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RE: st: Predicted probabilities after mlogit


From   Richard Williams <Richard.A.Williams.5@ND.edu>
To   statalist@hsphsun2.harvard.edu, <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Predicted probabilities after mlogit
Date   Mon, 05 Sep 2005 11:51:53 -0500

At 10:52 AM 9/5/2005, Little, Allan wrote:
3. I use the predict command as follows, and it suggest to me that the predicted probability is equivalent to the sample proportions (above) - e.g. a mean of 80.66 % is equivalent to the probability, 0.8066.

.predict p0 p1 p2 if e(sample)
(option pr assumed; predicted probabilities)

. su p0 p1 p2
Variable Obs Mean
p0 23877 .806634
p1 23877 .0422582
p2 23877 .1511078


4. However, using the prvalue command, the 'predicted probability' of employment is calculated to be higher (0.8764). I dont understand why.

.prvalue
mlogit: Predictions for euivar
Predicted probabilities for each category:
Pr(y=unemployx): 0.0295
Pr(y=inactivex): 0.0942
Pr(y=employmex): 0.8764
OK, that helps. What prvalue does is plug in the predicted probabilities when all explanatory variables have a value equal to their means. This need not produce the same proportions as you see in the sample. i think you'll see this with just about any data set. I'm not sure how best to explain why, but I think the explanation would involve some discussion of the fact that nonlinear relationships are involved. Here is another example:

. use "http://www.nd.edu/~rwilliam/gologit2/ordwarm2.dta";
(77 & 89 General Social Survey)

. qui mlogit warm yr89 male white age ed prst

. tab warm if e(sample)

Mom can |
have warm |
relations |
with child | Freq. Percent Cum.
------------+-----------------------------------
SD | 297 12.95 12.95
D | 723 31.53 44.48
A | 856 37.33 81.81
SA | 417 18.19 100.00
------------+-----------------------------------
Total | 2,293 100.00

. predict p0 p1 p2 p3 if e(sample)
(option pr assumed; predicted probabilities)

. sum p0 p1 p2 p3

Variable | Obs Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
p0 | 2293 .1295246 .0811282 .0078837 .479314
p1 | 2293 .3153075 .0960695 .0805404 .6003724
p2 | 2293 .3733101 .0828089 .1300312 .5650222
p3 | 2293 .1818578 .0983226 .0199486 .516334

. prvalue

mlogit: Predictions for warm

Confidence intervals by delta method

95% Conf. Interval
Pr(y=SD|x): 0.1139 [ 0.0993, 0.1286]
Pr(y=D|x): 0.3254 [ 0.3049, 0.3459]
Pr(y=SA|x): 0.1664 [ 0.1495, 0.1834]
Pr(y=A|x): 0.3942 [ 0.3728, 0.4156]

yr89 male white age ed prst
x= .39860445 .46489315 .8765809 44.935456 12.218055 39.585259



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Richard Williams, Notre Dame Dept of Sociology
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