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# Re: st: equality across quantile regressions WITHOUT sqreg

 From Maarten buis To statalist@hsphsun2.harvard.edu Subject Re: st: equality across quantile regressions WITHOUT sqreg Date Mon, 27 Sep 2010 14:29:29 +0000 (GMT)

```--- On Mon, 27/9/10, Lim, Raymond wrote:
> > If so, would the calculation be the usual "coefficient
> > +or- 1.96*SE" and see whether the 95% confidence
> > intervals overlap?

--- On Mon, 27/9/10, Maarten buis wrote:
> Unfortunately no, that method never works. Basically you
> are missing the covariance of the joint sampling distribution.

To illustrate this point, consider the simulation below. We
know that the coefficients of 2.u and 3.u are equal in the
popultion, I created the data that way. So, I should reject
that hypothesis in 5% of the samples. That is the logic behind
a statistical test. As you can see, if I used the appropriate
command -test-, I get the right coverage (mean of sig is approx.
0.05, i.e. 5%), but the coverage of the "overlapping confidence
intervals test" really misses the nominal 5% mark.

*------------------------ begin simulation --------------------
set seed 12345
set more off
program drop _all
program define sim, rclass
drop _all
set obs 500
gen u = ceil(3*runiform())
gen y = .5* (u >= 2) + .5*rnormal()
reg y i.u
local lb_2 = _b[2.u] - invttail(e(df_r),0.025)*_se[2.u]
local ub_2 = _b[2.u] + invttail(e(df_r),0.025)*_se[2.u]
local lb_3 = _b[3.u] - invttail(e(df_r),0.025)*_se[3.u]
local ub_3 = _b[3.u] + invttail(e(df_r),0.025)*_se[3.u]
return scalar sig_f = ( `lb_2'  > `ub_3' ) | ( `ub_2' < `lb_3' )
test 3.u = 2.u
return scalar sig = r(p) < .05
end
simulate sig_f=r(sig_f) sig=r(sig), reps(10000) : sim
sum
*-------------------------- end simulation ----------------------------

Hope this helps,
Maarten

--------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany

http://www.maartenbuis.nl
--------------------------

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