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

From   Richard Williams <>
Subject   Re: st: How can I assess relative importance of two coefficients in an equation?
Date   Sat, 27 Dec 2003 04:55:05 -0500

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

Richard Williams, Associate Professor
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