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Double logistic curve in regression modeling

机译：回归建模中的双逻辑曲线

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摘要

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.
机译：logistic Sigmoid曲线广泛用于非线性回归和二进制响应建模中。存在与双乙状结肠行为相对应的问题，该问题包括第一次增加到中间水平的早期饱和，而第二种乙状结肠最终达到饱和。通常使用logit的加法或乘法组合以及具有众多参数的更复杂函数来实现双S形行为。在这项工作中，双S形函数被构造为逻辑函数，带有定义拐点的符号和附加的供电参数。详尽的模型仅通过四个或五个参数描述了相当复杂的双重饱和行为，可以通过非线性优化技术对其进行有效估计。讨论了模型的理论特点和实际应用。

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