Plot of melogit model

[Man Yang]

Hello all, I am running a single level logit model cluster at kindergarten level. Below is the model output.

 logit gedtimehi c.grade##c.grade ib6.RACE ib6.RACE#c.grade ib6.RACE#c.grade#c.grade, cluster(kinde
> rgarten)

Iteration 0:   log pseudolikelihood =  -6318.348  
Iteration 1:   log pseudolikelihood =  -6219.052  
Iteration 2:   log pseudolikelihood = -6218.0061  
Iteration 3:   log pseudolikelihood = -6218.0061  

Logistic regression                               Number of obs   =      11088
                                                  Wald chi2(11)   =      76.81
                                                  Prob > chi2     =     0.0000
Log pseudolikelihood = -6218.0061                 Pseudo R2       =     0.0159

                                        (Std. Err. adjusted for 41 clusters in kindergarten)
--------------------------------------------------------------------------------------------
                           |               Robust
                 gedtimehi |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------------------+----------------------------------------------------------------
                  gradelvl |   .1603621   .0765065     2.10   0.036     .0104121     .310312
                           |
     c.gradelvl#c.gradelvl |  -.0272459   .0092321    -2.95   0.003    -.0453405   -.0091512
                           |
                      RACE |
         African American  |  -.4808764   .1205788    -3.99   0.000    -.7172065   -.2445462
                    Asian  |  -.2261637   .1346057    -1.68   0.093    -.4899861    .0376587
                 Hispanic  |   .0902261   .1429301     0.63   0.528    -.1899117     .370364
                           |
           RACE#c.gradelvl |
         African American  |  -.0361761   .0762349    -0.47   0.635    -.1855937    .1132415
                    Asian  |   .1960031   .1015358     1.93   0.054    -.0030035    .3950097
                 Hispanic  |  -.0600909   .0959935    -0.63   0.531    -.2482346    .1280528
                           |
RACE#c.gradelvl#c.gradelvl |
         African American  |   .0081719   .0094204     0.87   0.386    -.0102918    .0266357
                    Asian  |    -.02058   .0134071    -1.54   0.125    -.0468575    .0056974
                 Hispanic  |   .0001009    .012092     0.01   0.993    -.0235989    .0238007
                           |
                     _cons |   1.156505    .157408     7.35   0.000     .8479907    1.465019
--------------------------------------------------------------------------------------------

Based from the model results, it seems none of the interaction terms is significant. So, I suppose the plot by racial groups generated based on the model should have parallel lines.

Below is the plot I generated using margins and marginsplot.

. margins RACE, at(grade=(0(1)9))

Adjusted predictions                              Number of obs   =      11088
Model VCE    : Robust

Expression   : Pr(gedtimehi), predict()

