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
------------------------------------------------------------------------------