Test whether coefficients that are stored in stata matrices are equal

[Andreas Tetlock]

Hello,

I am running two multinomial logistic regressions and I store the results:

mlogit A i.wave##c.B, noconstant base(0) noomitted noemptycells
est store m1

mlogit C i.wave##c.B, noconstant base(0) noomitted noemptycells
est store m2

( 1) = -.0004935

Then, I run the margins commands to get the marginal effects, which I save in two matrices:

forval i = 1/1 {
est res m1
margins, dydx(B) over(wave) pr(out(`i')) atmeans post  
margins, coeflegend
matrix b_1 = e(b)
est res m2
margins, dydx(B) over(wave) pr(out(`i')) atmeans post
margins, coeflegend
matrix b_2 = e(b)
}

Finally, I am trying to compare the marginal effects,

test b_1[1,1]=b_2[1,1]
test b_1[1,2]=b_2[1,2]
test b_1[1,3]=b_2[1,3]

but I am getting an error:

. test b_1[1,1]=b_2[1,1]

 ( 1) = -.0004935
       Constraint 1 dropped

           chi2(  0) =       .
         Prob > chi2 =         .

. test b_1[1,2]=b_2[1,2]

 ( 1) = -.0781045
       Constraint 1 dropped

           chi2(  0) =       .
         Prob > chi2 =         .

. test b_1[1,3]=b_2[1,3]

 ( 1) = -.0161702
       Constraint 1 dropped

           chi2(  0) =       .
         Prob > chi2 =         .

What am I doing wrong?

What do these

( 1) = -.0004935

mean?

How can I fix it and compare whether the marginal effects are equal or not?

Thanks

[Clyde Schechter]

You can't "fix" this -test- command. -test- is designed for testing of coefficients from the current estimates in e(). While it can have a scalar (which could be a matrix element) on one side of the equation, you can't even run -test 2 = 3- and get anything better than what you have. Actually, it would have been better for -test to just declare a syntax error rather than give you some number whose meaning is an enigma to everyone, except perhaps the person who coded -test- for Stata Corp.

In general, if you wanted to test equality of coefficients across models, you would store both sets of model estimates and then combine them with -suest-. Following -suest-, you can then use -test- to contrast coefficients from different models.

But -suest- will not accept the estimates that come out of -margins, dydx()-, so that path is blocked. I do not know of any way to contrast marginal effects across models in Stata. And I think at least some statisticians would say that it isn't meaningful to do in any case even if you figure out a way.

[Andreas Tetlock]

Hi Clyde,

How can I then compare whether the effect of B on A is any different than the effect of B on C for each of the outcomes?

[Clyde Schechter]

As I said, if you back away from marginal effects and look at the coefficients in -mlogit-, you can do it with -suest- followed by -test-. I will leave it to you to think about whether that is even a reasonable thing to do, but that is how you could do it. If you really want a contrast of the marginal effect of B on A with B on C, I don't know how it can be done, and I don't think it can.

[Andreas Tetlock]

Hi Clyde,

Thanks. You gave me some good information, and at least I can try to do the suest with the coefficients of the mlogit, as you suggested.
My econometrics knowledge is not too advanced, so I would imagine that such a comparison would make sense.

But I guess this discussion is more philosophical, since there is no obvious way to do it in Stata. And I searched on line and I couldn't find a way in R as well.

Actually this is requested by a reviewer in a journal, to check whether any difference exists between the effect of the independent variable on the two different dependent variables. So I gotta do something so that the reviewer doesn't get completely pissed off, if (s)he thinks I ignore him (her)!
But I am not sure if the reviewer was aware of the story with the marginal effects and whether this can actually be implemented.

I will try to do something with the suest and see what happens!

Thanks for your help Clyde, you were really helpful!