# RE: st: Predicted probabilities after mlogit

 From "Jun Xu" To statalist@hsphsun2.harvard.edu Subject RE: st: Predicted probabilities after mlogit Date Mon, 05 Sep 2005 13:13:36 -0500

An additional note that applies to all nonlinear models:

E(g(x)) != g(E(x)) [the expectation of a nonlinear function of random variable is not equation to the function of the expectation of random variables

I think what you did with predict is E(g(x)), and what prvalue does is g(E(x))

Jun Xu
Ph.D. Candidate
Department of Sociology
Indiana University at Bloomington

From: "Little, Allan" <a.little@lancaster.ac.uk>
To: <statalist@hsphsun2.harvard.edu>
Subject: st: Predicted probabilities after mlogit
Date: Mon, 5 Sep 2005 16:10:36 +0100

Dear all,

I'm trying to calculate predicted probabilities following a multinomial logit regression. My dependant variable has three states - employment (coded 0), unemployment (1) and inactivity (2).

I would like to calculate the predicted probability, firstly evaluated at the mean, and secondly evaluated a number of different specified values. However, I am encountering some apparent inconsistencies according to which command I use.

1. If I use 'predict p0 p1 p2 if e(sample)' [option 'pr' is assumed to be the default]. The predicted probabilities are equivalent to the proportion (sample mean) for each category.

2. If I use the 'prvalue' command, the predicted probabilties are different to the above (for example, the predicted probability of being employed is much higher than the sample proportion of people who are actually employed).

3. Similarly, the value given by 'mfx compute, predict(pr outcome(0))' also gives a predicted probability which is the same as the value from 'prvalue', but different to the 'predict' command.

Could anyone explain the difference between the predicted probabilities given by the prvalue, predict and mfx commands? I believe that the predicted probability (evaluated at the mean values of X) should be equivalent to the sample proportion in each category - am I right?

Allan Little
Lancaster University

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