Getting listcoef to display marginal effects for cross categorical comparison after mlogit

[Annina Hittmeyer]

Hello everyone,

I'm working with a multinomial logit model with three possible outcomes and clustered standard errors. My goal is to obtain the marginal effects at mean for a cross categorical comparison. After running mlogit, I used mchange, atmeans from the SPost13 package to obtain the marginal effects at mean. I thought subsequently running listcoef , help pvalue(.1) would give me the cross categorical comparison with the coefficients of the MEMs. Apparently I was wrong. listcoef , help pvalue(.1) just displays the cross categorical comparison from the mlogit using it's coefficients and not the MEM ones. Any ideas on how to get a cross categorcial comparison including the MEMs?

[Richard Williams]

Does margins, pwcompare give you what you want? For example

webuse nhanes2f, clear
quietly mlogit health weight age height
margins
margins, pwcompare

. margins

Predictive margins                              Number of obs     =     10,335
Model VCE    : OIM

1._predict   : Pr(health==poor), predict(pr outcome(1))
2._predict   : Pr(health==fair), predict(pr outcome(2))
3._predict   : Pr(health==average), predict(pr outcome(3))
4._predict   : Pr(health==good), predict(pr outcome(4))
5._predict   : Pr(health==excellent), predict(pr outcome(5))

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    _predict |
          1  |    .070537   .0024645    28.62   0.000     .0657067    .0753674
          2  |   .1615868   .0035162    45.95   0.000     .1546951    .1684785
          3  |   .2842767   .0044195    64.32   0.000     .2756147    .2929388
          4  |   .2507015   .0042205    59.40   0.000     .2424295    .2589735
          5  |   .2328979   .0040155    58.00   0.000     .2250276    .2407682
------------------------------------------------------------------------------

. margins, pwcompare

Pairwise comparisons of predictive margins
Model VCE    : OIM

1._predict   : Pr(health==poor), predict(pr outcome(1))
2._predict   : Pr(health==fair), predict(pr outcome(2))
3._predict   : Pr(health==average), predict(pr outcome(3))
4._predict   : Pr(health==good), predict(pr outcome(4))
5._predict   : Pr(health==excellent), predict(pr outcome(5))

--------------------------------------------------------------
             |            Delta-method         Unadjusted
             |   Contrast   Std. Err.     [95% Conf. Interval]
-------------+------------------------------------------------
    _predict |
     2 vs 1  |   .0910498    .004636      .0819633    .1001363
     3 vs 1  |   .2137397   .0054505      .2030569    .2244225
     4 vs 1  |   .1801645   .0051669      .1700375    .1902914
     5 vs 1  |   .1623609   .0049374      .1526838     .172038
     3 vs 2  |   .1226899   .0064246      .1100979    .1352818
     4 vs 2  |   .0891147    .006082      .0771942    .1010351
     5 vs 2  |   .0713111   .0058282      .0598881    .0827341
     4 vs 3  |  -.0335752   .0071302     -.0475502   -.0196002
     5 vs 3  |  -.0513788   .0069096     -.0649215   -.0378362
     5 vs 4  |  -.0178036   .0068148     -.0311603   -.0044468
--------------------------------------------------------------

[Annina Hittmeyer]

Dear Richard,

thank you for your suggestion. However, I am afraid that this is not exactly what I am after. I'm interested in getting listcoef, help pvalue(.01) to display the MEM instead of the coeffients of the mlogit which it does now (or to do something else to enable cross-categorical comparisons using the MEMs).

. webuse nhanes2f, clear

.
. mlogit health weight age height

Iteration 0:   log likelihood = -15764.397 
Iteration 1:   log likelihood = -14948.196 
Iteration 2:   log likelihood = -14908.508 
Iteration 3:   log likelihood =  -14908.18 
Iteration 4:   log likelihood = -14908.179 

Multinomial logistic regression                 Number of obs     =     10,335
                                                LR chi2(12)       =    1712.44
                                                Prob > chi2       =     0.0000
Log likelihood = -14908.179                     Pseudo R2         =     0.0543

