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# st: margins "not estimable" collinear variable

 From Robert Duval To statalist@hsphsun2.harvard.edu Subject st: margins "not estimable" collinear variable Date Sat, 12 May 2012 09:19:10 -0500

```Dear Friends,

I estimate a probit model with a set of (regional) dummies Z1,...,Zk,
and the interaction between a categorical variable (3 levels of
education at the individual level) with a continuous regressor x
defined at the regional level.

In particular the model is

probit y i.region i.edu i.edu#c.x

The estimation presents problems of collinearity and it drops the last
interaction between the 3rd educational category and x:

note: 3.edu#c.x omitted because of collinearity

[Output Omitted] [...]

edu |
2  |   .2202739   .0785022     2.81   0.005     .0664123    .3741354
3  |    .284186   .0887165     3.20   0.001     .1103049    .4580672
|
edu#c.x |
1  |   .2472436    .224275     1.10   0.270    -.1923273    .6868146
2  |   .1672766    .241174     0.69   0.488    -.3054158    .6399691
3  |  (omitted)
|
_cons |   .3254296   .1255826     2.59   0.010     .0792922    .5715671

Since I am most interested in comparing the coefficients for
educ(1)#c.x with educ(3)#c.x I tried omitting the interaction
edu(2)#c.x using

probit y i.region ib2.edu##c.x

This gives me coefficients for the dummies edu(1) and edu(3) and their
respective interactions with x. Of course x on it's own is dropped due
to perfect collinearity with the regional dummies i.region.

[Output Omitted] [...]

edu |
1  |  -.2202739   .0785022    -2.81   0.005    -.3741354   -.0664123
3  |   .0639122   .0935549     0.68   0.495    -.1194521    .2472764
|
x |  (omitted)
|
edu#c.x |
1  |    .079967   .1907966     0.42   0.675    -.2939875    .4539215
3  |  -.1672766    .241174    -0.69   0.488    -.6399691    .3054158
|
_cons |   .4591956   .0927699     4.95   0.000     .2773699    .6410213

However, my problems begin when I try to estimate margins comparing
marginal effects of edu(3) wrt edu(1) at different levels of x

margins, dydx(3.edu) at(x=1)

as it gives me that the margin is not estimable. (Btw the margin at
the mean IS estimable). Exploring the matrix H of estimability

mat H = get(H)
mat l H

I indeed get that not all of its entries are -1,0,1 (some are +/-
fractions between these numbers).

I read in another post
(http://www.stata.com/statalist/archive/2011-07/msg00514.html) that
sometimes it is ok to ask Stata not to perform the estimability check
as in

margins, dydx(3.edu) at(x=1) noestimcheck

Average marginal effects                          Number of obs   =       2153
Model VCE    : OIM

Expression   : Pr(y), predict()
dy/dx w.r.t. : 3.edu
at           : x               =           1

------------------------------------------------------------------------------
|            Delta-method
|      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
3.edu |  -.0378778   .1084452    -0.35   0.727    -.2504265    .1746709
------------------------------------------------------------------------------

But I don't know if that same advice can be applied in my case here.

Any advice on whether it is safe to estimate the effects using with
the noestimcheck option would be greatly appreciated.

Many thanks again,
robert
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```

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