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  • Interpretation of marginal effects (Multinomial Logit ) Please help

    Dear Folks,

    My code is like....

    mlogit
    margins, dydx(*) atmeans predict(pr outcome(1))
    margins, dydx(*) atmeans predict(pr outcome(2))
    margins, dydx(*) atmeans predict(pr outcome(3))

    Outcome 3 is my reference category (No turnover), 1 for Forcecd (Turnover) and 2 for (Voluntarily Turnover)

    For a continuous variable
    a 1-unit increase in 3-year EPS volatility results in 2.7 percentage points decrease in the probability of facing forced turnover

    For a dummy variable

    The probability of firms doing forced turnover in basic materials, financials, healthcare and utilities industries is 0.27, 0.25, 0.31 and 0.35 higher respectively than firms in the consumer services group.

    Concerning voluntarily turnover sample, only financial industry has a significant coefficient, so that the choice of financials is associated with a 35 percentage point reduction in the probability of voluntarily turnover.

    Is it still compulsory to mention percentage points or both of these interpretations are right? Are marginal effects relative to the base category like mlogit, or is it related to the category we are discussing?

    Regards,
    Michael

  • #2
    Michael: Assuming you've estimated a standard MNL model (e.g. mlogit) the marginal effects on the probabilities should not be base-category dependent. There is an adding-up restriction that the marginal effects must obey—for a particular covariate they necessarily sum to zero across all outcomes—but this is not dependent on the base category selected.

    As for percentage points vs. probabilities: Maybe this is a matter of taste, but with probabilities being your outcome of interest then why not express all marginal effects—for continuous or binary covariates—in terms of probability changes?

    Comment


    • #3
      Thanks a lot sir. Yes, I guess the probability of outcome is a better option.

      What is the different between margins, dydx(*) at means predict(pr outcome(1)) and dydx(*) at means predict(pr outcome(1))



      One quick question concerning marginal effects, did you estimate the marginal effects at the same averages of the explanatory variables?


      http://data.princeton.edu/wws509/stata/mlogit.html

      Comment


      • #4
        Andy: I'm not sure I understand your first question ("What is the..."). Can you clarify?

        On your second question, I'm not sure to what estimates you are referring. In any event, as a general matter I do not use the estimate-at-sample-average approach but rather generally take averages of sample estimates ("average partial effects" or "average marginal effects").

        Comment


        • #5
          Is there any difference in calculating marginal effects at means or not at means

          dydx(*) at means predict(pr outcome(1)) ( I used this code ) or


          http://data.princeton.edu/wws509/stata/mlogit.html... according to this paper

          margins, dydx(black) pr(out(3)) http://data.princeton.edu/wws509/stata/mlogit.html

          yes, one of my friends replied me this and I did not understand as
          This papers recommends that you do not need to estimate the effects at the same averages of the explanatory variables, (contrary to what I did in the paper)

          Comment


          • #6
            I think one of them is marginal effect at means (MEM) and other is average marginal effects (AEM)

            Comment


            • #7
              This might help:

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

              Also possibly see

              http://www3.nd.edu/~rwilliam/xsoc73994/Margins05.pdf
              -------------------------------------------
              Richard Williams, Notre Dame Dept of Sociology
              Stata Version: 17.0 MP (2 processor)

              EMAIL: [email protected]
              WWW: https://www3.nd.edu/~rwilliam

              Comment


              • #8
                Dear John,

                Referring to #2 in this thread, when you say that "the marginal effects on the probabilities should not be base-category dependent", shall we understand that marginal effects of a given covariate should be interpreted regardless of the base outcome that has been stated in the mlogit line of command?. For instance, let's say that I formulate the following model, for a three-way dependent variable

                Code:
                mlogit vardep x1 x2 x3, baseoutcome(2)
                And I am particularly interested in the effect of my independent variables on the first outcome. Thus....

                Code:
                margins, dydx(*) predict(outcome(1))
                Let us say that the first independent variable (x1) is gender (0=male / 1=female). Shall we understand that the output obtained for x1 is the average marginal effect of being women on the probability of obtaining the outcome 1, regardless of the "...baseoutcome" part of the mlogit command?; that is, shall we understand that we should not refer this AME to the reference category in the dependent variable (baseoutcome(2), but all the other two categories in it?

                Thanks a lot for your attention

                And for the interventions in this thread

                Kind regards

                Comment


                • #9
                  Luis, If I understand correctly your question then I agree with what you are saying. The parameter estimates obtained will depend on the base outcome you specify but the marginal effects and average marginal effects will not. The latter should be interpreted without reference to a base category but instead as changes in the outcomes' probabilities due to a change in the covariates.

