I like graphs for these type of non-linear models. The thing to keep
track of is that the mean of a variable after a non-linear
transformation is not the mean the original variable. For that reason
I like to use -glm- with the log link, rather than manually compute
the log of wage and use that in -regress-. For the same reason I like
to use the means of the original explanatory variables and transform
those means, rather than compute the means of the transformed
variables. See the example below:
Hope this helps,
Maarten
*-------------- begin example ---------------
sysuse nlsw88, clear
// collect means
sum grade, meanonly
local mgrade = r(mean)
sum ttl_exp, meanonly
local mexp = r(mean)
// ln transform the dependent variables
gen lngrade = ln(grade)
gen lnexp = ln(ttl_exp)
// center and generate the polynomial terms
sum lngrade if !missing(lngrade, lnexp, wage)
gen zlngrade = (lngrade-r(mean))/r(sd)
gen zlngrade2 = zlngrade^2
local zlnmgrade = (ln(`mgrade')-r(mean))/r(sd)
sum lnexp if !missing(lngrade, lnexp, wage)
gen zlnexp = (lnexp-r(mean))/r(sd)
gen zlnexp2 = zlnexp^2
local zlnmexp = (ln(`mexp')-r(mean))/r(sd)
// generate the interaction term
gen gradeXexp = zlngrade*zlnexp
// estimate the model
glm wage zln* gradeXexp , link(log)
// prepare data for graphing
preserve
// fix grade at mean
replace zlngrade = `zlnmgrade'
replace zlngrade2 = `zlnmgrade'^2
replace gradeXexp = `zlnmgrade'*zlnexp
// create predictions
predict wagehat, mu
// create graph
twoway line wagehat ttl_exp, sort
restore
*--------------- end example -----------------
-----------------------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany
http://home.fsw.vu.nl/m.buis/
-----------------------------------------
--- On Tue, 14/7/09, [email protected] <[email protected]> wrote:
> From: [email protected] <[email protected]>
> Subject: Re: re: st: STATA drops squared terms from the model
> To: [email protected]
> Date: Tuesday, 14 July, 2009, 8:38 AM
> Hi Dave,
> thanks for the hint. Now the terms remain in the
> regression. But I am sill unsure about the interpretation.
> How does that change when the polynomial terms are centred?
> Best Phil
>
> -------- Original-Nachricht --------
> > Datum: Mon, 13 Jul 2009 12:53:57 -0500
> > Von: David Airey <[email protected]>
> > An: Statalist <[email protected]>
> > Betreff: re: st: STATA drops squared terms from the
> model
>
> > .
> >
> > Does centering before making the polynomial terms
> help?
> >
> > -Dave
> >
> >
> > > Dear Statalist, I estimate a log-log model with
> interaction term of
> > > the following form: lnY = b0 + b1lnX + b2lnZ +
> b3lnX*lnZ + e I want
> > > to test whether X and Z have a nonlinear effect
> on Y. Therefore, I
> > > add squared terms of X and Z to the model. When I
> estimate this
> > > model STATA drops X and Z from the model due to
> multicollinearity.
> > > The correlation coefficients between the
> unsquared and squared terms
> > > are very high (> 0,96). I have some problems
> interpreting this
> > > result. Does this mean that there is no
> non-linear effect? Best
> > > regards Phil
> > >
> > *
> > * For searches and help try:
> > * http://www.stata.com/help.cgi?search
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> > * http://www.ats.ucla.edu/stat/stata/
>
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