A Power Transformation for Generalized Logistic Response Function with Application to Quantal Bioassay

Abstract

AbstractIt is known that when the logistic response function is generalized by introducing shape parameters, the usual computational simplicity afforded by statistical softwares such as GLIM and S‐Plus may be lost. This fact is illustrated by Prentice (1976), Brown (1982), Stukel (1985, 1988), and El‐Saidi (1986). In this paper, we consider a power transformation of the generalized logistic model and show how the use of such transformation simplifies the computational difficulties associated with generalized logistic models. Furthermore, applying this technique to some data sets previously analyzed by D'Angio et al. (1981) and Brown (1982) shows an improvement in the fit in comparison to other models such as the logistic, the unstratified multiplicative model GMU and the additive model GA described by Storer et al. (1983).