                  A simple example should make this clear

                  Code:
                  sysuse auto
                  
                  mlogit rep foreign mpg, nolog base(1)
                  margins, dydx(*)
                  
                  mlogit rep foreign mpg, nolog base(2)
                  margins, dydx(*)
                  The results
                  Code:
                  . sysuse auto
                  (1978 automobile data)
                  
                  .
                  . mlogit rep foreign mpg, nolog base(1)
                  
                  Multinomial logistic regression                         Number of obs =     69
                                                                          LR chi2(8)    =  35.56
                                                                          Prob > chi2   = 0.0000
                  Log likelihood = -75.91106                              Pseudo R2     = 0.1898
                  
                  ------------------------------------------------------------------------------
                         rep78 | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
                  -------------+----------------------------------------------------------------
                  1            |  (base outcome)
                  -------------+----------------------------------------------------------------
                  2            |
                       foreign |   .3707596   2596.208     0.00   1.000    -5088.103    5088.844
                           mpg |  -.0810761   .1586764    -0.51   0.609    -.3920762     .229924
                         _cons |   3.008769   3.352039     0.90   0.369    -3.561107    9.578645
                  -------------+----------------------------------------------------------------
                  3            |
                       foreign |   14.30099   2342.179     0.01   0.995    -4576.286    4604.888
                           mpg |  -.0827881   .1432153    -0.58   0.563    -.3634849    .1979087
                         _cons |   4.257887    3.07217     1.39   0.166    -1.763455    10.27923
                  -------------+----------------------------------------------------------------
                  4            |
                       foreign |   16.36085   2342.179     0.01   0.994    -4574.226    4606.947
                           mpg |  -.0428211   .1487764    -0.29   0.773    -.3344175    .2487753
                         _cons |   2.379904   3.196148     0.74   0.457    -3.884432     8.64424
                  -------------+----------------------------------------------------------------
                  5            |
                       foreign |   17.34956   2342.179     0.01   0.994    -4573.237    4607.936
                           mpg |   .0976519   .1573085     0.62   0.535    -.2106671     .405971
                         _cons |   -2.19371   3.573387    -0.61   0.539    -9.197419    4.809999
                  ------------------------------------------------------------------------------
                  
                  . margins, dydx(*)
                  
                  Average marginal effects                                    Number of obs = 69
                  Model VCE: OIM
                  
                  dy/dx wrt: foreign mpg
                  
                  1._predict: Pr(rep78==1), predict(pr outcome(1))
                  2._predict: Pr(rep78==2), predict(pr outcome(2))
                  3._predict: Pr(rep78==3), predict(pr outcome(3))
                  4._predict: Pr(rep78==4), predict(pr outcome(4))
                  5._predict: Pr(rep78==5), predict(pr outcome(5))
                  
                  ------------------------------------------------------------------------------
                               |            Delta-method
                               |      dy/dx   std. err.      z    P>|z|     [95% conf. interval]
                  -------------+----------------------------------------------------------------
                  foreign      |
                      _predict |
                            1  |  -.3464387   64.99789    -0.01   0.996      -127.74    127.0471
                            2  |  -1.334331   108.5949    -0.01   0.990    -214.1764    211.5078
                            3  |   .8592877   82.47663     0.01   0.992    -160.7919    162.5105
                            4  |   .5768328   27.48051     0.02   0.983    -53.28398    54.43764
                            5  |   .2446493   6.139374     0.04   0.968     -11.7883     12.2776
                  -------------+----------------------------------------------------------------
                  mpg          |
                      _predict |
                            1  |   .0017744   .0038376     0.46   0.644    -.0057471    .0092959
                            2  |  -.0018762    .008144    -0.23   0.818    -.0178381    .0140857
                            3  |  -.0104903   .0114212    -0.92   0.358    -.0328754    .0118948
                            4  |  -.0032187   .0095602    -0.34   0.736    -.0219564     .015519
                            5  |   .0138108   .0057643     2.40   0.017      .002513    .0251085
                  ------------------------------------------------------------------------------
                  
                  .
                  . mlogit rep foreign mpg, nolog base(2)
                  
                  Multinomial logistic regression                         Number of obs =     69
                                                                          LR chi2(8)    =  35.56
                                                                          Prob > chi2   = 0.0000
                  Log likelihood = -75.91106                              Pseudo R2     = 0.1898
                  
