(Generalized) Ordered Logit marginal effects

[Francisco Benita]

Dear Statalist,

I'm having trouble to derive marginal effects after computing a Generalized Ordered Logit (correcting by the parallel-lines assumption violated using the gologit2 command).

I have three levels (1, 2 and 3) of my response variable, then, after running the gologit2 command with the autofit lrforce option, the output gives me the estimates of the cumulative effects (1 vs 2 and 3; and 1 and 2 vs 3).

This is a sample of how the output looks like:

gologit2  response pop_density pp_college pp_no_citizen pp_no_car income_Gini, autofit lrforce

------------------------------------------------------------------------------
Testing parallel lines assumption using the .05 level of significance...

Step  1:  Constraints for parallel lines imposed for pp_no_citizen (P Value = 0.8867)
Step  2:  Constraints for parallel lines imposed for income_Gini (P Value = 0.7025)
Step  3:  Constraints for parallel lines are not imposed for
          pop_density (P Value = 0.04162)
          pp_college (P Value = 0.00746)
          pp_no_car (P Value = 0.02939)

Wald test of parallel lines assumption for the final model:

 ( 1)  [1]pp_no_citizen - [2]pp_no_citizen = 0
 ( 2)  [1]income_Gini - [2]income_Gini = 0

           chi2(  2) =    0.17
         Prob > chi2 =    0.9203

An insignificant test statistic indicates that the final model
does not violate the proportional odds/ parallel lines assumption

If you re-estimate this exact same model with gologit2, instead
of autofit you can save time by using the parameter

pl(pp_no_citizen income_Gini)

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

Generalized Ordered Logit Estimates               Number of obs   =       1182
                                                  LR chi2(8)      =     223.80
                                                  Prob > chi2     =     0.0000
Log likelihood =  -1056.791                       Pseudo R2       =     0.0957

 ( 1)  [1]pp_no_citizen - [2]pp_no_citizen = 0
 ( 2)  [1]income_Gini - [2]income_Gini = 0
-------------------------------------------------------------------------------
     response |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
1             |
  pop_density |  -.0005147   .0002311    -2.23   0.026    -.0009676   -.0000619
   pp_college |  -.0821576   .0159082    -5.16   0.000    -.1133371   -.0509781
pp_no_citizen |   .0412044   .0049467     8.33   0.000      .031509    .0508997
    pp_no_car |   .0312774   .0307727     1.02   0.309    -.0290359    .0915907
  income_Gini |   2.607472   2.304695     1.13   0.258    -1.909648    7.124592
        _cons |  -2.476667   .8911029    -2.78   0.005    -4.223196   -.7301372
--------------+----------------------------------------------------------------
2             |
  pop_density |  -.0033817   .0014051    -2.41   0.016    -.0061356   -.0006278
   pp_college |  -.1726428   .0338568    -5.10   0.000     -.239001   -.1062847
pp_no_citizen |   .0412044   .0049467     8.33   0.000      .031509    .0508997
    pp_no_car |  -.0691822   .0464367    -1.49   0.136    -.1601966    .0218321
  income_Gini |   2.607472   2.304695     1.13   0.258    -1.909648    7.124592
        _cons |  -3.368429   .9342685    -3.61   0.000    -5.199562   -1.537297
-------------------------------------------------------------------------------

Finally, to derive the marginal effects, I'm using the margins command as follows:

margins, dydx(*) predict(xb)

Average marginal effects                          Number of obs   =       1182
Model VCE    : OIM

Expression   : Linear prediction, response==1, predict(xb)
dy/dx w.r.t. : pop_density pp_college pp_no_citizen pp_no_car income_Gini

-------------------------------------------------------------------------------
              |            Delta-method
              |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
  pop_density |  -.0005147   .0002311    -2.23   0.026    -.0009676   -.0000619
   pp_college |  -.0821576   .0159082    -5.16   0.000    -.1133371   -.0509781
pp_no_citizen |   .0412044   .0049467     8.33   0.000      .031509    .0508997
    pp_no_car |   .0312774   .0307727     1.02   0.309    -.0290359    .0915907
  income_Gini |   2.607472   2.304695     1.13   0.258    -1.909648    7.124592
-------------------------------------------------------------------------------

My question is: How can I derive the corresponding marginal effects of the Generalized Ordered Logit model of the first table, e.g., two different sets of marginal per explanatory variable (1 vs 2 and 3; and 1 and 2 vs 3)? As far as I can see the margins command (second table) is computing average values which are the same for every level of the response variable.

Thanks in advance.

[Richard Williams]

Welcome to Statalist.

What version of Stata are you using? Margins got better with multiple-outcome commands in V. 14. Also, why use XB? XB will just give you the original coefficients back.