1._at        : gradelvl        =           0

2._at        : gradelvl        =           1

3._at        : gradelvl        =           2

4._at        : gradelvl        =           3

5._at        : gradelvl        =           4

6._at        : gradelvl        =           5

7._at        : gradelvl        =           6

8._at        : gradelvl        =           7

9._at        : gradelvl        =           8

10._at       : gradelvl        =           9

--------------------------------------------------------------------------------------
                     |            Delta-method
                     |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------------+----------------------------------------------------------------
            _at#RACE |
 1#African American  |   .6627623   .0450391    14.72   0.000     .5744873    .7510373
            1#Asian  |   .7171445   .0382939    18.73   0.000     .6420897    .7921992
         1#Hispanic  |   .7767334   .0330955    23.47   0.000     .7118675    .8415994
            1#White  |    .760697   .0286541    26.55   0.000      .704536     .816858
 2#African American  |   .6858397    .035863    19.12   0.000     .6155494    .7561299
            2#Asian  |   .7753691   .0274055    28.29   0.000     .7216552    .8290829
         2#Hispanic  |   .7891579   .0260394    30.31   0.000     .7381217    .8401942
            2#White  |    .784083   .0215603    36.37   0.000     .7418256    .8263405
 3#African American  |   .7000854   .0304276    23.01   0.000     .6404483    .7597225
            3#Asian  |   .8102704   .0224043    36.17   0.000     .7663588     .854182
         3#Hispanic  |    .792275   .0227092    34.89   0.000     .7477658    .8367842
            3#White  |   .7970965   .0197392    40.38   0.000     .7584084    .8357846
 4#African American  |   .7061007     .02703    26.12   0.000     .6531229    .7590786
            4#Asian  |   .8276415   .0201961    40.98   0.000      .788058     .867225
         4#Hispanic  |   .7863797     .02188    35.94   0.000     .7434958    .8292637
            4#White  |   .8009716   .0201024    39.84   0.000     .7615715    .8403717
 5#African American  |   .7041605    .024499    28.74   0.000     .6561433    .7521777
            5#Asian  |   .8306987   .0193026    43.04   0.000     .7928664    .8685311
         5#Hispanic  |    .770917   .0227636    33.87   0.000     .7263012    .8155328
            5#White  |   .7960876   .0207723    38.32   0.000     .7553746    .8368007
 6#African American  |   .6941747   .0228595    30.37   0.000     .6493708    .7389786
            6#Asian  |   .8200254   .0197917    41.43   0.000     .7812345    .8588163
         6#Hispanic  |   .7444948    .025372    29.34   0.000     .6947667    .7942229
            6#White  |   .7819674   .0212253    36.84   0.000     .7403665    .8235683
 7#African American  |   .6757004   .0240232    28.13   0.000     .6286159     .722785
            7#Asian  |    .793606   .0234798    33.80   0.000     .7475864    .8396255
         7#Hispanic  |   .7049829   .0306699    22.99   0.000     .6448709    .7650948
            7#White  |   .7572802   .0221361    34.21   0.000     .7138943    .8006661
 8#African American  |   .6480108   .0311325    20.81   0.000     .5869922    .7090294
            8#Asian  |   .7467642   .0339852    21.97   0.000     .6801545     .813374
         8#Hispanic  |   .6498835   .0401807    16.17   0.000     .5711308    .7286362
            8#White  |   .7199052   .0260306    27.66   0.000     .6688862    .7709242
 9#African American  |   .6102549   .0455753    13.39   0.000     .5209289    .6995809
            9#Asian  |   .6726963   .0546883    12.30   0.000     .5655092    .7798833
         9#Hispanic  |   .5772817   .0547091    10.55   0.000     .4700537    .6845096
            9#White  |    .667226   .0366886    18.19   0.000     .5953177    .7391344
10#African American  |   .5617611   .0666693     8.43   0.000     .4310916    .6924306
           10#Asian  |   .5655531   .0850815     6.65   0.000     .3987964    .7323098
        10#Hispanic  |   .4876104   .0726647     6.71   0.000     .3451903    .6300306
           10#White  |    .596968   .0557985    10.70   0.000      .487605    .7063311
--------------------------------------------------------------------------------------

. marginsplot, noci recast(line)

Is the plot correct based on the model result? Shouldn't the lines be parallel instead of crossing over? Is it always the case that if no interaction effects is significant, the lines should not cross each other?

[Joseph Coveney]

An interaction term is not necessarily negligible even if a test fails to reject the null hypothesis that its components are jointly equal to zero.

Also, the marginal proportions are nonlinear; if you want to see how far the lines deviate from parallel, then plot the linear predictions

margins RACE, at(grade=(0(1)9)) predict(xb)

[Man Yang]

Hi Joseph, thanks for your reply. I tried the code you provided below

. margins RACE, at(grade=(0(1)9)) predict(xb)

Adjusted predictions                              Number of obs   =      11088
Model VCE    : Robust

Expression   : Linear prediction (log odds), predict(xb)

