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From |
Chiara Mussida <cmussida@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: predict |

Date |
Mon, 6 Jun 2011 10:07:46 +0200 |

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 > 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 > -------------------------- > * > * 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/

**Follow-Ups**:**Re: st: predict***From:*Maarten Buis <maartenlbuis@gmail.com>

**References**:**st: predict***From:*Chiara Mussida <cmussida@gmail.com>

**Re: st: predict***From:*Richard Williams <richardwilliams.ndu@gmail.com>

**Re: st: predict***From:*Chiara Mussida <cmussida@gmail.com>

**Re: st: predict***From:*Chiara Mussida <cmussida@gmail.com>

**Re: st: predict***From:*Maarten Buis <maartenlbuis@gmail.com>

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