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Re: st: predict


From   Maarten Buis <maartenlbuis@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: predict
Date   Fri, 3 Jun 2011 09:42:42 +0200

--- On 2 June 2011 18:08, Chiara Mussida wrote:
> I simply want the coefficients (of my covariates) which allow me to
> get the predicted outcome of each equation of my MNL.
>
> example: I get a predicted probability (say to move from employment to
> unemployment) of 0.4:
> what is the contribution (numerical) of each covariate I included in
> my equation (suc as sex, individual age, etc.). Is it given by the
> exponential of the coef I find in the Stata output? therefore by
> summing/subtracting the exp of each coef I get my predicted of 0.4
> (but there is also a standard error)

The contribution of each variable to the predicted probability is
neither its coefficient nor the exponential of that coefficient. It is
a non-linear function you can find in any introductory text on
multinomial regression. So you cannot use a set of additions of
coefficients to get to the predicted probability.

If you want to give a exact representation of the model you will have
to look at relative risks or odds(*) (**), this is:

relative risk = exp(b0 + b1 x1 + b2 x2 + ...)

or, equivalently

relative risk = exp(b0) * exp(b1 x1) * exp(b2 x2) * ...

Alternatively, you can fit a linear model on top of your multinomial
logistic regression, and use those results to summarize the results.
This is what you do when you compute marginal effects. As this is the
result of a model on top of a model it will not be an exact
representation of the original multinomial regression model, so the
addition of coefficients will in all likelihood lead to deviations
from the actual predicted probabilities. on the plus side, you can now
interpret your results in terms of probabilities instead of relative
risks.

The fact that marginal effects are not exact representation of the
model results is not necessarily bad. Marginal effects form a model of
your multinomial regression model, and models aren't supposed to be
exact, they are only supposed to be useful. Whether or not this model
of a model is useful depends on the exact aim of the exercise. If you
do this in order to compute some kind of decomposition of effects,
than I would stick to the exact representation, if I were presenting
results than I would look at who my audience is. There are also cases
where the underlying multinomial regression model is so complicated,
that the linear approximation implicit in the marginal effects starts
to struggle. For example it is not uncommon for correctly computed
marginal effects of interaction terms to be significantly positive for
some respondents, significantly negative for others, and
non-significant for the remaining respondents. In most cases, that is
hardly a useful conclusion.

Hope this helps,
Maarten

(*) There are some differences between disciplines in whether the
outcomes of a multinomial logistic regression can be called an odds or
whether a new term like relative risk has to be invented for it. See,
for example: <http://www.stata.com/statalist/archive/2007-02/msg00085.html>

(**) Notice that I say here relative risk or odds, I did not say
relative risk ratio or odds ratio. It is a common mistake to assume
that these things are the same.


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


http://www.maartenbuis.nl
--------------------------
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