# st: RE: Prvalue after mlogit is returning probabilities <0 and >1

 From Art Maxwell <[email protected]> To [email protected] Subject st: RE: Prvalue after mlogit is returning probabilities <0 and >1 Date Thu, 14 Jan 2010 10:55:36 -0500

```This time with the first line...
Q: Why would the command prvalue after mlogit predict probabilities for some
of my outcomes that are less than zero and/or greater than 1?

I am using mlogit as follows:

. mlogit outcome time rterrain sumpop bofadj democ strat mtype_irtv mindep_t
mspeed_iA, b(3) nolog

Multinomial logistic regression                   Number of obs   =
193
LR chi2(27)     =
116.90
Prob > chi2     =
0.0000
Log likelihood = -153.72377                       Pseudo R2       =
0.2755

----------------------------------------------------------------------------
--
outcome |      Coef.   Std. Err.      z    P>|z|     [95% Conf.
Interval]
-------------+--------------------------------------------------------------
--
0            |
time |   .0196269   .0114223     1.72   0.086    -.0027605
.0420142
rterrain |   1.755239   1.478646     1.19   0.235    -1.142853
4.653332
sumpop |   3.55e-06   2.16e-06     1.64   0.100    -6.86e-07
7.79e-06
bofadj |   1.144988   1.629517     0.70   0.482    -2.048807
4.338783
democ |  -.0265406   .1154767    -0.23   0.818    -.2528708
.1997895
strat |  -2.127686   .7351234    -2.89   0.004    -3.568501
-.6868702
mtype_irtv |   .7123837   .5424878     1.31   0.189    -.3508729
1.77564
mindep_t |  -.5384454   .3762239    -1.43   0.152    -1.275831
.19894
mspeed_iA |   -.093531   .0632883    -1.48   0.139    -.2175737
.0305117
_cons |   4.748362   2.020012     2.35   0.019      .789211
8.707512
-------------+--------------------------------------------------------------
--
1            |
time |  -.0080828   .0165733    -0.49   0.626    -.0405658
.0244002
rterrain |   4.552035   1.818222     2.50   0.012     .9883868
8.115684
sumpop |   2.52e-06   2.31e-06     1.09   0.275    -2.00e-06
7.04e-06
bofadj |   4.579028   1.807127     2.53   0.011     1.037125
8.120931
democ |   .1167351   .1258467     0.93   0.354    -.1299199
.3633902
strat |  -4.886501   .9443589    -5.17   0.000     -6.73741
-3.035592
mtype_irtv |   1.450813   .6552834     2.21   0.027     .1664809
2.735145
mindep_t |  -1.315626   .5053572    -2.60   0.009    -2.306108
-.3251446
mspeed_iA |   -.212409   .0744667    -2.85   0.004    -.3583611
-.0664569
_cons |   7.557182   2.477052     3.05   0.002     2.702249
12.41211
-------------+--------------------------------------------------------------
--
2            |
time |   .0315131   .0147056     2.14   0.032     .0026906
.0603355
rterrain |    5.93971    2.33391     2.54   0.011     1.365329
10.51409
sumpop |   5.40e-06   2.34e-06     2.31   0.021     8.19e-07
9.98e-06
bofadj |   3.346192   2.015841     1.66   0.097    -.6047844
7.297168
democ |  -.0162111   .1568147    -0.10   0.918    -.3235622
.2911401
strat |  -2.664387   .9756863    -2.73   0.006    -4.576697
-.7520769
mtype_irtv |   .3681514   .8120946     0.45   0.650    -1.223525
1.959828
mindep_t |  -.5097898   .5677939    -0.90   0.369    -1.622645
.6030658
mspeed_iA |   -.109111    .086819    -1.26   0.209     -.279273
.0610511
_cons |   1.542303   2.761025     0.56   0.576    -3.869206
6.953812
----------------------------------------------------------------------------
--
(outcome==3 is the base outcome)

I next use prvalue to predict outcomes for specific values of particular
variables:

. prvalue, x(time=6 democ=8.7) rest(mean)

mlogit: Predictions for outcome

Confidence intervals by delta method

95% Conf. Interval
Pr(y=0|x):          0.4913   [ 0.2866,    0.6960]
Pr(y=1|x):          0.4034   [ 0.1863,    0.6205]
Pr(y=2|x):          0.0383   [-0.0211,    0.0977]
Pr(y=3|x):          0.0670   [-0.0256,    0.1596]

Q: Why would the predicted confidence intervals for outcomes 2 and 3 include
values that are less than zero?

The same model also returns predictions that are greater than 1:

. prvalue, x(mspeed_iA=2 democ=8.7) rest(mean)

mlogit: Predictions for outcome

Confidence intervals by delta method

95% Conf. Interval
Pr(y=0|x):          0.2107   [-0.0932,    0.5146]
Pr(y=1|x):          0.7579   [ 0.4253,    1.0904]
Pr(y=2|x):          0.0278   [-0.0541,    0.1096]
Pr(y=3|x):          0.0037   [-0.0082,    0.0156]

Q: Why would the predicted confidence interval for outcome 1 exceed 1? And
why would the confidence interval for the other outcomes include values that
are less than zero?

Art M.

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```