Determination of Number and Position of Knots in Cubic Spline Regression for Modeling Individual Lactation Curves in Three Different Breed

Abstract

Lactation curves are one of the basic tools in animal breeding. Therefore, modeling lactation curves with appropriate and precise equations are of great importance for obtaining estimates. Lactation curves have different tendencies in different breeds. To examine the tendencies and differences Jersey (J), Brown Swiss (BS) and Holstein Friesian (HF) breeds which are commonly raised in Turkey were used in this study. This study aimed to statistically determine the optimal position and number of knots in cubic spline regression used for modeling lactation curves. Knots were taken as 60, 90, 120 and 150 days and combinations of them for every breed. To compare the Mean Square Errors (MSE) of the models, the autocorrelation values of Durbin Watson (DW), the information criteria of Akaike (AIC) and the coefficient of determination (R2) were used as comparison criteria. Kruskal Wallis H test was used to compare comparison criteria in different models. The Mann Whitney U test was used to compare the groups in pairs. Results showed that four knots was sufficient for J breed MSE: 0.640 ± 0.0652, DW: 2.272 ± 0.0232, AIC: 16.927 ± 1.0649, R2: 0.982 ± 0.0020) and BS breed (MSE: 0.131 ± 0.0156, DW: 2.326 ± 0.1093, AIC: 3.567 ± 0.9193, R2: 0,985 ± 0.0008), but three knot was sufficient for HF breed (MSE: 1.600 ± 0.132, DW: 2.114 ± 0.020, AIC: 22.596 ± 0.783, R2: 0.972 ± 0.002). As a general result of the study show that four knots (60, 90, 120 and 150 days) for J and BS breeds and three knots (90, 120 and 150 days) for HF breed were sufficient to estimate lactation curve by cubic spline regression model. © 2020 Zoological Society of Pakistan