inverse of 'predict' function

Question

Using predict() one can obtain the predicted value of the dependent variable (y) for a certain value of the independent variable (x) for a

Answer 1

Came across this old thread but thought I would add some other info. Package MASS has function dose.p for logit/probit models. SE is via delta method.

> dose.p(model,p=.6)
             Dose       SE
p = 0.6: 48.59833 1.944772

Fitting the inverse model (x~y) would not makes sense here because, as @VitoshKa says, we assume x is fixed and y (the 0/1 response) is random. Besides, if the data weren’t grouped you’d have only 2 values of the explanatory variable: 0 and 1. But even though we assume x is fixed it still makes sense to calculate a confidence interval for the dose x for a given p, contrary to what @VitoshKa says. Just as we can reparameterize the model in terms of ED50, we can do so for ED60 or any other quantile. Parameters are fixed, but we still calculate CI's for them.