Testing difference in coefficients of a conditional logit

[Tom Ford]

Hello,
I am estimating a conditional logit (multinomial) model and would like to report the appropriate statistical test for evaluating differences between coefficients. Can I simply use a linear combination approach?
I would greatly appreciate any guidance on the correct procedure to follow.

take the following example:

webuse lowbirth2
clogit low lwt smoke ptd ht ui i.race, group(pairid) robust
Conditional (fixed-effects) logistic regression         Number of obs =    112
                                                        Wald chi2(7)  =  16.17
                                                        Prob > chi2   = 0.0236
Log pseudolikelihood = -25.794271                       Pseudo R2     = 0.3355

                                 (Std. err. adjusted for clustering on pairid)
------------------------------------------------------------------------------
             |               Robust
         low | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
         lwt |  -.0183757   .0117751    -1.56   0.119    -.0414544    .0047031
       smoke |   1.400656   .6015348     2.33   0.020     .2216696    2.579643
         ptd |   1.808009   .5609264     3.22   0.001     .7086133    2.907404
          ht |   2.361152   1.242939     1.90   0.057     -.074964    4.797268
          ui |   1.401929   .5898166     2.38   0.017     .2459099    2.557948
             |
        race |
      Black  |   .5713643   .6882843     0.83   0.406     -.777648    1.920377
      Other  |  -.0253148   .6732398    -0.04   0.970    -1.344841    1.294211
------------------------------------------------------------------------------

How can I examine for example if the effect of smoke is greater than the effect of ui
I tried this but I do not think I am doing it right, as the size of the coefficient appears too large to be correct

. lincom ptd-ui

 ( 1)  [low]ptd - [low]ui = 0

------------------------------------------------------------------------------
         low | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
         (1) |   .4060797   .6918446     0.59   0.557    -.9499108     1.76207
------------------------------------------------------------------------------

Thanks a lot in advance for your help.

[Felix Bittmann]

I think this approach is fine as the result agrees with the largely overlapping CIs. You could also directly use test (which gives the identical p-value). You can also test whether the ratio of the two coefficients differs from one, which also gives a very similar result:

. test ptd = ui

 ( 1)  [low]ptd - [low]ui = 0

           chi2(  1) =    0.34
         Prob > chi2 =    0.5572

. testnl _b[ui] / _b[ptd] = 1

  (1)  _b[ui] / _b[ptd] = 1

               chi2(1) =        0.42
           Prob > chi2 =        0.5179