Inference for the Richards growth model using Box and Cox transformation and bootstrap techniques

Abstract

The paper considers the parameter identification of the Richards population growth model, a class of models that generalizes the logistic and the Gompertz growth model classes. The use of the Richards class presents an identifiability problem that is worsened when handling small data samples, a situation often encountered in animal population modeling. This paper tackles the identifiability problem by regarding the growth rate form parameter ( q) in the Richards’ model as the parameter in the corresponding Box–Cox data transformation, leading to a model that can be interpreted as a logistic growth model. In order to assure better interval estimation for the model parameters, the approach is complemented with the profile maximum likelihood estimates of the q parameter of the Richards model combined with the bootstrap technique. Some tests using generated and measured data are presented to illustrate the technique.