Prediction of Inner Quality Characteristics of Eggs Using Partial Least Squares Regression

Abstract

This study was carried out to obtain a prediction model for egg albumen and yolk weight, which are the internal quality characteristics of egg predicted from external quality characteristics of egg. For this purpose partial least squares regression method was applied to the data set used in the study and the results were compared with the principal component regression method. In the partial least squares regression analysis for egg albumen and yolk weight, the number of latent factor was 1 and the determination coefficients were 68.44% and 63.40%, respectively. For the egg albumen weight, the coefficients of determination for the principal component regression with one latent factor were 63.40% and 53.80%. When there is no restriction for the number of factors in the principal component regression, for the egg albumen weight the number of latent factors was five and the coefficients of determination was 79.77%; for the egg yolk weight the values were two and 75.35%, respectively. The results shown that the partial least squares regression method was more effective than the principal component regression method in dimension reduction, and more reliable predictions can be obtained in small sample sets with multicollinearity using the partial least squares regression method.

Keywords

• Multicollinearity,Ordinary least square,Partial least square,Principal component

Yumurta İç Kalite Özelliklerinin Kısmi En küçük Kareler Regresyonu Kullanılarak Tahmin Edilmesi

Öz

Bu çalışma, yumurta dış kalite özellikleri kullanılarak iç kalite özellikleri olan yumurta ak ve sarı ağırlığı için bir tahmin modeli elde etmek amacıyla yapılmıştır. Bu amaçla, çalışmada kullanılan veri setine kısmi en küçük kareler regresyon yöntemi uygulanmış ve elde dilen sonuçlar temel bileşenler regresyon yöntemi ile karşılaştırılırmıştır. Yumurta ak ve sarı ağırlığı için kısmi en küçük kareler regresyon analizinde gizil faktör sayısı bir ve belirleme katsayıları sırasıyla % 68.44 ve % 63.40 olmuştur. Yumurta ak ve sarı ağırlığı için bir faktörlü temel bileşenler regresyonu için belirleme katsayısı sırasıyla % 63.40 ve %53.80 olarak elde edilmiştir. Temel bileşenler regresyonunda faktör sayısı için kısıtlama olmadığı durumda, yumurta ak ağırlığı için gizil faktör sayısı beş ve belirleme katsayısı % 79.77; yumurta sarı ağırlığı için bu değerler sırasıyla iki ve % 75.35 olmuştur. Elde edilen bu sonuçlar, boyut indirgeme konusunda kısmi en küçük kareler regresyon yönteminin temel bileşenler regresyon yönteminden daha etkin olduğunu ve çoklu bağlantıya sahip küçük örnek setlerinde daha güvenilir tahminler elde edilebileceğini ortaya koymuştur. 

Anahtar Kelimeler

• Çoklu bağlantı,En küçük kareler,Kısmi en küçük kareler,Temel bileşenler

References

1. Abanikannda OTF, Olutogun O, Leigh AO, Ajayi LA (2007). Statistical modeling of egg weight and egg dimensions in commercial layers. International Journal of Poultry Science 6(1): 59-63.
2. Abdi H (2003). Partial least square regression (PLS regression). Encyclopedia for research methods for the social sciences 6(4): 792-795.
3. Albayrak SA (2005). Çoklu bağlantı halinde en küçük kareler teknikleri ve bir uygulama, Zonguldak Kara Elmas Üniversitesi, Sosyal Bilgiler Dergisi 1: 105-126.
4. Alkan S, Karabağ K, Galiç A, Karslı T, Balcıoğlu MS (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.
5. Belsley, D. A.: Conditioning Diagnostics, Collinearity and Weak Data in Regression. John Wiley and Sons, New York, NY, USA, 1991.
6. Boulesteix AL (2004). PLS dimension reduction for classification with microarray data. Stat Appl Genet Mol Biol, 3(1):33.
7. Carrascal LM, Galván I, Gordo O (2009). Partial least squares regression as an alternative to current regression methods used in ecology. Oikos, 118(5), 681-690.
8. Çiftsüren MN, Akkol S (2018). Prediction of internal egg quality characteristics and variable selection using regularization methods: ridge, LASSO and elastic net. Archives Animal Breeding, 61(3): 279-284.

