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Re: st: Probit/Logit - implied probability

From   Maarten Buis <>
Subject   Re: st: Probit/Logit - implied probability
Date   Tue, 17 May 2011 09:56:29 +0200

--- Ben Hoen asked
> does anyone know how to calculate the "implied probability" after a logit regression, meaning that each independent variable is kept at its mean value? Perhaps there is an after-regression tool like margins?

--- Steven Samuels answered:
> I assume that you don't have Stata 11 and can't use -margins-.   Pre-11, -adjust- will do what you ask, but that doesn't mean its answer will be what you would expect. See  and the following post by Michael Norman Mitchell.

The problem discussed in that post is that there is a subtle
distinction between a typical predicted probability for someone within
group and the predicted probability for someone with typical values on
the explanatory variables for someone within that group. If you
compute what you call "implied probability" than you are computing the
latter and Steve's point is that you often want the former.

I agree, but there is a catch in that the former requires more from
your data than the latter. The latter, predictions at typical values
of the explanatory variables, requires only that the probability of
being in the data does not depend on once value on the
explained/left-hand-side/y-variable (*), while the former, average
predicted values, requires that the probability of being in the data
does not depend on both the explained/left-hand-side/y-variable and
the explanatory/right-hand-side/x-variables. David Drukker pointed
this out at the 2010 Italian Stata Users' meeting: page 20 of
<>. For a proof of
the statement that the probability of being in the data only needs to
be independent with respect to y see footnote 1 in Paul D. Allison
(2002) "Missing Data". Quantitative Applications in the Social
Sciences, 136. Thousand Oaks: Sage.

I gave a more elaborate explanation of the distinction between average
predicted probability and predicted probability at average values of
the explanatory variables and how to compute both in Stata < 11 in:
Buis, M.L. (2007) "predict and adjust with logistic regression" The
Stata Journal, 7(2):221-226.

Hope this helps,

(*) As long as you decide for yourself what typical values for your
explanatory variables are and thus do not take the averages in your
data too strict, which often makes sense, as we often have a fair idea
what those typical values are from other sources.

Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen

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