Multinomial logit model: coefficients and marginal effects p-value

[Vivian Phan]

Dear all,

my question is in this post already.
http://www.statalist.org/forums/foru...1362586-mlogit

But as a suggestion of Carlo Lazzaro I start a new thread. I am really sorry for this inconvenience.

I have a problem with Multinomial Logit model.

After mlogit command, I got coefficients and p-value also. (1)
And then after margins command with dydx option, I got dy/dx and p-value. (2)

But p-value between (1) & (2) is different. I mean that some variables seems to be significant at 1% in terms of (1) but not significant at 10% in terms of (2).
Which p-value should I consider?

[Carlo Lazzaro]

Vivian:
thanks for starting a new thread.
However, set aside some guess-work, I find difficult to reply positively without taking a look at what you typed and what Stata gave you back (as reminded by the FAQ). Thanks.

[Vivian Phan]

Please refer to my stata result.

First, I run mlogit

mlogit empstatus age agesq i.eduColabove i.eduVoc i.eduUpperSe i.eduLowerSe i.eduPri i.eduMissing i.georegion if female==0, b(4)

Iteration 0:   log likelihood = -2192.2608  
Iteration 1:   log likelihood = -1944.7985  
Iteration 2:   log likelihood = -1900.3097  
Iteration 3:   log likelihood = -1898.2383  
Iteration 4:   log likelihood =  -1898.186  
Iteration 5:   log likelihood =  -1898.186  

Multinomial logistic regression                   Number of obs   =       2098
                                                  LR chi2(39)     =     588.15
                                                  Prob > chi2     =     0.0000
Log likelihood =  -1898.186                       Pseudo R2       =     0.1341

-------------------------------------------------------------------------------
    empstatus |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
1             |
          age |   .6349135   .0829887     7.65   0.000     .4722587    .7975683
        agesq |  -.8096193   .1088989    -7.43   0.000    -1.023057   -.5961813
1.eduColabove |   1.176517    .383472     3.07   0.002      .424926    1.928108
     1.eduVoc |   1.314357   .4163629     3.16   0.002     .4983011    2.130414
 1.eduUpperSe |  -.4251786   .3707952    -1.15   0.252    -1.151924    .3015667
 1.eduLowerSe |   .3525474   .3915664     0.90   0.368    -.4149087    1.120004
     1.eduPri |   .0882141   .3913071     0.23   0.822    -.6787337    .8551618
 1.eduMissing |  -.9270267   .5954786    -1.56   0.120    -2.094143      .24009
              |
    georegion |
           2  |  -.4161115    .335425    -1.24   0.215    -1.073532    .2413093
           3  |  -.1767313   .2737416    -0.65   0.519    -.7132549    .3597924
           4  |  -.2874983   .4000771    -0.72   0.472    -1.071635    .4966384
           5  |    .068221   .2817976     0.24   0.809    -.4840922    .6205342
           6  |   .1658998   .3217105     0.52   0.606    -.4646412    .7964408
              |
        _cons |  -9.901457   1.534569    -6.45   0.000    -12.90916   -6.893756
--------------+----------------------------------------------------------------
2             |
          age |   .5240457   .1134374     4.62   0.000     .3017125    .7463789
        agesq |  -.6108449   .1460393    -4.18   0.000    -.8970767   -.3246132
1.eduColabove |  -2.949208   .7161136    -4.12   0.000    -4.352765   -1.545652
     1.eduVoc |   -.846245   .5206113    -1.63   0.104    -1.866624    .1741344
 1.eduUpperSe |  -1.208182   .4556197    -2.65   0.008     -2.10118   -.3151842
 1.eduLowerSe |     .10055   .4439979     0.23   0.821    -.7696698    .9707699
     1.eduPri |   .1733305   .4398401     0.39   0.694    -.6887402    1.035401
 1.eduMissing |  -2.797139   1.158914    -2.41   0.016    -5.068569    -.525708
              |
    georegion |
           2  |   .0022765   .4280674     0.01   0.996    -.8367201    .8412731
           3  |   -.503817   .3687728    -1.37   0.172    -1.226598    .2189644
           4  |   .9608885   .4549927     2.11   0.035     .0691192    1.852658
           5  |  -1.234734   .4129959    -2.99   0.003    -2.044192   -.4252774
           6  |  -.0131681   .4009658    -0.03   0.974    -.7990467    .7727104
              |
        _cons |  -9.599534   2.149131    -4.47   0.000    -13.81175   -5.387314
--------------+----------------------------------------------------------------
3             |
          age |   .7071444   .0936897     7.55   0.000     .5235159    .8907728
        agesq |  -.8440346   .1212804    -6.96   0.000     -1.08174   -.6063293
1.eduColabove |  -.1345583   .4597233    -0.29   0.770    -1.035599    .7664827
     1.eduVoc |   1.400845   .4671221     3.00   0.003     .4853028    2.316388
 1.eduUpperSe |   .4280042   .4238992     1.01   0.313     -.402823    1.258831
 1.eduLowerSe |   1.219725   .4392012     2.78   0.005     .3589067    2.080544
     1.eduPri |   .6497277   .4430752     1.47   0.143    -.2186837    1.518139
 1.eduMissing |  -.5719237   .6933842    -0.82   0.409    -1.930932    .7870844
              |
    georegion |
           2  |  -.4454329   .3622749    -1.23   0.219    -1.155479     .264613
           3  |  -.4721475   .2980677    -1.58   0.113    -1.056349    .1120545
           4  |  -.4089055   .4328618    -0.94   0.345    -1.257299    .4394879
           5  |  -.3283888   .3041755    -1.08   0.280    -.9245618    .2677842
           6  |  -.1416735   .3456094    -0.41   0.682    -.8190555    .5357084
              |
        _cons |  -13.16255   1.773584    -7.42   0.000    -16.63871   -9.686389
--------------+----------------------------------------------------------------
4             |  (base outcome)
-------------------------------------------------------------------------------