9. Dimauro C, Steri R, Pintus M A, Gaspa G, Macciotta NPP (2011). Use of partial least squares regression to predict single nucleotide polymorphism marker genotypes when some animals are genotyped with a low-density panel. Animal, 5(6):833-837.
10. El-Fallah M., El-Salam A (2014). A Note on Partial Least Squares Regression for Multicollinearity (A Comparative Study). International Journal of Applied Science and Technology. 4(1):163-169.
11. Farooq M, Durrani FR, Sarbiland K, Chand, N (2003). Predicting egg weight, shell weight, shell thickness and hatching chick weight of Japanese quails using various egg traits as regressors. International Journal of Poultry Science.
12. Feddern V, Prá MCD, Mores R, Nicoloso RDS, Coldebella A, Abreu PGD (2017). Egg quality assessment at different storage conditions, seasons and laying hen strains. Ciência e Agrotecnologia, 41(3): 322-333.
13. Garthwaite PH (1994). An interpretation of partial least squares, Journal of the American Statistical Association, 89:122-127.
14. Hoerl, AE, Kennard RW (1970). Ridge regression: biased estimation for non-orthogonal problems, Technometrrics, 12 :55-82. DOI:10.1080/00401706.1970.10488634
15. Hotelling H (1933). Analysis of a complex of statistical variables into principal components. Journal of educational psychology, 24(6): 417.
16. Kul S, Seker İ ( 2004). Phenotypic correlations between some external and ınternal egg quality traits in the japanese quail (Coturnix coturnix japonica) International Journal of Poultry Science3 (6): 400-405.
17. Macciotta NPP, Dimauro C, Catillo G, Coletta A, Cappio-Borlino A (2006). Factors affecting individual lactation curve shape in Italian river buffaloes. Livestock Science, 104(1-2):33-37.
18. Maitra S, Yan J (2008). Principal Component Analysis and Partial Least Squares: Two Dimension Reduction Techniques for Regression. Casualty Actuarial Society Discussion paper Program. 79-90
19. Marquardt, D. W Snee, R. D., 1975. Ridge Regression in Pratice. The American Statistician, 29: 3-20.
20. Montgomery DC, Peck EA, Vining GG (2001). Introduction to Linear Regression Analysis, 3rd Edition, John Wiley&Sons, New York.
21. Özçelik M (2002). Japon bıldırcını yumurtalarında bazı iç ve dış kalite özellikleri arasındaki fenotipik korelasyonlar. Ankara Üniversitesi Veterinerlik Fakültesi, 49: 67-62.
22. Phatak A, De Jong S (1997). The geometry of partial least squares. Journal of Chemometrics: A Journal of the Chemometrics Society, 11(4): 311-338.
23. Rathert TÇ, ÜçkardeşF, Narinç D, Aksoy T (2011). Comparision of Principal Component Regression with the Least Square Method in Prediction of Internal Egg Quality Characteristics in Japanese Quails. Kafkas Universitesi Veteriner Fakultesi Dergisi, 17: 687-692.DOI:10.9775/kvfd.2010.3974
24. Sahin M, Yavuz E, Uckardes F (2018). Multicollinearity Problem and Bias Estimates in Japanese Quail. Pakistan J. Zool., 50(2): 757-761, 2018.
25. SAS (2014) SAS/STAT User’s Guide: Version 9.4, SAS Institute Inc., Cary, NC, USA, 64.Tatlıdil H (1996). Uygulamalı Çok Değişkenli İstatistiksel Analiz, Cem Web Ofset Ltd. Şti., Ankara.
26. Tibshirani R (1996). Regression shrinkage and selection via the lasso, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 58: 267–288.
27. Ukwu HO, Abari PO, Kuusu DJ (2017). Principal Component Analysis of Egg Quality Characteristics of Isa Brown Layer Chickens in Nigeria. World Scientific News, 70(2): 304-311.
28. Üçkardeş F, Efe E, Narinç D, Aksoy, T (2011). Japon bıldırcınlarında yumurta ak indeksinin ridge regresyon yöntemiyle tahmin edilmesi.Akademik Ziraat Dergisi 1(1): 11-20.
29. Wold H (1975). Perspectives in Probability and Statistics. In Gani J (ed). Soft modeling by latent variables: the nonlinear iterative partial least squares approach. London, UK: Academic Press. p. 520–540.
30. Wold, H. (1966). Estimation of principal components and related models by iterative least squares. In: Krishnaiaah, P. R., ed., Multivariate Analysis. New York: Academic Press, pp. 391–420.
31. Wold, S. (1994). “PLS for Multivariate Linear Modeling,” QSAR: Chemometric Methods in Molecular Design. Methods and Principles in Medicinal Chemistry.
32. Wold, S., Ruhe, A., Wold, H., Dunn, III, W. (1984). The collinearity problem in linear regression. The partial least squares (PLS) approach to generalized inverses. SIAM Journal of Scientific Statistical Computing 5:735–744.
33. Zou, H., Hastie, T., 2005. Regularization and variable selection via the elastic net. Statistical Society: Series B,67: 301–320.