Plotting marginal effects from a multinomial logit model

[Luis Ortiz]

Dear members of the list,

I am trying to plot the marginal effects from a multinomial logit model. For this purpose, I am following the nice guidance provided by Benn Jann in the following resource, available on-line:

https://www.stata.com/meeting/german.../de13_jann.pdf

As prescribed in slides 60/62, I am running a very simple multinomial logit model. The dependent variable is educational attainment (educa_3bis) and has three categories. There is a single independent variable (father's education) and it has three categories as well. The name of the variable is educafth. My ultimate goal is to plot the marginal effect of each category of the independent variable for the three possible outcomes.

. mlogit educa_3bis i.edufath if cntryid!=826

Iteration 0:   log likelihood = -98507.417  
Iteration 1:   log likelihood = -94413.377  
Iteration 2:   log likelihood = -94177.934  
Iteration 3:   log likelihood = -94177.302  
Iteration 4:   log likelihood = -94177.302  

Multinomial logistic regression                 Number of obs     =    140,495
                                                LR chi2(4)        =    8660.23
                                                Prob > chi2       =     0.0000
Log likelihood = -94177.302                     Pseudo R2         =     0.0440

-----------------------------------------------------------------------------------------------------
                         educa_3bis |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
------------------------------------+----------------------------------------------------------------
Less_than_university                |  (base outcome)
------------------------------------+----------------------------------------------------------------
Tertiary_BA                         |
                          edufather |
ISCED 3 (excluding 3C short) and 4  |   .4809713   .0199718    24.08   0.000     .4418274    .5201153
                     ISCED 5 and 6  |    1.31509   .0213543    61.58   0.000     1.273236    1.356943
                                    |
                              _cons |  -2.326141   .0148464  -156.68   0.000    -2.355239   -2.297042
------------------------------------+----------------------------------------------------------------
Tertiary_MA                         |
                          edufather |
ISCED 3 (excluding 3C short) and 4  |   .8095096    .022792    35.52   0.000     .7648382     .854181
                     ISCED 5 and 6  |   1.788769   .0235119    76.08   0.000     1.742686    1.834852
                                    |
                              _cons |  -2.748311   .0180525  -152.24   0.000    -2.783693   -2.712929
-----------------------------------------------------------------------------------------------------

After that, and following Benn Jann's guidelines, I proceed as follows:

estimates store educa

quietly margins, dydx(edufath) predict(outcome(1)) post
estimates store basic
estimates restore educa

quietly margins, dydx(edufath) predict(outcome(2)) post
estimates store middle
estimates restore educa

quietly margins, dydx(edufath) predict(outcome(3)) post
estimates store high 

My next step would be to use the command regplot. I try to use reproducing Benn Jann's example in slide 62 of the PDF (presentation) posted above:

regplot basic middle low, legend(row(1)) xline(0) title(AMEs with 95% CIs) 

Yet, I obtain the next error message:

. regplot basic middle low, legend(row(1)) xline(0) title(AMEs with 95% CIs)
variable basic not found

I cannot understand what I did wrong in reproducing Benn Jann's example.

My ultimate goal would be actually to get the contrast of the average marginal effect of subsequent categories of the independent variable for the different outcomes in the dependent variable. For instance, to assess if the contrast between the average marginal effect of father's higher education and father's middle education is higher for one given outcome (Tertiary MA) than for another one (Tertiary BA). I would like to get these estimates (contrasts of AMEs) and to plot them. I know the command contrast is very useful in this regard, but I do not know how to get this sort of "contrast of contrasts".

But I guess this is a matter of another post.

At any rate, thanks a lot for your attention

Kind regards

Luis Ortiz

[John Mullahy]

Luis: For your first question it may be more efficient to use marginsplot. For instance, consider this example

preserve
capture drop _all
set obs 1000
gen y=floor(3*runiform())
gen x=floor(4*runiform())
mlogit y i.x
margins, dydx(x)
marginsplot
restore

Does this give the kind of result you are trying to obtain?

I'm not sure of the best way to approach your second question ("contrast of contrasts"), however. If you use margins...post then the AMEs are returned in e(b) and you could then manually difference the relevant elements of e(b) to obtain and plot those contrasts. But there is almost certainly a more efficient way to do this.