Contradictory outcome xtologit OR vs margins dydx(*)

[Rocio Aguilar]

Hi Stata users,
Please I'd help for this issue. I run a xtologit model where my dependent variable is exportation ranking from 1 to 3 (where 1 is the best option). The results of the odds ratio are:

. . xtologit RANKING_EXPORT i.CEO_WOMEN LOG_SIZE ROA , nolog or

Random-effects ordered logistic regression      Number of obs     =      2,322
Group variable: IDENT                           Number of groups  =        271

Random effects u_i ~ Gaussian                   Obs per group:
                                                              min =          1
                                                              avg =        8.6
                                                              max =         12

Integration method: mvaghermite                 Integration pts.  =         12

                                                Wald chi2(3)      =     218.37
Log likelihood  = -1226.6616                    Prob > chi2       =     0.0000

--------------------------------------------------------------------------------
RANKING_EXPORT | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
               |
   1.CEO_WOMEN |   .4024663   .1804177    -2.03   0.042     .1671678    .9689613
      LOG_SIZE |   .0083885   .0027659   -14.50   0.000     .0043957    .0160082
           ROA |    .997986   .0075322    -0.27   0.789     .9833318    1.012859
---------------+----------------------------------------------------------------
         /cut1 |  -34.37714   2.235956   -15.37   0.000    -38.75953   -29.99475
         /cut2 |  -28.91801   2.127807   -13.59   0.000    -33.08844   -24.74759
---------------+----------------------------------------------------------------
     /sigma2_u |   18.97392   2.703147                      14.35124    25.08561
--------------------------------------------------------------------------------
LR test vs. ologit model: chibar2(01) = 1772.14       Prob >= chibar2 = 0.0000

The odds ratio if the CEO is woman is .402 (p=0.042), it means that if the CEO of the company is a woman (CEO_WOMAN=1), the odds of high export versus the combined 2-3 categories are (1/0,40=2,5) 2.5 smaller, given that all of the other variables in the model are held constant.
However, when I run the marginal effect, for the otcome=1, we can say that if the CEO of the company is a woman, the probability of belonging to the first group in the exportation ranking is 7.6% higher. I notice that these results are contradictories. Please, could someone help me?
Thanks!

. . margins, dydx(*) predict(pu0 outcome(1))

Average marginal effects                        Number of obs     =      2,322
Model VCE    : OIM

Expression   : Predicted mean (1.RANKING_EXPORT), assuming u_i=0, predict(pu0 outcome(1))
dy/dx w.r.t. : 1.CEO_WOMEN LOG_SIZE ROA

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
 1.CEO_WOMEN |   .0766569   .0399485     1.92   0.055    -.0016407    .1549545
    LOG_SIZE |   .3866462   .0248591    15.55   0.000     .3379232    .4353691
         ROA |    .000163   .0006111     0.27   0.790    -.0010347    .0013608
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

. . margins, dydx(*) predict(pu0 outcome(2))

Average marginal effects                        Number of obs     =      2,322
Model VCE    : OIM

Expression   : Predicted mean (2.RANKING_EXPORT), assuming u_i=0, predict(pu0 outcome(2))
dy/dx w.r.t. : 1.CEO_WOMEN LOG_SIZE ROA

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
 1.CEO_WOMEN |  -.0070803    .012385    -0.57   0.568    -.0313544    .0171938
    LOG_SIZE |   .0028512   .0474311     0.06   0.952    -.0901121    .0958146
         ROA |   1.20e-06   .0000202     0.06   0.952    -.0000384    .0000408
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

. . margins, dydx(*) predict(pu0 outcome(3))

Average marginal effects                        Number of obs     =      2,322
Model VCE    : OIM

Expression   : Predicted mean (3.RANKING_EXPORT), assuming u_i=0, predict(pu0 outcome(3))
dy/dx w.r.t. : 1.CEO_WOMEN LOG_SIZE ROA

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
 1.CEO_WOMEN |  -.0695766   .0319731    -2.18   0.030    -.1322426   -.0069106
    LOG_SIZE |  -.3894974   .0334593   -11.64   0.000    -.4550764   -.3239183
         ROA |  -.0001642   .0006144    -0.27   0.789    -.0013684    .0010399
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

[Clyde Schechter]

The analysis you are doing here, despite its superficial simplicity, has a large number of "moving parts" and you are looking at summary statistics that fold together several competing effects, making them difficult to interpret. In particular, because -ologit- is a non-linear model, the marginal effect of 1.woman_ceo depends on the values of log_size and roa. In your -margins- commands you do not specify any particular values of log-size and roa, so that what you are getting are marginal effects of 1.woman_ceo averaged over all of the values in your data set. Moreover, the marginal effects are on the probability scale, not the odds scale, and large differences in odds sometimes correspond to negligible differences in probability.

I think that to understand what is going on in your data you should look at some graphs. Choose values of log_size and roa that span the range of observed values in your data. For purposes of illustration, I'll assume that log_size runs from about 5 to 8, and that roa runs from 0 to 1. Re-run your -xtologit- and do this:

margins ceo_women, at(log_size = (5 6.5 8) roa = (0(.25)1)) predict(pu0 outcome(1))
marginsplot, xdimension(roa)

Then do the analogous code for outcomes 2 and 3. Study these graphs, which give, not marginal effects, but the probabilities of the corresponding outcomes. Each graph will contain 6 curves, corresponding to male and female ceo's crossed with three values of log size. You can visually estimate the marginal effects of ceo_women by the vertical distance between the points on the male and female graphs of the same value of log_size. But you will see that these effects differ at differing values of log_size and also along the roa continuum. You will also notice that the effects on outcomes 1, 2, and 3 are different.

I think if you ponder these graphs, it will be easier to understand the results you show in your post.

[Rocio Aguilar]

Dear Clyde,
As ever, you are right! In spite of the simplicity of the model, the variables are widely disperse. And, I notice that even some cross has not enough observations. I need to transform the variables or proving alternative ones. I know that the key of a good fitness is working previously the variables, but ... beeing in hurry is not a good adviser. I am very sorry for that!
Your comments are ver very useful!!!!!!!!
Thanks a lot, now I unsertand better how ordered logit models run.
Best,
Rocio