动物生长曲线拟合方法的探讨

本文提出了一种近似估计生长曲线参数的方法,即先用差商代替导数(或),由生长曲线的微分模型估计出部分参数,剩余参数在原模型中通过最小二乘加权处理法求得。并以肉鸡的体重生长资料为例,拟合了指数生长曲线,Logistic方程和Gom-pertz三种常用的动物生长模型。拟合结果(拟合度)分别为:0.9342,0.9796,0.9554,而高精度法(Marquardt法)的拟合度对应是:0.9314,0.9988,0.9941。可见,两种方法的拟合结果顺序一致,精度相差并不太大。若追求更高的拟合精度,近似估计法可作为Marquardt法确定参数初值的方法。

PRELIMINARY DISCUSSION ON THE FITTING METHODS OF ANIMAL GROWTH CURVES

This paper presents a method to estimate the approximete parma-ters in growth curves. First of all difference quotient is subsitutc for deriative ( dw/dt or dw/wdt ) , then, the partial parameters from the differential model of a given growth curve is estimated , finally , the other parameters is obtained by means of weighted originary least square method on basis of the original model. Taking the growth data of broiler body weights as an examaple, we have fitted in form of exponential growth curve, Logistic model and Gompertz model which are commonly met. The goodness of fit is 0.9342,0.9796 and 0.9554 respectively, meanwhile the counterpart for the high precision method ( Mar-quardt method ) is 0.9501, 0.9992 and 0.9990 respectively. It can be seen clearly that the two methods have the same sequence in goodness of fit, and have similar fitting precisions. If higher fitting precision is required, this method presented in this paper can be used for determining the initial values of parameters in Marquardt method.