Reducing bias in estimates of the richards growth function shape parameter.

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.