The Solution of Multicollinearity Problem via Biased Regression Analysis in Southern Anatolian Red Cattle

The aim of this study is to investigate the effectiveness of biased estimation methods, principal component regression (PC) and ridge regression (RR) methods, according to unbiased the least squares (LS) method, against the multiple linearity problem (multicollinearity) encountered in regression methods. For this purpose to fit a model on account to predict body weight from some body measurements of 32 South Anatolian Red Kilis (SAR) cattle of different ages. R2, RMSE, MSE, and CV were used as the goodness of fit criteria for the performance of the models. According to these criteria respectively, 0.9970, 0.0224, 0.0005, 0.0099 for LS; 0.9970, 0.0224, 0.0005, 0.0099 for PC; and 0.9876, 0.0455, 0.0021, 0.0201 of k=0.02 for RR gave the best fit values. According to these results, LR and PC showed the best fit. But RR and PC techniques from biased prediction techniques provided more consistent, valid, stable, and theoretical expectations than LS technique, since LR did not provide the necessary assumptions.

PDF

___

Akçay A, Sarıözkan S. 2015. Yumurta tavukçuluğunda gelirin ridge regresyon analizi ile tahmini. Ankara Üniversitesi Veteriner Fakültesi Dergisi, 62, 69-74.
Büyükuysal MÇ, Öz İİ. 2016. Çoklu doğrusal bağıntı varlığında en küçük kareler alternatif yaklaşım: Ridge regresyonu. Düzce Üniversitesi Sağlık Bilimleri Enstitüsü Dergisi, 6(2), 110-114.
Çankaya S, Eker S, Abacı SH. 2019. Comparison of Least Squares, Ridge Regression and Principal Component Approaches in the Presence of Multicollinearity in Regression Analysis. Turkish Journal of Agriculture-Food Science and Technology, 7(8), 1166-1172.
Çelik Ş, Şengül T, Söğüt B, İnci H, Şengül AY, Kayaokay A, Ayaşan T. 2018. Analysis of variables affecting carcass weight of white turkeys by regression analysis based on factor analysis scores and ridge regression. Brazilian Journal Poultry Science, 273-280.
Çiftsüren MN, Akkol S. 2018. Prediction of internal egg quality characteristics and variable selection using regularization methods: Ridge, LASSO and Elastic Net. Arch. Anim. Breed, 61, 279-284.
Draper NR., and Smith H. 1981. Applied Regression Analysis, John Willey, NY.
Erzin Y, Çetin T. 2017. The prediction of the critical factor of safety of homogeneous finite slopes using neural networks and multiple regressions, Computers & Geosciences, 51:305- 313, 2017geliştirilmiş 3. Basım, VIII, 386 S, ISBN:978-605- 320-644-6, İstanbul.
Hastie T. 2020. Ridge Regularizaton: an Essential Concept in Data Science, https://arxiv.org/pdf/2006.00371.pdf
Hoerl AE. and Kennard RW.1970a. Ridge regression: biased estimation for nonortogonal problems. Technometrics, 12(1), 55-56.
Hoerl AE, Kennard RW. 1970b. Ridge regression: applications to nonortogonal problems, Technometrics, 12(1), 69-82.
Kayaalp GT, Güney O, Çelik M, Cebeci Z. 2015. Çoklu doğrusal regresyon modelinde değişken seçiminin zootekniye uygulanışı. Çukurova Üniv. Zir. Fak. Der., 30(1), 1-8.
Kim J. H. 2019. Multicollinearity and misleading statistical results. Korean journal of anesthesiology, 72(6): 558–569. https://doi.org/10.4097/kja.19087
Kleinbaum DG, Lawrence L, Kupper and Keith E. Muller 1988. Applied Regression Analysis and Other Multivariable Methods, Duxbury Press, New Jersey.
Maxwell, Scott E. 2000. Sample Size in Multiple Regression Analysis, Psychological Methods, Vol. 5, No: 4, s. 435-458.
NCSS 2021 Statistical Software 2021. NCSS, LLC. Kaysville, Utah, USA, ncss.com/software/ncss.
NCSS Inc. 2001. NCSS User Guide 2001, Kaysville, NCSS Inc. Neter J, Wasserman W, Kunter M. 1990. Applied Linear Statistical Models, 3rd Ed., New Jersey.
Orhunbilge N. 2017. Uygulamalı regresyon ve korelasyon analizi. Nobel Yayınevi, gözden gözden geçirilmiş 3. Basım, VIII, 386 S, ISBN:978-605-320-644-6, İstanbul.
Rawlings JO. 1998. Applied Regression Analysis: A Research Tool, California.
Shafey TM, Hussein ES, Mahmoud AH, Abouheif MA, Al- Batshan HA. 2015. Managing collinearity in modeling the effect of age in the prediction of egg components of laying hens using stepwise and ridge regression analysis. Brazilian Journal Poultry Science, 473-482.
Shrestha N. 2020. Detecting Multicollinearity in Regression Analysis. American Journal of Applied Mathematics and Statistics, vol. 8(2):39-42. https://doi:10.12691/ajams-8-2-1
Şahinler S. 2000. En Küçük Kareler Yöntemi ile Doğrusal Regresyon Modeli Oluşturmanın Temel Prensipleri. MKÜ. Ziraat Fakültesi Dergisi 5 (1-2). Hatay, 57–73.
Tırınk C, Abacı Sh, Önder H. 2020. Comparison of Ridge Regression and Least Squares Methods in the Presence of Multicollinearity for Body Measurements in Saanen Kids, Journal of the Institute of Science and Technology, 10(2): 1429-1437, https://DOI:10.21597/jist.671662
Topal M, Eyduran E, Yağanoğlu AM, Sönmez A, Keskin S. 2010. Çoklu Doğrusal Bağlantı Durumunda Ridge ve Temel Bileşenler Regresyon Analiz Yöntemlerinin Kullanımı. Atatürk Üniversitesi, Ziraat Fakültesi Dergisi, 41(1): 53-57.
Vinod HD. 1995. Double Bootstrap for Shrinkage Estimators, Journal of Econometrics.
Yılmaz F, Bayyurt L, Abacı SH, Tahtalı Y. 2020. Comparison of Least Squares and Some Bias Estimators in Multicollinearity, Turkish Journal of Agriculture-Food Science and Technology, 8(3): 793-799, DOI: https://doi.org/10.24925/ turjaf.v8i3.793-799.3405