Re: st: How can I assess relative importance of two coefficients in an equation?

[Richard Williams <Richard.A.Williams.5@nd.edu>]

At 12:17 AM 12/27/2003 -0600, Dr. Stephen Owusu-Ansah wrote:
> Dear Colleagues:
>
> How can I assess the relative importance of two coefficients using Wald 
> test? Thus, I want toi test a null hypothesis that the explanatory powers 
> of X_3 and X_4 of the following equation are equal by comparing their Wald 
> chi-square statistic:
>
> Y = b1 + b2X_1 + b3X_2 + b4X_3 + b5X_4.
First off, what estimation command are you using (-regress-, -logit-, or 
what?) and 2nd, what do you have against using the F statistic?  If you are 
doing regular old OLS regression, my understanding is that -test- is fine; 
but if doing logistic regression -lrtest- is better.

Anyway, I think you could do something like the following, using the -est- 
and -lrtest- commands.  The idea is you run the unconstrained model and 
store the results.  Then, you create a new var which is the sum of the 2 
vars you want to constrain to be equal.  Then, run a 2nd regression using 
this new var instead of the 2 original vars; this is the constrained 
model.  Then run lrtest to see whether the difference between constrained 
and unconstrained is significant.  Somebody can correct me if I am doing 
this wrong or let us know if there is a better alternative.  (I'm using 
Stata 8 here.)

. quietly reg  income educ jobexp race
. test  educ=jobexp

 ( 1)  educ - jobexp = 0

       F(  1,    16) =   12.21
            Prob > F =    0.0030

. est store m1
. gen edjob = educ + jobexp
. quietly reg  income edjob race
. lrtest m1

likelihood-ratio test                                  LR chi2(1)  =     11.34
(Assumption: . nested in m1)                           Prob > chi2 =    0.0008



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