M. Grossman

Effects of smoothing data on estimation of parameters for multiphasic lactation curves of dairy goats

Abstract Lactation curves were simulated for 6000 dairy goat does using a multiphasic function, which is the sum of logistic functions. Curves were simulated for weekly and monthly observations over the course of a 305-day lactation, for first and second-or-greater parity, and for low, medium, and high magnitude of error. Smoothing data assists in estimating parameters of a diphasic function when data are few or “noisy”. Data were smoothed with LOWESS, a nonparametric, polynomial regression procedure. Two approaches to smoothing were investigated: individual smoothing using individual f values computed from individual curves and global smoothing using a single f computed as a mean of f values, where f is the proportion of data used in smoothing. Parameters of a diphasic function were then estimated from non-smoothed, individually smoothed and globally smoothed data. Individual and global smoothing produced a higher percentage of estimates within the parameter space and also estimates with smaller bias, sampling variance and mean squared error compared with non-smoothed data. Global smoothing was preferred over individual smoothing because of ease of computing.

Algebraic Equivalence of Matrix Inversion, Elimination, and Absorption for Use in Animal Breeding

Abstract The equivalence of several methods of solving linear simultaneous equations is demonstrated for use in teaching applied animal breeding. Matrix notation represents equations concisely and allows ease of algebraic treatment.