How do I obtain the standard error of the predicted probability with
logistic regression analysis?
| Title |
|
Obtaining a standard error of the predicted probability with logistic regression analysis |
| Author |
Roberto Gutierrez |
| Date |
March 2001 |
The predicted probability in a logistic regression is a transformation of
the linear combination x^t beta. Thus, by the delta method, the predicted
probability for
H(t) = (1+exp(-t))^{-1}
is
pi = H(x^t beta) = H(linear combination)
Applying the delta method, we get
se(pi) = H'(linear combination) * stdp
= pi*(1-pi)*stdp,
by properties of the logistic function H().
Thus, to get standard errors for your predicted probabilities, the following
sequence of commands will work nicely:
. logit y x
. predict p
. predict stdp, stdp
. gen se = p * (1-p) * stdp
|