1._at        : gradelvl        =           0

2._at        : gradelvl        =           1

3._at        : gradelvl        =           2

4._at        : gradelvl        =           3

5._at        : gradelvl        =           4

6._at        : gradelvl        =           5

7._at        : gradelvl        =           6

8._at        : gradelvl        =           7

9._at        : gradelvl        =           8

10._at       : gradelvl        =           9

--------------------------------------------------------------------------------------
                     |            Delta-method
                     |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------------+----------------------------------------------------------------
            _at#RACE |
 1#African American  |   .6756283   .2015097     3.35   0.001     .2806767     1.07058
            1#Asian  |    .930341   .1887812     4.93   0.000     .5603366    1.300345
         1#Hispanic  |   1.246731   .1908416     6.53   0.000     .8726881    1.620773
            1#White  |   1.156505    .157408     7.35   0.000     .8479907    1.465019
 2#African American  |   .7807404   .1664459     4.69   0.000     .4545124    1.106968
            2#Asian  |    1.23888   .1573476     7.87   0.000     .9304847    1.547276
         2#Hispanic  |   1.319857   .1564982     8.43   0.000     1.013126    1.626588
            2#White  |   1.289621   .1273522    10.13   0.000     1.040015    1.539227
 3#African American  |   .8477045   .1449171     5.85   0.000     .5636722    1.131737
            3#Asian  |   1.451768   .1457357     9.96   0.000     1.166131    1.737405
         3#Hispanic  |   1.338693   .1379867     9.70   0.000     1.068244    1.609142
            3#White  |   1.368245   .1220476    11.21   0.000     1.129036    1.607454
 4#African American  |   .8765207    .130251     6.73   0.000     .6212335    1.131808
            4#Asian  |   1.569004   .1415766    11.08   0.000     1.291518    1.846489
         4#Hispanic  |    1.30324   .1302483    10.01   0.000     1.047958    1.558522
            4#White  |   1.392378   .1261005    11.04   0.000     1.145226     1.63953
 5#African American  |   .8671891   .1176037     7.37   0.000     .6366901    1.097688
            5#Asian  |   1.590587   .1372496    11.59   0.000     1.321583    1.859592
         5#Hispanic  |   1.213496   .1288962     9.41   0.000     .9608646    1.466128
            5#White  |   1.362019   .1279619    10.64   0.000     1.111218     1.61282
 6#African American  |   .8197095   .1076776     7.61   0.000     .6086654    1.030754
            6#Asian  |    1.51652   .1341046    11.31   0.000     1.253679     1.77936
         6#Hispanic  |   1.069463   .1333806     8.02   0.000     .8080421    1.330884
            6#White  |   1.277168   .1244929    10.26   0.000     1.033167     1.52117
 7#African American  |   .7340821     .10963     6.70   0.000     .5192112     .948953
            7#Asian  |     1.3468   .1433483     9.40   0.000     1.065843    1.627757
         7#Hispanic  |   .8711401   .1474643     5.91   0.000     .5821153    1.160165
            7#White  |   1.137826   .1204311     9.45   0.000     .9017851    1.373866
 8#African American  |   .6103068   .1364905     4.47   0.000     .3427903    .8778233
            8#Asian  |   1.081429   .1797136     6.02   0.000     .7291964    1.433661
         8#Hispanic  |   .6185272   .1765913     3.50   0.000     .2724147    .9646396
            8#White  |   .9439914   .1290932     7.31   0.000     .6909735    1.197009
 9#African American  |   .4483837   .1916187     2.34   0.019      .072818    .8239493
            9#Asian  |   .7204054   .2483844     2.90   0.004     .2335809     1.20723
         9#Hispanic  |   .3116243   .2241925     1.39   0.165    -.1277849    .7510335
            9#White  |   .6956654   .1652376     4.21   0.000     .3718056    1.019525
10#African American  |   .2483126   .2708093     0.92   0.359    -.2824639    .7790891
           10#Asian  |   .2637304   .3462782     0.76   0.446    -.4149624    .9424232
        10#Hispanic  |  -.0495684   .2908372    -0.17   0.865    -.6195988    .5204621
           10#White  |   .3928477   .2319167     1.69   0.090    -.0617006     .847396
--------------------------------------------------------------------------------------

But the marginsplot I got is quite similar to what I got without using predict(xb). Are they supposed to be the same or different?

[Joseph Coveney]

Your model has a quadratic term c.gradelvl#c.gradelvl that your plotting over. That's why the plots are curved. The degree to which the curves share the same shape and location is what you're looking for in terms of assessing the interaction of grade and race.

[Man Yang]

Thanks Joseph, so can you tell me what is the difference between not adding predict(xb) versus adding it? I suppose predict(xb) is the linear prediction from the fitted model but what are the predictions without adding predict(xb)? Are there supposed to be a preference over which one I should plot?

[Joseph Coveney]

I suppose predict(xb) is the linear prediction from the fitted model but what are the predictions without adding predict(xb)?

You get the default prediction for the estimation command. In your case the proportions, Look at the y-axis title of the -marginsplot-. It tells you what it is. You can also find out from -help logit_postestimation- what the default is.

Are there supposed to be a preference over which one I should plot?

The choice depends upon the purpose. If you're trying to assess an interaction, then use the linear predictions. If you're trying to communicate the results to an audience that has trouble with log odds, then proportions might be helpful.

[Man Yang]

Thanks a lot for your answer!