RE: st: Predicted probabilities after mlogit

[Richard Williams <Richard.A.Williams.5@ND.edu>]

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



-------------------------------------------
Richard Williams, Notre Dame Dept of Sociology
OFFICE: (574)631-6668, (574)631-6463
FAX:    (574)288-4373
HOME:   (574)289-5227
EMAIL:  Richard.A.Williams.5@ND.Edu
WWW (personal):    http://www.nd.edu/~rwilliam
WWW (department):    http://www.nd.edu/~soc 
*
*   For searches and help try:
*   http://www.stata.com/support/faqs/res/findit.html
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/