Double logistic curve in regression modeling

Abstract

The logistic sigmoid curve is widely used in nonlinear regression and in binary response modeling. There are problems corresponding to a double sigmoid behavior which consists of the first increase to an early saturation at an intermediate level, and the second sigmoid with the eventual plateau of saturation. A double sigmoid behavior is usually achieved using additive or multiplicative combinations of logit and more complicated functions with numerous parameters. In this work, double sigmoid functions are constructed as logistic ones with a sign defining the point of inflection and with an additional powering parameter. The elaborated models describe rather complicated double saturation behavior via only four or five parameters which can be efficiently estimated by nonlinear optimization techniques. Theoretical features and practical applications of the models are discussed.

Keywords:

• logistic function
• double sigmoid function
• two levels of saturation

Acknowledgements

The author thanks two referees for the comments which helped in improving this paper.