Intrinsically Nonlinear Regression Models - General Logistic Regression Model

y = b₀/{1 + b₁*exp(b₂*x)}

You can think of this model as an extension of the logit or logistic model for binary responses. However, while the logit model restricts the dependent response variable to only two values, this model allows the response to vary within a particular lower and upper limit. For example, suppose we are interested in the population growth of a species that is introduced to a new habitat, as a function of time. The dependent variable would be the number of individuals of that species in the respective habitat. Obviously, there is a lower limit on the dependent variable, since fewer than 0 individuals cannot exist in the habitat; however, there also is most likely an upper limit that will be reached at some point in time.