McCallum D A, Dixon P M
Savannah River Ecology Laboratory, Aiken, SC 29802.
Growth Dev Aging. 1990 Winter;54(4):135-41.
A process error model developed by White and Brisbin (1980) is used frequently for estimation of the parameters of the Richards sigmoid growth function. The Richards function includes a parameter, m, that describes the shape of familiar three-parameter functions, such as the monomolecular (m = 0), von Bertalanffy (m = 2/3), Gompertz (m----1) and logistic m = 2), as well as other sigmoid functions. We show that this model systematically underestimates the shape parameter, m. In calibration runs and simulations, bias decreased with increased frequency of sampling during the period of rapid growth and with smaller values of true m. Relative bias was insensitive to the magnitude of m. A simple correction reduced the bias to negligible values for both deterministic and stochastic process error models. Biases in estimated asymptote, A, and growing time, T, were small for a variety of sampling intervals and shape parameters.
怀特和布里宾（1980年）开发的过程误差模型经常用于估计理查兹S形生长函数的参数。理查兹函数包含一个参数m，它描述了常见的三参数函数的形状，如单分子函数（m = 0）、冯·贝塔朗菲函数（m = 2/3）、冈珀茨函数（m = 1）和逻辑斯蒂函数（m = 2），以及其他S形函数。我们表明，该模型系统地低估了形状参数m。在校准运行和模拟中，偏差随着快速生长期间采样频率的增加以及真实m值的减小而降低。相对偏差对m的大小不敏感。对于确定性和随机过程误差模型，一个简单的校正将偏差降低到可以忽略不计的值。对于各种采样间隔和形状参数，估计的渐近线A和生长时间T的偏差都很小。
