Using quantile regression for fitting lactation curve in dairy cows

Abstract

The main objective of this study was to compare the performance of different ‘nonlinear<br>quantile regression’ models evaluated at the τth quantile -0·25, 0·50, and 0·75- of milk production<br>traits and somatic cell score -SCS- in Iranian Holstein dairy cows. Data were collected by<br>the Animal Breeding Center of Iran from 1991 to 2011, comprising 101 051 monthly milk<br>production traits and SCS records of 13 977 cows in 183 herds. Incomplete gamma<br>-Wood-, exponential -Wilmink-, Dijkstra and polynomial -Ali &amp; Schaeffer- functions were<br>implemented in the quantile regression. Residual mean square, Akaike information criterion<br>and log-likelihood from different models and quantiles indicated that in the same quantile,<br>the best models were Wilmink for milk yield, Dijkstra for fat percentage and Ali &amp;<br>Schaeffer for protein percentage. Over all models the best model fit occurred at quantile<br>0·50 for milk yield, fat and protein percentage, whereas, for SCS the 0·25th quantile was<br>best. The best model to describe SCS was Dijkstra at quantiles 0·25 and 0·50, and Ali &amp;<br>Schaeffer at quantile 0·75. Wood function had the worst performance amongst all traits.<br>Quantile regression is specifically appropriate for SCS which has a mixed multimodal<br>distribution.