------------------------------------------------------------------------------
      health |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
poor         |
      weight |   .0050543    .003102     1.63   0.103    -.0010255     .011134
         age |   .0496011    .003269    15.17   0.000     .0431939    .0560082
      height |   .0043417   .0050761     0.86   0.392    -.0056073    .0142907
       _cons |  -5.217091   .8226843    -6.34   0.000    -6.829523   -3.604659
-------------+----------------------------------------------------------------
fair         |
      weight |   .0074132   .0022395     3.31   0.001     .0030238    .0118026
         age |   .0279478   .0020718    13.49   0.000     .0238873    .0320084
      height |  -.0110006   .0037503    -2.93   0.003     -.018351   -.0036502
       _cons |  -.7533259   .5979496    -1.26   0.208    -1.925286    .4186337
-------------+----------------------------------------------------------------
average      |  (base outcome)
-------------+----------------------------------------------------------------
good         |
      weight |  -.0053888    .002043    -2.64   0.008     -.009393   -.0013847
         age |  -.0181946   .0016593   -10.97   0.000    -.0214466   -.0149425
      height |   .0163555   .0033477     4.89   0.000     .0097941    .0229169
       _cons |  -1.636976   .5244043    -3.12   0.002    -2.664789   -.6091622
-------------+----------------------------------------------------------------
excellent    |
      weight |  -.0135704   .0021938    -6.19   0.000    -.0178702   -.0092705
         age |  -.0283615   .0017416   -16.28   0.000    -.0317749   -.0249481
      height |   .0357709   .0035283    10.14   0.000     .0288555    .0426863
       _cons |  -3.984935   .5485795    -7.26   0.000    -5.060131   -2.909739
------------------------------------------------------------------------------

.
. mchange, atmeans

mlogit: Changes in Pr(y) | Number of obs = 10335

Expression: Pr(health), predict(outcome())

             |      poor       fair    average       good  excellent
-------------+-------------------------------------------------------
weight       |                                                      
          +1 |     0.000      0.002      0.001     -0.001     -0.002
     p-value |     0.003      0.000      0.006      0.075      0.000
         +SD |     0.007      0.025      0.013     -0.011     -0.034
     p-value |     0.007      0.000      0.015      0.039      0.000
    Marginal |     0.000      0.002      0.001     -0.001     -0.002
     p-value |     0.003      0.000      0.006      0.078      0.000
age          |                                                      
          +1 |     0.003      0.005      0.001     -0.004     -0.005
     p-value |     0.000      0.000      0.000      0.000      0.000
         +SD |     0.071      0.090     -0.001     -0.072     -0.088
     p-value |     0.000      0.000      0.818      0.000      0.000
    Marginal |     0.003      0.005      0.001     -0.004     -0.005
     p-value |     0.000      0.000      0.000      0.000      0.000
height       |                                                      
          +1 |    -0.000     -0.003     -0.003      0.001      0.006
     p-value |     0.130      0.000      0.000      0.012      0.000
         +SD |    -0.004     -0.030     -0.034      0.011      0.057
     p-value |     0.070      0.000      0.000      0.051      0.000
    Marginal |    -0.000     -0.003     -0.003      0.001      0.006
     p-value |     0.139      0.000      0.000      0.010      0.000

Predictions at base value

             |      poor       fair    average       good  excellent
-------------+-------------------------------------------------------
  Pr(y|base) |     0.053      0.148      0.308      0.266      0.225

Base values of regressors

             |    weight        age     height
-------------+---------------------------------
          at |      71.9       47.6        168

1: Estimates with margins option atmeans.

. listcoef, help pvalue(.01)

mlogit (N=10335): Factor change in the odds of health (P<0.01)

Variable: weight (sd=15.356)
------------------------------------------------------------------------------
                             |         b        z    P>|z|       e^b   e^bStdX
-----------------------------+------------------------------------------------
poor         vs good         |    0.0104    3.249    0.001     1.010     1.174
poor         vs excellent    |    0.0186    5.593    0.000     1.019     1.331
fair         vs average      |    0.0074    3.310    0.001     1.007     1.121
fair         vs good         |    0.0128    5.376    0.000     1.013     1.217
fair         vs excellent    |    0.0210    8.284    0.000     1.021     1.380
average      vs fair         |   -0.0074   -3.310    0.001     0.993     0.892
average      vs good         |    0.0054    2.638    0.008     1.005     1.086
average      vs excellent    |    0.0136    6.186    0.000     1.014     1.232
good         vs poor         |   -0.0104   -3.249    0.001     0.990     0.852
good         vs fair         |   -0.0128   -5.376    0.000     0.987     0.822
good         vs average      |   -0.0054   -2.638    0.008     0.995     0.921
good         vs excellent    |    0.0082    3.648    0.000     1.008     1.134
excellent    vs poor         |   -0.0186   -5.593    0.000     0.982     0.751
excellent    vs fair         |   -0.0210   -8.284    0.000     0.979     0.725
excellent    vs average      |   -0.0136   -6.186    0.000     0.987     0.812
excellent    vs good         |   -0.0082   -3.648    0.000     0.992     0.882
------------------------------------------------------------------------------

