Predict most likely outcome using mlogit

[philippe le coent]

Hello,
I'm trying to predict the most likely outcome using an logit model depending on a set of binomial variables.

The mlogit model is:

mlogit choix2 vegetation_high irrig zone_nat zone_urb past_ag, b(4) rrr

Where choix2 takes value 1, 2 3 or 4.

The results are:

Iteration 0: log pseudolikelihood = -5397.4332
Iteration 1: log pseudolikelihood = -5304.7697
Iteration 2: log pseudolikelihood = -5304.4855
Iteration 3: log pseudolikelihood = -5304.4855

Multinomial logistic regression Number of obs = 4,008
Wald chi2(15) = 107.91
Prob > chi2 = 0.0000
Log pseudolikelihood = -5304.4855 Pseudo R2 = 0.0172

(Std. Err. adjusted for 334 clusters in id1)
---------------------------------------------------------------------------------
| Robust
choix2 | RRR Std. Err. z P>|z| [95% Conf. Interval]
----------------+----------------------------------------------------------------
1 |
vegetation_high | .7389016 .0804811 -2.78 0.005 .5968618 .9147438
irrig | 1.376595 .1505122 2.92 0.003 1.111063 1.705586
zone_nat | 1.06628 .1265931 0.54 0.589 .8449154 1.345642
zone_urb | 1.386156 .1758677 2.57 0.010 1.080977 1.777492
past_ag | 1.200294 .1165183 1.88 0.060 .9923328 1.451837
_cons | .8356073 .1297989 -1.16 0.248 .6162842 1.132983
----------------+----------------------------------------------------------------
2 |
vegetation_high | .6956982 .0664302 -3.80 0.000 .5769552 .8388796
irrig | 2.21371 .2282089 7.71 0.000 1.80872 2.709382
zone_nat | 1.145 .1144466 1.35 0.176 .9412932 1.392791
zone_urb | 1.418373 .1581533 3.13 0.002 1.139931 1.764827
past_ag | 1.152378 .1016185 1.61 0.108 .9694706 1.369794
_cons | 1.181396 .1665893 1.18 0.237 .8961224 1.557485
----------------+----------------------------------------------------------------
3 |
vegetation_high | .788454 .0778471 -2.41 0.016 .6497316 .9567946
irrig | .8747794 .0818569 -1.43 0.153 .7281954 1.05087
zone_nat | 1.054481 .1019148 0.55 0.583 .8725108 1.274403
zone_urb | 1.036925 .1151115 0.33 0.744 .834168 1.288966
past_ag | 1.054526 .0930386 0.60 0.547 .8870692 1.253594
_cons | 1.963311 .2560553 5.17 0.000 1.520461 2.535146
----------------+----------------------------------------------------------------
4 | (base outcome)
---------------------------------------------------------------------------------

In order to predict the most likely outcome can I estimate the "combined RRR" for each outcome based on the coefficients.

For example, in order to estimate a "combined RRR" for outcome 3 when all explanatory variables take value 1.
I can estimate a combined RRR=the product of all coefficients for outcome 3: 0.78*0.87*1.05*...*1.96
If I do this for each outcome, can I say that if all values of combined RRR are below 1, the most probable outcome is the base outcome (4) and otherwise the one with the highest combined RRR.

Is this wrong or should I used predicted probabilities for each outcome and each explanatory variables and make the same calculations.

[Rich Goldstein]

I don't understand the latter part of your text but I think getting what you want is easier; first, see

help mlogit postestimation##predict

to see how to get predicted probabilities for each outcome category; then use -egen- with the "rowmax" to find the highest probability for each unit; see

h egen

[Clyde Schechter]

You could do what you proposed. But it's a lot of unnecessary work for your purpose. You can get the predicted probabilities for each outcome level conditional on the specified values of the predictive variables from the -margins- command and compare those. Let your computer do the work for you! Along these lines:

sysuse auto, clear

mlogit rep78 price mpg headroom, rrr

margins, at(price = 4000 mpg = 20 headroom = 3)

The margins output gives you the predicted probability for each outcome at those values of price, mpg, and headroom.

Added: Crossed with #2.

[philippe le coent]

Thanks a lot to both of you. This is very helpful