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  • Properly interpreting odds ratios vs marginal effects

    Dear Statalist, I would like to kindly ask for help in the interpretation of these variables in a logit model. Where y1 is the likelihood of innovating (dummy), x1 is if the firm collaborates (dummy), and z1 is the number of partners with which firms collaborate. I would like to understand the interpretation of these coefficients (x1 and z1) in the odds ratios and marginal effects cases.

    Odds ratio case: collaborating (x1=1) implies that firms are a 68% more likely to innovative than firms that do not collaborate? Or this mean that collaborating increase the odds of innovating 68%? Therefore, if odd is different than the probability, how do you interpret this “odd”?
    Marginal effects: collaborating implies an increase in the probability of innovating of 3.9%?

    Thanks for your help!

    Odds ratios estimation:
    Code:
    Integration method: mvaghermite                 Integration pts.  =         15
    
                                                    Wald chi2(4)      =     903.54
    Log pseudolikelihood = -3849.3419               Prob > chi2       =     0.0000
                                      (Std. Err. adjusted for 17 clusters in ri_2)
    ------------------------------------------------------------------------------
                 |               Robust
               y | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
    -------------+----------------------------------------------------------------
              x1 |
             L1. |    1.68158   .2786766     3.14   0.002     1.215217    2.326919
                 |
              x2 |
             L1. |   1.048653   .0298201     1.67   0.095     .9918053    1.108759
                 |
              x3 |
             L1. |   4.002165   .2412754    23.00   0.000     3.556144    4.504128
                 |
              z1 |   1.014237    .019708     0.73   0.467     .9763368    1.053609
           _cons |   .0001135   .0000345   -29.88   0.000     .0000625    .0002059
    -------------+----------------------------------------------------------------
    ri_2         |
       var(_cons)|   .0585249   .0487641                      .0114315    .2996252
    -------------+----------------------------------------------------------------
    ri_2>ri_1    |
       var(_cons)|   6.221522   .5014663                      5.312369    7.286267
    ------------------------------------------------------------------------------
    Marginal effects estimation (margins, dydx(*) post):
    Code:
    Average marginal effects                        Number of obs     =     11,606
    Model VCE    : Robust
    
    Expression   : Marginal predicted mean, predict()
    dy/dx w.r.t. : L.x1 L.x2 L.x3 z1
    
    ------------------------------------------------------------------------------
                 |            Delta-method
                 |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
    -------------+----------------------------------------------------------------
              x1 |
             L1. |   .0390277   .0125668     3.11   0.002     .0143973    .0636581
                 |
              x2 |
             L1. |   .0035673   .0021207     1.68   0.093    -.0005892    .0077239
                 |
              x3 |
             L1. |   .1041398   .0046034    22.62   0.000     .0951173    .1131624
                 |
              z1 |   .0010616   .0014628     0.73   0.468    -.0018054    .0039285
    ------------------------------------------------------------------------------

  • #2
    An odds is the expected number of successes per failure, while a probability is the expected number of successes per trial. They are different but related ways of measuring the same concept.
    ---------------------------------
    Maarten L. Buis
    University of Konstanz
    Department of history and sociology
    box 40
    78457 Konstanz
    Germany
    http://www.maartenbuis.nl
    ---------------------------------

    Comment


    • #3
      Dear Maarten, thanks for your help. Can I ask for your advice on how to obtain the table with the marginal effects including a quadratic effect? Basically, I need a table with the estimations as marginal effects. However, when doing the following command it gives error. As you can see in the first table below, the table reports z1 and z1*z1. However, the margins command fail to report it. I have also tried without the "##" (see second table below) but the marginal effects table do not report z1 and z1*z1; it gives only z1 (and it is not significant, which is different from the previous table).
      Any idea of what am I doing wrong?

      Code:
      Integration method: mvaghermite                 Integration pts.  =          7
      
                                                      Wald chi2(11)     =    1966.80
      Log pseudolikelihood = -3825.7884               Prob > chi2       =     0.0000
                                        (Std. Err. adjusted for 17 clusters in ri_2)
      ------------------------------------------------------------------------------
                   |               Robust
                 y |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
      -------------+----------------------------------------------------------------
                x1 |
               L1. |   .5111601   .1612871     3.17   0.002     .1950432    .8272771
                   |
                x2 |
               L1. |   .0493833   .0278291     1.77   0.076    -.0051608    .1039274
                   |
                x3 |
               L1. |   1.408232   .0591578    23.80   0.000     1.292285    1.524179
                   |
                z1 |  -.1406241   .0525853    -2.67   0.007    -.2436893   -.0375589
                   |
         c.z1#c.z1 |   .0083582   .0026748     3.12   0.002     .0031157    .0136007
                   |
              year |
             2008  |          0  (empty)
             2009  |  -.2015642   .1409789    -1.43   0.153    -.4778778    .0747495
             2010  |   .4922232    .157827     3.12   0.002      .182888    .8015584
             2011  |   .1960216   .1460827     1.34   0.180    -.0902952    .4823383
             2012  |   .1510818   .1553798     0.97   0.331    -.1534569    .4556206
             2013  |   .0082289    .139861     0.06   0.953    -.2658936    .2823513
             2014  |   .2251473   .1157892     1.94   0.052    -.0017953      .45209
             2015  |          0  (omitted)
                   |
             _cons |  -9.027902   .3402367   -26.53   0.000    -9.694754    -8.36105
      -------------+----------------------------------------------------------------
      ri_2         |
         var(_cons)|   7.87e-37   1.79e-36                      9.03e-39    6.86e-35
      -------------+----------------------------------------------------------------
      ri_2>ri_1    |
         var(_cons)|    6.69641   .6128996                      5.596731     8.01216
      ------------------------------------------------------------------------------
      
