Mchange after Mlogit

[Elin Vimefall]

Dear all

I'm running a multinominal logit and use the mchange command to estimate the average marginal effects.

Can someone help me understand why the mchange gives estimations of the marginal effect also for the "reference category" and how to interpret this?
I run:
mlogit div x1 x2 x3
Where div consist of 5 different strategies
I then run
mchange, stats(se pvalue) brief width(8)
Which reports the average marginal effect for all five strategies.

Can someone please help me understand this (or tell me were I can read more)?

//Elin

[Richard Williams]

Elin, a few suggestions for making your post more effective.

• Mention that mchange is part of the spost13 user-written package. Always be clear where user-written commands come from.
• Posting both code and output will make your question clearer.
• Use code tags. See point #12 of the FAQ.

I am not sure what your concern is. But I might if I saw what you are talking about.

If you want to read more on mchange and related commands, see

https://www3.nd.edu/~rwilliam/xsoc73994/Margins04.pdf

https://www3.nd.edu/~rwilliam/xsoc73994/Margins05.pdf

[Elin Vimefall]

Thank you Richard. I will try to make my post more effective.

I’m estimating the model
[mlogit div i.Fmono i.Fpoly i.Fdivorced i.Fwidow i.Fnever [pweight=weight], cluster(id_clust)]

Where div includes 5 different income diversification strategies.
This produces the output:

Using strategy 1 as the base outcome.

I then use the mchange command from the spost13 user-written package to get the average marginal effects (findit spost13_ado).

[mchange, stats(se pvalue) brief width(8)]

This produces the following output:

Now to my question. The mlogit uses one of the strategies in div as base outcome. However when running the mchange I got the marginal effects for all strategies (ie there is no base outcome).

Why is there no base outcome? How should I interpret this?

(I got a reviwer telling me that this is wrong... I'm pretty sure it is not but I can not explain why).

Best regards /Elin Vimefall

[Richard Williams]

First off, it would be better to post using code tags than to post an image (which I can't cut and paste from).

Margins does the same thing, albeit not as nicely formatted:

. webuse nhanes2f, clear

. mlogit health i.female

Iteration 0:   log likelihood = -15764.397  
Iteration 1:   log likelihood = -15742.617  
Iteration 2:   log likelihood = -15742.599  
Iteration 3:   log likelihood = -15742.599  

Multinomial logistic regression                 Number of obs     =     10,335
                                                LR chi2(4)        =      43.60
                                                Prob > chi2       =     0.0000
Log likelihood = -15742.599                     Pseudo R2         =     0.0014

------------------------------------------------------------------------------
      health |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
poor         |
    1.female |  -.2721791   .0828957    -3.28   0.001    -.4346516   -.1097065
       _cons |  -1.255004   .0580006   -21.64   0.000    -1.368683   -1.141325
-------------+----------------------------------------------------------------
fair         |
    1.female |   .0962461   .0617409     1.56   0.119    -.0247639    .2172562
       _cons |  -.6183998   .0461661   -13.40   0.000    -.7088837   -.5279158
-------------+----------------------------------------------------------------
average      |  (base outcome)
-------------+----------------------------------------------------------------
good         |
    1.female |  -.0485467   .0540568    -0.90   0.369    -.1544962    .0574028
       _cons |   -.099573   .0396317    -2.51   0.012    -.1772497   -.0218963
-------------+----------------------------------------------------------------
excellent    |
    1.female |  -.2567252   .0551051    -4.66   0.000    -.3647292   -.1487211
       _cons |  -.0679273   .0393064    -1.73   0.084    -.1449664    .0091117
------------------------------------------------------------------------------

. margins, dydx(*)

Conditional marginal effects                    Number of obs     =     10,335
Model VCE    : OIM

dy/dx w.r.t. : 1.female
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
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
0.female     |  (base outcome)
-------------+----------------------------------------------------------------
1.female     |
    _predict |
          1  |  -.0138649   .0050646    -2.74   0.006    -.0237914   -.0039384
          2  |   .0276375     .00722     3.83   0.000     .0134867    .0417884
          3  |   .0215399   .0088724     2.43   0.015     .0041504    .0389295
          4  |   .0068652   .0085332     0.80   0.421    -.0098596      .02359
          5  |  -.0421778   .0083417    -5.06   0.000    -.0585271   -.0258284
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

. mchange, stats(se pvalue) brief width(8)

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

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

             |     poor      fair   average      good  excell~t 
-------------+--------------------------------------------------
female       |                                                  
      1 vs 0 |   -0.014     0.028     0.022     0.007    -0.042 
     Std Err |    0.005     0.007     0.009     0.009     0.008 
     p-value |    0.006     0.000     0.015     0.421     0.000 

.

Note that the 1 versus 0 rows all sum to zero. mchange is telling you how going from 0 to 1 increases or decreases the probability of each of the possible outcomes. So, in your case, being a 1 on Fmono increases the probability of outcome 1 by .123, and decreases the probability of each of the other 4 outcomes.

[Elin Vimefall]

Thank you Richard.
But why does the marginal effects give results for all the cathegories poor, fair, average, good, excellent? (Instead of using one of these as the base outcome).
If there is no base outcome, what is the difference from running five separat logits and then taking the marginal effects?

[Richard Williams]

It gives it for all the categories because the probability of being in each can change as an independent variable changes, e.g. as category 2 becomes more likely, category 1 can become less likely.