Variable: age (sd=17.218)
------------------------------------------------------------------------------
                             |         b        z    P>|z|       e^b   e^bStdX
-----------------------------+------------------------------------------------
poor         vs fair         |    0.0217    6.205    0.000     1.022     1.452
poor         vs average      |    0.0496   15.173    0.000     1.051     2.349
poor         vs good         |    0.0678   20.443    0.000     1.070     3.213
poor         vs excellent    |    0.0780   23.156    0.000     1.081     3.828
fair         vs poor         |   -0.0217   -6.205    0.000     0.979     0.689
fair         vs average      |    0.0279   13.490    0.000     1.028     1.618
fair         vs good         |    0.0461   21.612    0.000     1.047     2.213
fair         vs excellent    |    0.0563   25.488    0.000     1.058     2.637
average      vs poor         |   -0.0496  -15.173    0.000     0.952     0.426
average      vs fair         |   -0.0279  -13.490    0.000     0.972     0.618
average      vs good         |    0.0182   10.966    0.000     1.018     1.368
average      vs excellent    |    0.0284   16.285    0.000     1.029     1.630
good         vs poor         |   -0.0678  -20.443    0.000     0.934     0.311
good         vs fair         |   -0.0461  -21.612    0.000     0.955     0.452
good         vs average      |   -0.0182  -10.966    0.000     0.982     0.731
good         vs excellent    |    0.0102    5.739    0.000     1.010     1.191
excellent    vs poor         |   -0.0780  -23.156    0.000     0.925     0.261
excellent    vs fair         |   -0.0563  -25.488    0.000     0.945     0.379
excellent    vs average      |   -0.0284  -16.285    0.000     0.972     0.614
excellent    vs good         |   -0.0102   -5.739    0.000     0.990     0.839
------------------------------------------------------------------------------

Variable: height (sd=9.660)
------------------------------------------------------------------------------
                             |         b        z    P>|z|       e^b   e^bStdX
-----------------------------+------------------------------------------------
poor         vs fair         |    0.0153    2.863    0.004     1.015     1.160
poor         vs excellent    |   -0.0314   -5.829    0.000     0.969     0.738
fair         vs poor         |   -0.0153   -2.863    0.004     0.985     0.862
fair         vs average      |   -0.0110   -2.933    0.003     0.989     0.899
fair         vs good         |   -0.0274   -6.914    0.000     0.973     0.768
fair         vs excellent    |   -0.0468  -11.276    0.000     0.954     0.636
average      vs fair         |    0.0110    2.933    0.003     1.011     1.112
average      vs good         |   -0.0164   -4.886    0.000     0.984     0.854
average      vs excellent    |   -0.0358  -10.138    0.000     0.965     0.708
good         vs fair         |    0.0274    6.914    0.000     1.028     1.302
good         vs average      |    0.0164    4.886    0.000     1.016     1.171
good         vs excellent    |   -0.0194   -5.443    0.000     0.981     0.829
excellent    vs poor         |    0.0314    5.829    0.000     1.032     1.355
excellent    vs fair         |    0.0468   11.276    0.000     1.048     1.571
excellent    vs average      |    0.0358   10.138    0.000     1.036     1.413
excellent    vs good         |    0.0194    5.443    0.000     1.020     1.206
------------------------------------------------------------------------------
       b = raw coefficient
       z = z-score for test of b=0
   P>|z| = p-value for z-test
     e^b = exp(b) = factor change in odds for unit increase in X
 e^bStdX = exp(b*SD of X) = change in odds for SD increase in X

[Richard Williams]

I don't think listcoef will give you what you want. Is this closer to what you have in mind?

. margins, dydx(*) pwcompare(pveffects)

Pairwise comparisons of average marginal effects
Model VCE    : OIM

dy/dx w.r.t. : weight age height
1._predict   : Pr(health==poor), predict(pr outcome(1))
2._predict   : Pr(health==fair), predict(pr outcome(2))
3._predict   : Pr(health==average), predict(pr outcome(3))
4._predict   : Pr(health==good), predict(pr outcome(4))
5._predict   : Pr(health==excellent), predict(pr outcome(5))

