Comparative Evaluation of Some Penalty Regression Techniques in the Multicollinearity Problem

Year 2025, Volume: 12 Issue: 4, 1166 - 1174, 17.10.2025

Tolga Tolun

https://doi.org/10.30910/turkjans.1757995

Abstract

This study aimed to predict an important biological trait, such as egg albumen height, in the presence of multicollinearity problem using some external quality parameters (egg weight, width, length, shape index, Haugh unit). Although a high coefficient of determination (R²=0.995) was obtained in the multiple regression model generated using the Classical Least Squares Method (LSM), serious multicollinearity problem was detected among the independent variables, negatively impacting the model's reliability. To address this issue, LASSO and Liu regression techniques were applied; in models generated with both methods, the explanatory factor R² decreased to approximately 89 %, but the multicollinearity problem was effectively mitigated. Comparisons also showed that the Liu regression model outperformed the LASSO model in terms of information criteria (AIC, cAIC, BIC). The results show that regression methods with penalty terms provide reliable and consistent estimates in data sets with multicollinearity problems, and these techniques are recommended for the analysis and modeling of biological data.

Keywords

Multicollinearity problem , LASSO and Liu regression methods , MATLAB , Egg albumen height.

References

• Akbaş, Y., Altan, O., & Koçak, C. (1996). Effects of hen’s age on external and internal egg quality characteristics. Turkish Journal of Veterinary Animal Science, 20, 455-460. http://dx.doi.org/10.55730/1300-0128.4074
• Akçay, A., & Sarıözkan, S. (2015). Yumurta tavukçuluğunda gelirin Ridge Regresyon analizi ile tahmini. Ankara Üniversitesi Veterinerlik Fakülte Dergisi, 62, 69-74.
• Albayrak, S. A. (2005). Çoklu bağlantı halinde en küçük kareler tekniğinin alternatifi yanlı tahmin teknikleri ve bir uygulama. Zonguldak Kara Elmas Üniversitesi Sosyal Bilimler Dergisi, 1, 105-126.
• Alkan, S., Karabağ, K., Galiç, A., Karslı, T., & Balcıoğlu, M. S. (2010). Effects of selection for body weight and egg production on egg quality traits in Japanese quails (Coturnix coturnix japonica) of different lines and relationships between these traits. Kafkas Üniversitesi Veteriner Fakültesi Dergisi, 16(2), 239-244. http://dx.doi.10.9775/kvfd.2009.633
• Aktan, S. (2004). Determination of some internal and external quality traits and their relationships in quail eggs by digital image analysis. Animal Production 45(1), 7-13.
• Amerah, A. M., Ravindran, V., Lentle, R. G., & Thomas, D. G. (2007). Feed particle size: Implications on the digestion and performance of poultry. World's Poultry Science Journal, 63(3), 439-455. https://doi.org/10.1017/S0043933907001560
• Çetenak, T., Gök, İ., Yavuz, E., & Şahin, M. (2024). Statistical models and evaluation criteria used in poultry farming. Black Sea Journal of Agriculture, 7(6), 710-719. http://dx.doi.10.47115/bsagriculture.1532659
• Çiftsüren, M. N. (2017). Yumurta iç ve dış kalite özellikleri arasındaki ilişkiyi belirlemede Ridge ve Lasso regülarizasyon yöntemlerinin karşılaştırılması. (Master Thesis) Yüzüncü Yıl Üniversity, The Institute of Natural Sciences, Van, Türkiye.
• Çokluk, Ö., Şekercioğlu, G., & Büyüköztürk, Ş. (2014). Sosyal bilimler için çok değişkenli istatistik SPSS ve lisrel uygulamaları [3.Basım]. Ankara: Pegem Akademi.
• Demir, Y., Keskin, S., & Çavuşoğlu, Ş. (2021). Doğrusal olmayan temel bileşenler analizinin tanıtımı ve uygulanabilirliği. Kahramanmaraş Sütçü İmam Üniversitesi Tarım Ve Doğa Dergisi, 24(2), 442-450.
• Friedman, J., Hastie, T., & Tibshirani, R. (2010). Regularization paths for generalized linear models via coordinate descent. Journal of Statistical Software, 33(1), 1-22. https://doi.org/10.18637/jss.v033.i01 arXiv+7jstatsoft.org+7PubMed+7
• Gök İ., Şahin M., & Tolun T. (2023). Determination of Impact Size by Canonic Correlation Analysis of the Factors Affecting the Buying or Selling Agricultural Lands. Cumhuriyet Science Journal, 44(2),411-417. https://doi.org/10.17776/csj.1139858
• Gök, İ., & Kurşun, K. (2025a). Prediction model of albumen index and height in Japanese quail eggs via external quality characteristics. International Journal of Agriculture Environment and Food Sciences, 9(2), 493-501. https://doi.org/10.31015/2025.2.22