Second, I run margins

 margins, dydx(*) pr(outcome(1))

Average marginal effects                          Number of obs   =       2098
Model VCE    : OIM

Expression   : Pr(empstatus==1), predict(outcome(1))
dy/dx w.r.t. : age agesq 1.eduColabove 1.eduVoc 1.eduUpperSe 1.eduLowerSe 1.eduPri 1.eduMissing 2.georegion
               3.georegion 4.georegion 5.georegion 6.georegion

-------------------------------------------------------------------------------
              |            Delta-method
              |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
          age |   .0233066   .0101433     2.30   0.022     .0034261    .0431871
        agesq |  -.0388327   .0129868    -2.99   0.003    -.0642863   -.0133791
1.eduColabove |   .3026316   .0378455     8.00   0.000     .2284558    .3768073
     1.eduVoc |   .0971604   .0467012     2.08   0.037     .0056278    .1886931
 1.eduUpperSe |    -.11273   .0513654    -2.19   0.028    -.2134044   -.0120556
 1.eduLowerSe |  -.0959462   .0488899    -1.96   0.050    -.1917686   -.0001237
     1.eduPri |  -.0720536   .0483095    -1.49   0.136    -.1667384    .0226312
 1.eduMissing |  -.0665242   .0923126    -0.72   0.471    -.2474536    .1144053
              |
    georegion |
           2  |   -.033324    .038527    -0.86   0.387    -.1088354    .0421875
           3  |   .0413392    .030908     1.34   0.181    -.0192393    .1019178
           4  |  -.0741591   .0424795    -1.75   0.081    -.1574174    .0090993
           5  |   .0922051   .0306146     3.01   0.003     .0322017    .1522086
           6  |   .0515696   .0339975     1.52   0.129    -.0150642    .1182035
-------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

Take eduVoc or eduUpperSe as example, you can see the difference in p-value. Which should I consider?

Many thanks

[Richard Williams]

There is nothing that says the p-values for the coefficients and marginal effects have to be similar. For a discussion, see

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

[Vivian Phan]

Thank you for all discussions.