-----------------------------------------------------
             |   Contrast Delta-method    Unadjusted
             |      dy/dx   Std. Err.      z    P>|z|
-------------+---------------------------------------
weight       |
    _predict |
     2 vs 1  |   .0010101   .0003346     3.02   0.003
     3 vs 1  |   .0003256   .0004018     0.81   0.418
     4 vs 1  |  -.0008809   .0003881    -2.27   0.023
     5 vs 1  |  -.0026114   .0003824    -6.83   0.000
     3 vs 2  |  -.0006845   .0004652    -1.47   0.141
     4 vs 2  |  -.0018911   .0004479    -4.22   0.000
     5 vs 2  |  -.0036215   .0004415    -8.20   0.000
     4 vs 3  |  -.0012066   .0005309    -2.27   0.023
     5 vs 3  |   -.002937   .0005301    -5.54   0.000
     5 vs 4  |  -.0017305   .0005337    -3.24   0.001
-------------+---------------------------------------
age          |
    _predict |
     2 vs 1  |   .0009758   .0003539     2.76   0.006
     3 vs 1  |  -.0026218    .000363    -7.22   0.000
     4 vs 1  |  -.0064774   .0003308   -19.58   0.000
     5 vs 1  |  -.0081566   .0003155   -25.86   0.000
     3 vs 2  |  -.0035975   .0003848    -9.35   0.000
     4 vs 2  |  -.0074532   .0003501   -21.29   0.000
     5 vs 2  |  -.0091324   .0003349   -27.27   0.000
     4 vs 3  |  -.0038556   .0003828   -10.07   0.000
     5 vs 3  |  -.0055349   .0003792   -14.60   0.000
     5 vs 4  |  -.0016793   .0003915    -4.29   0.000
-------------+---------------------------------------
height       |
    _predict |
     2 vs 1  |  -.0028687   .0005525    -5.19   0.000
     3 vs 1  |  -.0027395   .0006546    -4.19   0.000
     4 vs 1  |    .001218   .0006256     1.95   0.052
     5 vs 1  |   .0053611   .0006063     8.84   0.000
     3 vs 2  |   .0001293   .0007728     0.17   0.867
     4 vs 2  |   .0040868    .000734     5.57   0.000
     5 vs 2  |   .0082298   .0007107    11.58   0.000
     4 vs 3  |   .0039575   .0008635     4.58   0.000
     5 vs 3  |   .0081006   .0008465     9.57   0.000
     5 vs 4  |    .004143   .0008447     4.90   0.000
-----------------------------------------------------

.

[Annina Hittmeyer]

Yes, this is what I am after. Thank you!
I am just wondering about the changes in some of the levels of significance. For example for the height variable:

average      vs fair         |    0.0110    2.933    0.003     1.011     1.112

(obatained from the listcoef after mlogit) seems to be of significance while

3 vs 2  |   .0001293   .0007728     0.17   0.867

(obtained after margins, dydx(*) pwcompare(pveffects)) seems not be significant. Is this possible?

Also, I am wandering what the direction of interpretation is. Intuitivley I would assume something along the lines of: A one unit increase in terms weight increases the propability of beeing in fair instead of poor health by 0.1 %. It seems a bit strange to me that Stata displays 2 vs. 1 instead of 1 vs. 2.

[Annina Hittmeyer]

Thanks again for all your help.
Just to reiterate: I'm interested in obtaining something which would allow me to make a statement along the lines of: A one unit increase in terms of weight increases the propability of being in fair instead of poor health by 0.1 %, for each variable for each cross categorical comparison (if significant). I think I may have unnecessarily complicated the question on how to obtain this.

[Richard Williams]

For significance of original effects vs marginal effects you may want to see

http://www.statalist.org/forums/foru...s-significance

For interpreting marginal effects in general, I suggest

http://www3.nd.edu/~rwilliam/stats3/Margins01.pdf

http://www3.nd.edu/~rwilliam/stats3/Margins02.pdf

http://www3.nd.edu/~rwilliam/stats3/Margins03.pdf

[expert carlos]

hello
I would like to estimate a multinomial logit model, but stata put "Mata object '__000003' not found r(111)"
What that's mean?
Thank for helping me

[Annina Hittmeyer]

Hello again, I reviewed the information Richard provided on interpreting marginal effects and also consulted "Regression Models for Categorical Dependent Variables Using Stata" (Long&Freese, 2014).
However, I'm still not sure how to interpret the results obtained via the pwcompare command.
My goal was to obtain information similar to the one gained from using relative risk ratios, that is how variables affect the choice of one outcome compared with another outcome.
Does the pwcompare margins command provide that info? And if it does, does it make sense to use marginal effects in this context?
Long & Freese suggest using the mchange command to obtain information on the marginal effects and then using relative risk ratios to show the dynamics among the outcomes.