Comparison of Diff erent Order and Heterogeneous Residual Variances Legendre Polynomials in Random Regression Models

In this study, it was aimed to estimate covariance function, covariance components, permanent environmental eff ect, additive genetic eff ect and heritability values, and comparison of models with diff erent order and heterogeneous residual variances Legendre Polynomials in the first lactation Turkish Holstein cows more than 10 test day milk yields. For this aim, 7340 test day records of 386 Holstein Friesian cows in the first lactation raised in private dairy farm calving from 2013 to 2018 in Kırşehir-Turkey were used. The six Legendre polynomial models by random regression described as L(2,2), L(3,3), L(4,4), L(5,5), L(6,6) and L(7,7) were evaluated using first lactation test day records. Heterogeneous residual variances (RV) were modeled by considering five sub-classes. Analyzes were performed using the WOMBAT statistical package. In comparison of the models, -2LogL, Akaike Information Criterion (AIC), Bayes Information Criterion (BIC) and RV were used. Also, the compatibility of random regression models was examined in terms of eigenvalues of covariance matrices. The values of -2LogL (between 28334.16 and 26610.07), AIC (between 28356.16 and 26732.07) and BIC values (between 28432.05 and 27129.21) obtained from the study result decreased as the model order increased. As a result, it was determined that the 3rd degree Legendre polynomial model can provide sufficient compliance. However, when looking at the values for -2LogL, AIC and RV, it was determined that the L(7,7) model fits well according to other models.

Şansa Bağlı Regresyon Modellerinde Farklı Dereceli ve Heterojen Hata Varyanslı Legendre Polinomlarının Karşılaştırılması

Bu çalışmada, 10’dan fazla test günü süt verimine sahip birinci laktasyondaki Holstein Friesian ineklerinde farklı dereceli Legendre Polinomları kullanılarak birinci test günü süt verimleri için kovaryans fonksiyonu, kovaryans bileşenleri, kalıcı çevresel etki, eklemeli genetik etki ve kalıtım derecelerinin tahmin edilmesi ve modellerin karşılaştırılması amaçlanmıştır. Bu amaçla Kırşehir-Türkiye’de 2013’ten 2018’e kadar buzağılayan özel süt çiftliğinde yetiştirilen birinci laktasyondaki 386 Holstein Friesian ineklerinin 7340 test günü kaydı kullanılmıştır. L(2,2), L(3,3), L(4,4), L(5,5), L(6,6) ve L(7,7) olarak tanımlanan rastgele regresyon ile altı Legendre polinom modeli birinci laktasyon test günü kayıtları kullanılarak değerlendirilmiştir. Heterojen hata varyansları (RV), beş alt sınıf dikkate alınarak modellenmiştir. Analizler, WOMBAT istatistik paketi kullanılarak yapılmıştır. Modellerin karşılaştırılmasında -2LogL, Akaike Bilgi Ölçütü (AIC), Bayes Bilgi Ölçütü (BIC) ve hata varyansları (RV) kullanılmıştır. Ayrıca, şansa bağlı regresyon modellerinin uyumluluğu kovaryans matrislerinin özdeğerleri açısından incelenmiştir. Çalışma sonucundan elde edilen -2LogL (28334.16 ve 26610.07 arasında), AIC (28356.16 ve 26732.07) ve BIC (28432.05 ile 27129.21 arasında) değerleri model sırası arttıkça azalmıştır. Sonuç olarak, 3. derece Legendre polinom modelinin yeterli uyumu sağlayabileceği belirlenmiştir. Ancak -2LogL, AIC ve RV değerlerine bakıldığında, L(7,7) modelinin diğer modellere göre iyi uyum gösterdiği belirlenmiştir.

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