For a single independent variable, such as a dosage
level, the models for the probabilities can be justified
on the basis of a population with mean and scale
parameter of tolerances for the subjects.
Then, given a dose x, the probability, P, of observing
a response in a particular subject is the probability
that the subject's tolerance is less than the dose or
Thus, in this case, the intercept parameter,
b0, and the regression parameter,
b1, are related to and by
Note: The parameter is not equal to the
standard deviation of the population of tolerances
for the logistic and extreme value distributions.
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