Dengan model logit multinomial Anda memaksakan kendala yang ditambahkan oleh semua probabilitas yang diprediksi hingga 1. Ketika Anda menggunakan model logit biner yang terpisah, Anda tidak lagi dapat memaksakan kendala itu, mereka diperkirakan dalam model terpisah. Jadi itu akan menjadi perbedaan utama antara kedua model ini.
Seperti yang Anda lihat pada contoh di bawah ini (Di Stata, karena itu adalah program yang saya tahu paling baik), modelnya cenderung serupa tetapi tidak sama. Saya akan sangat berhati-hati tentang memperkirakan probabilitas yang diprediksi.
// 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
-------------------------------------------------------------------------------