                  ------------------------------------------------------------------------------
                         rep78 | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
                  -------------+----------------------------------------------------------------
                  1            |
                       foreign |  -.3707596   2596.208    -0.00   1.000    -5088.844    5088.103
                           mpg |   .0810761   .1586764     0.51   0.609     -.229924    .3920762
                         _cons |  -3.008769   3.352039    -0.90   0.369    -9.578645    3.561107
                  -------------+----------------------------------------------------------------
                  2            |  (base outcome)
                  -------------+----------------------------------------------------------------
                  3            |
                       foreign |   13.93023   1120.041     0.01   0.990    -2181.311    2209.171
                           mpg |   -.001712   .0903742    -0.02   0.985    -.1788423    .1754182
                         _cons |   1.249118   1.774027     0.70   0.481    -2.227911    4.726146
                  -------------+----------------------------------------------------------------
                  4            |
                       foreign |   15.99009   1120.041     0.01   0.989    -2179.251    2211.231
                           mpg |    .038255   .1004354     0.38   0.703    -.1585947    .2351046
                         _cons |  -.6288651   2.010171    -0.31   0.754    -4.568728    3.310998
                  -------------+----------------------------------------------------------------
                  5            |
                       foreign |    16.9788   1120.041     0.02   0.988    -2178.262     2212.22
                           mpg |    .178728   .1137665     1.57   0.116    -.0442503    .4017063
                         _cons |  -5.202479   2.584513    -2.01   0.044    -10.26803   -.1369264
                  ------------------------------------------------------------------------------
                  
                  . margins, dydx(*)
                  
                  Average marginal effects                                    Number of obs = 69
                  Model VCE: OIM
                  
                  dy/dx wrt: foreign mpg
                  
                  1._predict: Pr(rep78==1), predict(pr outcome(1))
                  2._predict: Pr(rep78==2), predict(pr outcome(2))
                  3._predict: Pr(rep78==3), predict(pr outcome(3))
                  4._predict: Pr(rep78==4), predict(pr outcome(4))
                  5._predict: Pr(rep78==5), predict(pr outcome(5))
                  
                  ------------------------------------------------------------------------------
                               |            Delta-method
                               |      dy/dx   std. err.      z    P>|z|     [95% conf. interval]
                  -------------+----------------------------------------------------------------
                  foreign      |
                      _predict |
                            1  |  -.3464387   64.99789    -0.01   0.996      -127.74    127.0471
                            2  |  -1.334331   108.5949    -0.01   0.990    -214.1764    211.5078
                            3  |   .8592877   82.47663     0.01   0.992    -160.7919    162.5105
                            4  |   .5768328   27.48051     0.02   0.983    -53.28398    54.43764
                            5  |   .2446493   6.139374     0.04   0.968     -11.7883     12.2776
                  -------------+----------------------------------------------------------------
                  mpg          |
                      _predict |
                            1  |   .0017744   .0038376     0.46   0.644    -.0057471    .0092959
                            2  |  -.0018762    .008144    -0.23   0.818    -.0178381    .0140857
                            3  |  -.0104903   .0114212    -0.92   0.358    -.0328754    .0118948
                            4  |  -.0032187   .0095602    -0.34   0.736    -.0219564     .015519
                            5  |   .0138108   .0057643     2.40   0.017      .002513    .0251085
                  ------------------------------------------------------------------------------

                  Comment


                  • #10
                    Dear John,

                    Referring to #2 in this thread, when you say that "the marginal effects on the probabilities should not be base-category dependent", shall we understand that marginal effects of a given covariate should be interpreted regardless of the base outcome that has been stated in the mlogit line of command?. For instance, let's say that I formulate the following model, for a three-way dependent variable

                    Code:
                    mlogit vardep x1 x2 x3, baseoutcome(2)
                    And I am particularly interested in the effect of my independent variables on the first outcome. Thus....

                    Code:
                    margins, dydx(*) predict(outcome(1))
                    Let us say that the first independent variable (x1) is gender (0=male / 1=female). Shall we understand that the output obtained for x1 is the average marginal effect of being women on the probability of obtaining the outcome 1, regardless of the "...baseoutcome" part of the mlogit command?; that is, shall we understand that we should not refer this AME to the reference category in the dependent variable (baseoutcome(2), but all the other two categories in it?

                    Thanks a lot for your attention

                    And for the interventions in this thread

                    Kind regards

                    Comment


                    • #11
                      This is a paraphrase of the question posted, and answered, at https://www.statalist.org/forums/for...tinomial-logit.

                      Comment

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