• Gök, İ., & Kurşun, K. (2025b). Comparative Estimation Models of Egg Albumen Index in Atak-S Hens with Ridge and Principal Component Regression Methods . Turkish Journal of Agriculture - Food Science and Technology, 13(9), 2615–2622. https://doi.org/10.24925/turjaf.v13i9.2615-2622.7699.
• Hoerl, A. E., & Kennard, R. W. (1970). Ridge regression: Biased estimation for nonorthogonal problems. Technometrics, 12(1), 55-67. https://doi.org/10.1080/00401706.1970.10488634
• James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An Introduction to Statistical Learning with Applications in R. Springer.
• Kaya, E., & Aktan S. (2011). Flock age and hatching egg storage period in Japanese quail: 1. Effects on dark albumen traits. Süleyman Demirel University Journal of Agriculture Faculty, 6(2), 30-38, ISSN 1304-9984.
• Kul, S., & Şeker, I. (2004). Phenotypic correlations between some external and internal egg quality traits in the Japanese quail (Coturnix coturnix japonica). International Journal of Poultry Science, 3(6), 400-405. http://dx.doi.org/10.3923/ijps.2004.400.405
• Kurşun, K., & Gök, İ. (2025). Prediction model of albumen ındex in duck eggs via external egg quality characteristics in case of multicollinearity. Black Sea Journal of Agriculture, 8(4), 525-532.
• Küçük, A. (2019). Doğrusal regresyonda Rıdge, Liu ve lASSO tahmin edicileri üzerine bir çalışma. (Master Thesis) Hacetepe Üniversity, The Institute of Natural Sciences, Ankara, Türkiye.
• Liu, K. (1993). A new class of biased estimate in linear regression. Communications in Statistics-Theory and Methods, 22(2), 393-402.
• Maxwell, S. E. (2000). Sample size in multiple regression analysis. Psychological Methods, 5(4), 434-458. https://psycnet.apa.org/doi/10.1037/1082-989X.5.4.434
• Montgomery, D. C., Peck E. A., & Vining, G. G. (2001). Introduction to Linear Regression Analysis, 3rd Edition, John Wiley & Sons, New York.
• Montgomery, D. C., Peck, E. A., & Vining, G. G. (2012). Introduction to Linear Regression Analysis. John Wiley & Sons. Olawumi, S., & Chiristiana, B. (2017). Phenotypic correlations between external and internal egg quality traits of Coturnix quails reared under intensive housing system. Journal of Applied Life Sciences International, 12(3), 1-6. https://doi.org/10.9734/JALSI/2017/33802
• Özbey, F. (2012). Çoklu iç ilişki olması durumunda lineer regresyon modellerinin kullanımı ile kestirim ve öngörü. (Ph. D. Thesis), Çukurova Üniversity, The Institute of Natural Sciences, Adana, Türkiye.
• Samli, H. E., Okur, A. A., & Senkoylu, N. (2005). Effects of storage time and temperature on egg quality in old laying hens. Journal of Applied Poultry Research, 14(3), 548–553. https://doi.org/10.1093/japr/14.3.548
• Topal, M., Eyduran, E., Yağanoğlu, M., Sönmez, A.Y., & Keskin, S. (2010). Çoklu doğrusal bağlantı durumunda Ridge ve Temel Bileşenler regresyon analiz yöntemlerinin kullanımı. Atatürk Üniversitesi Ziraat Fakültesi Dergisi, (41), 53-57. ISSN : 1300-9036.
• Tolun, T., Yavuz, E., Şahin, M., & Gök, İ. (2023). Modeling egg curves ın partridges. Black Sea Journal of Agriculture, 6(1),21-25. https://doi.org/10.47115/bsagriculture.1139272
• Tolun, T., Gök, İ., & Şahin, M. (2024). Modeling of some egg characteristics in henna partridges. Black Sea Journal of Agriculture, 7(6), 729-742 ). https://doi.org/10.47115/bsagriculture.1555738
• Tibshirani, R. (1996). Regression shrinkage and selection via the LASSO. Journal of the Royal Statistical Society: Series B (Methodological), 58(1), 267-288. https://doi.org/10.1111/j.2517-6161.1996.tb02080.x
• Üçkardeş, F., Efe, E., Narinç, D., & Aksoy, T. (2012). Japon bıldırcınlarında yumurta ak indeksinin Ridge regresyon yöntemiyle tahmin edilmesi. Akademik Ziraat Dergisi, 1,11-20. ISSN: 2147-6403.
• Yannakopoulos, A. L., & Tserveni-Gousi, A. S. (1986). Qualitycharacteristics of quaileggs. British PoultryScience, 27, 171-176. . https://doi.org/10.4236/ojas.2021.112016
• Yalçınöz, E., & Şahin, M. (2020).Yumurtacı tavuklarda yumurta verim eğrilerinin modellenmesi. KSÜ Tarım ve Doğa Dergisi, 23(5),1373-1378 https://doi.org/10.18016/ksutarimdoga.vi.631937 Yavuz, E., Abacı, S. H., Erensoy, K., & Şahin, M. (2023). Modeling of ındividual egg weights of Lohmann-Brown layer hens. Turkish Journal of Veterinary & Animal Sciences, 47(3), 229-335. https://doi.org/10.55730/1300-0128.4290
• Zhang, H., & Lu, W. (2007). Adaptive Lasso for Cox's proportional hazards model. Biometrika, 94(3), 691-703. https://doi.org/10.1093/biomet/asm056