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 given model. Is there any function that predicts x for a given y?

For example:

kalythos <- data.frame(x = c(20,35,45,55,70), 
    n = rep(50,5), y = c(6,17,26,37,44))
kalythos$Ymat <- cbind(kalythos$y, kalythos$n - kalythos$y)
model <- glm(Ymat ~ x, family = binomial, data = kalythos)

If we want to know the predicted value of the model for x=50:

predict(model, data.frame(x=50), type = "response")

I want to know which x makes y=30, for example.

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.

Answer 2

Saw the previous answer is deleted. In your case, given n=50 and the model is binomial, you would calculate x given y using:

f <- function (y,m) {
  (logit(y/50) - coef(m)[["(Intercept)"]]) / coef(m)[["x"]]
}
> f(30,model)
[1] 48.59833

But when doing so, you better consult a statistician to show you how to calculate the inverse prediction interval. And please, take VitoshKa's considerations into account.