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# Re: st: predict

 From Maarten Buis To statalist@hsphsun2.harvard.edu Subject Re: st: predict Date Mon, 6 Jun 2011 10:18:19 +0200

```The reason is that you made an error in your computations. Since you
did not give use the code you used for your computations we cannot
tell you what that error is.

-- Maarten

On Mon, Jun 6, 2011 at 10:07 AM, Chiara Mussida <cmussida@gmail.com> wrote:
> Dear All,
> many thanks to Maarten and Richard for their precious help.
> One doubt remain unsolved:
> when I compute the predicted probabilities from my mlogit as:
>
> pr1 = exp(b0 + b1 x1)/(exp(b0 + b1 x1) + exp(b0 + b2 x2) + 1)
>
> where pr1 is the predicted prob of outcome 1, b0 is a constant, b1 and
> b2 the coefficients from outcome 1 and 2. here I assume that outcome 3
> is the base category, and a totalo of three outcomes.
>
> this computation, carried out by using the coefficients of the STATA
> output (mlogit commands) differs from the outcome predicted by using
> the predict command (which is a mlogit postestimation outcome), such
> as:
> Predict probabilities of outcome 1 for estimation sample
> predict p1 if e(sample), outcome(1)
>
> my question is: why the two computations offer different results for
> predicted probabilities? Maybe related to the method of computation
> behind predict command.
>
> Many Thanks
> C
>
>
>
>
>
>
>
>
> On 3 June 2011 09:42, Maarten Buis <maartenlbuis@gmail.com> wrote:
>> --- 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
>> from the actual predicted probabilities. on the plus side, you can now
>> 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
>> --------------------------
>> *
>> *   For searches and help try:
>> *   http://www.stata.com/help.cgi?search
>> *   http://www.stata.com/support/statalist/faq
>> *   http://www.ats.ucla.edu/stat/stata/
>>
>
>
>
> --
> Chiara Mussida
> PhD candidate
> Doctoral school of Economic Policy
> Catholic University, Piacenza (Italy)
>
> *
> *   For searches and help try:
> *   http://www.stata.com/help.cgi?search
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/
>

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

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

*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/
```