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# Re: st: predict

 From Chiara Mussida To statalist@hsphsun2.harvard.edu Subject Re: st: predict Date Mon, 6 Jun 2011 10:34:11 +0200

```The code I use was,
mlogit utr sex age loweduc compulsory diploma, b(3)

then I got my estimates in STATA.

by typing:
predict p1 if e(sample), outcome(1)

I did get a probability different from the one I got by using the
coefficient estimates to compute the relative odds ratio.
Many Thanks
Chiara

On 6 June 2011 10:18, Maarten Buis <maartenlbuis@gmail.com> wrote:
> 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/
>

--
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/
```