Avec un modèle logit multinomial, vous imposez la contrainte que toutes les probabilités prédites additionnent à 1. Lorsque vous utilisez un modèle logit binaire distinct, vous ne pouvez plus imposer cette contrainte, elles sont après tout estimées dans des modèles séparés. Ce serait donc la principale différence entre ces deux modèles.
Comme vous pouvez le voir dans l'exemple ci-dessous (dans Stata, car c'est le programme que je connais le mieux), les modèles ont tendance à être similaires mais pas les mêmes. Je serais particulièrement attentif à extrapoler les probabilités prédites.
// some data preparation
. sysuse nlsw88, clear
(NLSW, 1988 extract)
.
. gen byte occat = cond(occupation < 3 , 1, ///
> cond(inlist(occupation, 5, 6, 8, 13), 2, 3)) ///
> if !missing(occupation)
(9 missing values generated)
. label variable occat "occupation in categories"
. label define occat 1 "high" ///
> 2 "middle" ///
> 3 "low"
. label value occat occat
.
. gen byte middle = (occat == 2) if occat !=1 & !missing(occat)
(590 missing values generated)
. gen byte high = (occat == 1) if occat !=2 & !missing(occat)
(781 missing values generated)
// a multinomial logit model
. mlogit occat i.race i.collgrad , base(3) nolog
Multinomial logistic regression Number of obs = 2237
LR chi2(6) = 218.82
Prob > chi2 = 0.0000
Log likelihood = -2315.9312 Pseudo R2 = 0.0451
-------------------------------------------------------------------------------
occat | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------+----------------------------------------------------------------
high |
race |
black | -.4005801 .1421777 -2.82 0.005 -.6792433 -.121917
other | .4588831 .4962591 0.92 0.355 -.5137668 1.431533
|
collgrad |
college grad | 1.495019 .1341625 11.14 0.000 1.232065 1.757972
_cons | -.7010308 .0705042 -9.94 0.000 -.8392165 -.5628451
--------------+----------------------------------------------------------------
middle |
race |
black | .6728568 .1106792 6.08 0.000 .4559296 .889784
other | .2678372 .509735 0.53 0.599 -.7312251 1.266899
|
collgrad |
college grad | .976244 .1334458 7.32 0.000 .714695 1.237793
_cons | -.517313 .0662238 -7.81 0.000 -.6471092 -.3875168
--------------+----------------------------------------------------------------
low | (base outcome)
-------------------------------------------------------------------------------
// separate logits:
. logit high i.race i.collgrad , nolog
Logistic regression Number of obs = 1465
LR chi2(3) = 154.21
Prob > chi2 = 0.0000
Log likelihood = -906.79453 Pseudo R2 = 0.0784
-------------------------------------------------------------------------------
high | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------+----------------------------------------------------------------
race |
black | -.5309439 .1463507 -3.63 0.000 -.817786 -.2441017
other | .2670161 .5116686 0.52 0.602 -.735836 1.269868
|
collgrad |
college grad | 1.525834 .1347081 11.33 0.000 1.261811 1.789857
_cons | -.6808361 .0694323 -9.81 0.000 -.816921 -.5447512
-------------------------------------------------------------------------------
. logit middle i.race i.collgrad , nolog
Logistic regression Number of obs = 1656
LR chi2(3) = 90.13
Prob > chi2 = 0.0000
Log likelihood = -1098.9988 Pseudo R2 = 0.0394
-------------------------------------------------------------------------------
middle | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------+----------------------------------------------------------------
race |
black | .6942945 .1114418 6.23 0.000 .4758725 .9127164
other | .3492788 .5125802 0.68 0.496 -.6553598 1.353918
|
collgrad |
college grad | .9979952 .1341664 7.44 0.000 .7350339 1.260957
_cons | -.5287625 .0669093 -7.90 0.000 -.6599023 -.3976226
-------------------------------------------------------------------------------