This handout will hopefully be helpful. If you are condemned to using Stata 13 or earlier, the appendix shows how to modify margins commands.

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

Also make sure you have the latest version of gologit2, available from SSC:

. which gologit2
c:\ado\plus\g\gologit2.ado
*! version 3.2.5 17may2019 Richard Williams, [email protected]

[Francisco Benita]

Thank you for your kind response Prof. Williams, I'm working with Stata 14 and version 3.2.5 17may2019 of your command gologit2. I think I got a bit confused with the correct use of the margins command. I basically would like to compute the marginal effects corresponding to my original table 1 (the one that has two sets of coefficients, one for response=1 and response=2). After running the autofit lrforce option what I have are cumulative effects relative between groups.

If I run margins, dydx(*) I get:

margins, dydx(*)

Average marginal effects                        Number of obs     =      1,182
Model VCE    : OIM

dy/dx w.r.t. : pop_density pp_college pp_no_citizen pp_no_car income_Gini
1._predict   : Pr(response==1), predict(pr outcome(1))
2._predict   : Pr(response==2), predict(pr outcome(2))
3._predict   : Pr(response==3), predict(pr outcome(3))

-------------------------------------------------------------------------------
              |            Delta-method
              |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
pop_density   |
     _predict |
           1  |   .0001113   .0000496     2.24   0.025     .0000141    .0002084
           2  |   .0002276   .0001451     1.57   0.117    -.0000567    .0005119
           3  |  -.0003389   .0001402    -2.42   0.016    -.0006137   -.0000641
--------------+----------------------------------------------------------------
pp_college    |
     _predict |
           1  |   .0177607   .0032931     5.39   0.000     .0113062    .0242151
           2  |  -.0004614    .004019    -0.11   0.909    -.0083385    .0074157
           3  |  -.0172993   .0033288    -5.20   0.000    -.0238236    -.010775
--------------+----------------------------------------------------------------
pp_no_citizen |
     _predict |
           1  |  -.0089075   .0009733    -9.15   0.000    -.0108152   -.0069998
           2  |   .0047787   .0005671     8.43   0.000     .0036671    .0058903
           3  |   .0041288   .0005285     7.81   0.000     .0030929    .0051647
--------------+----------------------------------------------------------------
pp_no_car     |
     _predict |
           1  |  -.0067615   .0066402    -1.02   0.309    -.0197761    .0062531
           2  |   .0136937   .0066687     2.05   0.040     .0006233    .0267641
           3  |  -.0069323   .0046527    -1.49   0.136    -.0160514    .0021869
--------------+----------------------------------------------------------------
income_Gini   |
     _predict |
           1  |  -.5636791    .497252    -1.13   0.257    -1.538275     .410917
           2  |   .3024029   .2669899     1.13   0.257    -.2208877    .8256935
           3  |   .2612761   .2312865     1.13   0.259    -.1920371    .7145894
-------------------------------------------------------------------------------

which are the predicted marginal effects at each level of response, but they do not match the results from the first table (1 vs 2 and 3; and 1 and 2 vs 3). I would appreciate any hints on this problem – thanks!

[Richard Williams]

Francisco, I'm afraid I don't understand the question. What is it that is not matching? How can you even tell that they are not matching? As far as I know, all your results are fine, but I am not sure what you think the problem is, and why.

[Francisco Benita]

In the very first table, you can see that the coefficients for pp_no_car are 0.0312774 (for response=1), and -0.0691822 (for response=2). Hence, I would expect their respective marginal effects being positive (for response=1) and negative (for response=2). The table above/below shows the results after using margins, dydx(*) which gives:

--------------+----------------------------------------------------------------
pp_no_car     |
     _predict |
           1  |  -.0067615   .0066402    -1.02   0.309    -.0197761    .0062531
           2  |   .0136937   .0066687     2.05   0.040     .0006233    .0267641
           3  |  -.0069323   .0046527    -1.49   0.136    -.0160514    .0021869
--------------+----------------------------------------------------------------

You can notice that the signs do not correspond with expected ones because in this case the marginal effect for response=1 is negative (-.0067615) and for response=2 is positive (.0136937). This is why I'm getting confused and this is why I refer as the margins do not match. I'm convinced I'm doing something wrong here but so far I haven't been able to figure it out. My apology for the confusion and thank you again for your time.

[Richard Williams]

Your interpretation might be right if using mlogit but it isn’t right for gologit. A positive coefficient for x means that increases in x make it more likely that someone will be in a higher category than the current one. A negative coefficient means that increases in x increase the probability the person will be in the current category or a lower one.

In short, your interpretation of the coefficients is exactly the opposite of what it should be. People get confused because gologit output looks like mlogit output but the interpretations are very different.

[Francisco Benita]

Thank you for the clarification. I'll take a closer look at it as well as the materials you provide.