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Occasionally, there might be a need for generating the predicted probabilities manually from a multinomial logistic regression. The code below generates the predicted probabilities using a little bit of matrix calculation.
use http://www.ats.ucla.edu/stat/data/stata/mlogit_demo_data, clear mlogit y write female math, nolog Multinomial logistic regression Number of obs = 200 LR chi2(9) = 31.76 Prob > chi2 = 0.0002 Log likelihood = -159.59108 Pseudo R2 = 0.0905 ------------------------------------------------------------------------------ y | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- 1 | write | -.0592852 .0313425 -1.89 0.059 -.1207155 .002145 female | .0253633 .5020617 0.05 0.960 -.9586595 1.009386 math | -.0525018 .0349184 -1.50 0.133 -.1209407 .0159371 _cons | 3.818145 1.534455 2.49 0.013 .8106693 6.825621 -------------+---------------------------------------------------------------- 2 | write | .0339394 .0554246 0.61 0.540 -.0746909 .1425697 female | .7612508 .7302687 1.04 0.297 -.6700495 2.192551 math | .0238891 .0448113 0.53 0.594 -.0639394 .1117177 _cons | -6.297374 2.5963 -2.43 0.015 -11.38603 -1.20872 -------------+---------------------------------------------------------------- 3 | write | -.0414901 .0347647 -1.19 0.233 -.1096276 .0266475 female | .6969475 .5588378 1.25 0.212 -.3983546 1.79225 math | -.0748394 .0388773 -1.93 0.054 -.1510375 .0013586 _cons | 3.471735 1.698489 2.04 0.041 .1427571 6.800713 ------------------------------------------------------------------------------ (y==4 is the base outcome) predict p1 p2 p3 p4, p list in 1/4 +-----------------------------------------------------------------------+ | y female math write p1 p2 p3 p4 | |-----------------------------------------------------------------------| 1. | 4 male 41 52 .1678438 .0198305 .1198363 .6924894 | 2. | 4 female 53 59 .0674177 .0798579 .081622 .7711025 | 3. | 4 male 54 33 .2449829 .0132924 .0932966 .6484281 | 4. | 4 male 47 44 .1942302 .017215 .105188 .6833668 | +-----------------------------------------------------------------------+ mat a = e(b) mat list a a[1,12] 1: 1: 1: 1: 2: 2: 2: 2: write female math _cons write female math _cons y1 -.05928522 .02536326 -.05250177 3.8181451 .03393942 .76125081 .02388913 -6.2973737 3: 3: 3: 3: write female math _cons y1 -.04149009 .69694747 -.07483944 3.471735 preserve clear input y female math cons 52 0 41 1 59 1 53 1 end* converting everything to matrices mkmat y female math cons, mat(X) mat a1 = a[1, "1:"] mat a2 = a[1, "2:"] mat a3 = a[1, "3:"] mat biga = (a1 \ a2 \a3)' mat list biga biga[4,3] y1 y1 y1 1:write -.05928522 .03393942 -.04149009 1:female .02536326 .76125081 .69694747 1:math -.05250177 .02388913 -.07483944 1:_cons 3.8181451 -6.2973737 3.471735 mat xb = X*biga mat list xb xb[2,3] y1 y1 y1 r1 -1.4172591 -3.5530693 -1.7541665 r2 -2.4369136 -2.267573 -2.2457229* converting back to data svmat xb gen denom = 1+exp(xb1) + exp(xb2) + exp(xb3) gen p1 = exp(xb1)/denom gen p2 = exp(xb2)/denom gen p3 = exp(xb3)/denom list p1 p2 p3 +--------------------------------+ | p1 p2 p3 | |--------------------------------| 1. | .1678438 .0198305 .1198363 | 2. | .0674177 .0798579 .081622 | +--------------------------------+ restore
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