve parçalı regresyon modellerinin R2, HKO, ABK ve BBK değerleri bakımından performansları istatistiksel olarak birbirinden farklı bulundu (p

Comparison Of Piecewise Regression and Polynomial Regression Analyses In Health and Simulation Data Sets

Objective: Piecewise regression, which one or more piecesare combined in breakpoints, is widely used as a statisticaltechnique. It was aimed to compare piecewise regressionanalyses and polynomial regression analysis using bothsimulated data and real data sets.Material-Method: In the application step of the study,algorithms were created by using R software for simulationpractice. Polynomial and piecewise regression analysismethods were compared using data sets with n=100 unitsand 1000 times running simulation. Additionally, estimationperformances of piecewise and polynomial regression werebuilt by using the data sets which contained in the numberof tuberculosis cases according to age in 2010 year and thenumber of measles cases from 1970 to 2015 years in Turkeywere compared according to the coefficient of determination(R2), mean square error (MSE), Akaike information criteria(AIC) and Bayes information criteria (BIC).Results: It was found that there was a significant differencebetween all of the polynomial and piecewise regressionmodels (p

PDF

___

1. Freedman DA. Statistical models: theory and practice. Cambridge University Press. New York, 2009; 41-60.
2. Freund RJ, Wilson WJ, Sa P. Regression analysis. Academic Press. 2nd ed. New York, 2006; 270-95.
3. Hartley HO, Booker A. Nonlinear least-squares estimation. The Annals of mathematical statistics 1965; 36(2): 638-50.
4. Seber G, Wild C. Nonlinear regression. Hoboken: John Wiley & Sons Google Scholar, 2003, 325-65.
5. Park SH. Experimental designs for fitting segmented polynomial regression models. Technometrics 1978; 20(2): 151-4.
6. Wainer H. Piecewise regression: A simplified procedure. British Journal of Mathematical and Statistical Psychology 1971; 24(1): 83-92.
7. Eubank R. Approximate regression models and splines. Communications in Statistics-Theory and Methods 1984; 13(4): 433-84.
8. Gallant AR, Fuller WA. Fitting segmented polynomial regression models whose join points have to be estimated. Journal of the American Statistical Association 1973; 68(341): 144-7.
9. Berberoglu B, Berberoglu CN. Modeling the Structural Shifts in Real Exchange Rate with Cubic Spline Regression (CSR). Turkey 1987-2008. International Journal of Business and Social Science 2011; 2(17).
10. De Boor C, Rice JR. Least squares cubic spline approximation, II-variable knots. West Lafayette, Purdue University, 1968; 4-13.
11. Poirier DJ. Piecewise regression using cubic splines. Journal of the American Statistical Association 1973; 68(343): 515-24.
12. Porth RW. Application of least square cubic splines to the analysis of edges [The Master of Science Degree Thesis]. New York , Rochester Institute of Technology, 1984; 23-51.
13. Schwetlick H, Schütze T. Least squares approximation by splines with free knots. BIT Numerical mathematics 1995; 35(3): 361-84.
14. Draper NR, Smith H. Applied regression analysis. John Wiley & Sons. 3rd ed. Vol 326. New York, 2014; 158-75.
15. Harrell FE, Lee KL, Califf RM, Pryor DB, Rosati RA. Regression modelling strategies for improved prognostic prediction. Statistics in medicine 1984; 3(2): 143-52.
16. Chan S-h. Polynomial spline regression with unknown knots and AR (1) errors [Doctoral Thesis]. Columbus, The Ohio State University, 1989; 22-38.
17. De Boor C, Rice JR. Least squares cubic spline approximation I-Fixed knots. West Lafayette, Purdue University, 1968; 2-19.
18. Eubank RL. Nonparametric regression and spline smoothing. CRC press. 2nd ed. Vol 157. New York, 1999; 227-308.
19. Wold S. Spline functions in data analysis. Technometrics 1974; 16(1): 1-11.
20. Hawkins DM. On the choice of segments in piecewise approximation. IMA Journal of Applied Mathematics 1972; 9(2): 250-6.
21. Ruppert D. Selecting the number of knots for penalized splines. Journal of computational and graphical statistics 2002; 11(4): 735-57.
22. Agarwal GG, Studden W. An algorithm for selection of design and knots in the response curve estimation by spline functions. West Lafayette, Purdue University Department of Statistics, 1978; 78-85.
23. Marsh LC, Cormier DR. Spline regression models. Sage. London, 2001; 7-58.
24. Powell M. The local dependence of least squares cubic splines. SIAM Journal on Numerical Analysis 1969; 6(3): 398-413.
25. Smith PL. Splines as a useful and convenient statistical tool. The American Statistician 1979; 33(2): 57-62.
26. Wegman EJ, Wright IW. Splines in statistics. Journal of the American Statistical Association 1983; 78(382): 351-65.
27. Genç A, Oktay E, Alkan Ö. İhracatın İthalatı Karşılama Oranlarının Parçalı Regresyonlarla Modellenmesi. Atatürk Üniversitesi Sosyal Bilimler Enstitüsü Dergisi 2012; 16(1): 497-511.
28. Markov D. Information content in stock market technical patterns: A spline regression approach [Doctoral Thesis]. South Bend, University of Notre Dame, 2003; 58-72.
29. Marsh LC. Estimating the number and location of knots in spline regressions. Journal of Applied Business Research 1986; 2(2): 60-70.
30. Studden WJ, VanArman D. Admissible designs for polynomial spline regression. The Annals of Mathematical Statistics 1969; 40(5): 1557-69.
31. Hurley D, Hussey J, McKeown R, Addy C, editors. An evaluation of splines in linear regression. The 132nd Annual Meeting; 2004 Nov 6-10; Washington.
32. Mulla Z. Spline regression in clinical research. West indian medical journal 2007; 56(1): 77-9.
33. Parkhurst A, Spiers D, Hahn G. Spline models for estimating heat stress thresholds in cattle. Conference on Applied Statistics in Agriculture: 14th Annual Conference Proceedings. 2002, 137-48; New York.