Comparison of some functions describing the shape of the lactation curve for Holstein cows

A total of 260709 monthly test day milk records of 30903 first lactation Holstein cows was used to determine the best function to describe the lactation curve. The records were obtained from first lactation Holstein of 216 herds from 1988 to 2006 in Khorasan province. The functions used in current study were Wood’s incomplete gamma function, Ali and Schaeffer function, and Legendre function of fifth order. Six criteria including error sum of squares, mean error sum of squares, coefficient of determination, adjusted coefficient of determination, correlation coefficient and variance inflation factor were used to compare the performance of the functions. The results indicated that Ali and Schaeffer function was more preferable than other functions when the variance inflation factor was ignored. However the Legendre function was found to be more appropriate than other functions when the variance inflation factor was considered.