      .     margins, dydx(L.x1 L.x2 L.x3 z1##z1) post
      invalid matrix stripe;
      z1##z1
      Code:
      Integration method: mvaghermite                 Integration pts.  =          7
      
                                                      Wald chi2(11)     =    1966.80
      Log pseudolikelihood = -3825.7884               Prob > chi2       =     0.0000
                                        (Std. Err. adjusted for 17 clusters in ri_2)
      ------------------------------------------------------------------------------
                   |               Robust
                 y |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
      -------------+----------------------------------------------------------------
                x1 |
               L1. |   .5111601   .1612871     3.17   0.002     .1950432    .8272771
                   |
                x2 |
               L1. |   .0493833   .0278291     1.77   0.076    -.0051608    .1039274
                   |
                x3 |
               L1. |   1.408232   .0591578    23.80   0.000     1.292285    1.524179
                   |
                z1 |  -.1406241   .0525853    -2.67   0.007    -.2436893   -.0375589
                   |
         c.z1#c.z1 |   .0083582   .0026748     3.12   0.002     .0031157    .0136007
                   |
              year |
             2008  |          0  (empty)
             2009  |  -.2015642   .1409789    -1.43   0.153    -.4778778    .0747495
             2010  |   .4922232    .157827     3.12   0.002      .182888    .8015584
             2011  |   .1960216   .1460827     1.34   0.180    -.0902952    .4823383
             2012  |   .1510818   .1553798     0.97   0.331    -.1534569    .4556206
             2013  |   .0082289    .139861     0.06   0.953    -.2658936    .2823513
             2014  |   .2251473   .1157892     1.94   0.052    -.0017953      .45209
             2015  |          0  (omitted)
                   |
             _cons |  -9.027902   .3402367   -26.53   0.000    -9.694754    -8.36105
      -------------+----------------------------------------------------------------
      ri_2         |
         var(_cons)|   7.87e-37   1.79e-36                      9.03e-39    6.86e-35
      -------------+----------------------------------------------------------------
      ri_2>ri_1    |
         var(_cons)|    6.69641   .6128996                      5.596731     8.01216
      ------------------------------------------------------------------------------
      
      .     margins, dydx(L.x1 L.x2 L.x3 z1) post
      
      Average marginal effects                        Number of obs     =     11,606
      Model VCE    : Robust
      
      Expression   : Marginal predicted mean, predict()
      dy/dx w.r.t. : L.x1 L.x2 L.x3 z1
      
      ------------------------------------------------------------------------------
                   |            Delta-method
                   |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
      -------------+----------------------------------------------------------------
                x1 |
               L1. |   .0379276   .0121029     3.13   0.002     .0142065    .0616488
                   |
                x2 |
               L1. |   .0036642   .0020534     1.78   0.074    -.0003604    .0076888
                   |
                x3 |
               L1. |   .1044896   .0033275    31.40   0.000     .0979678    .1110114
                   |
                z1 |  -.0006927   .0009166    -0.76   0.450    -.0024892    .0011039
      ------------------------------------------------------------------------------

      Comment


      • #4
        The only thing you're doing wrong is expecting to find a "marginal effect" of the quadratic term. There is no such thing. That's why Stata doesn't give one. The marginal effect reported for z1 takes into account the fact that the outcome variable depends quadratically on z1. The marginal effect reported for z1 is an average marginal effect--the marginal effect of z1 differs for different values of z1 (precisely because of the quadratic relationship), and what is reported here is averaged over the joint distribution of all the independent variables in the data set.

        In fact, another thing to always keep in mind is that it is never meaningful to speak of anything about just the linear term or just the quadratic term in a quadratic model. They must always be used together. In the case of -margins-, Stata puts them together for you and just calls the result z1.

        Comment


        • #5
          Dear Clyde, thanks for your help. That is a very instructive answer. Then the marginal effects of z1 needs to be evaluated at different levels. Thanks again!

          Comment

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