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Beginning in Stata 8, standard errors for predictions can be computed using predictnl.
| Title | Obtaining a standard error of the predicted probability with logistic regression analysis | |
| Author | Roberto Gutierrez |
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
