R: re: Re: st: coefficient test in different regression models

["a.carrozzone@libero.it" <a.carrozzone@libero.it>]

Thanks Marteen and Kit for the very helpful replies.


Andrea



>----Messaggio originale----
>Da: maartenbuis@yahoo.co.uk
>Data: 4-ott-2010 21.44
>A: <statalist@hsphsun2.harvard.edu>
>Ogg: re: Re: st: coefficient test in different regression models
>
>--- On Mon, 4/10/10, Christopher F Baum wrote:
>> Maarten suggests estimating the two models by pooling. Not
>> a bad idea, but it does impose one additional constraint:
>> that the sigma^2 are the same across equations. For that
>> reason one should at minimum use robust VCE in that case.
>> 
>> An alternative is to use -suest-. Notice that you estimate
>> the individual equations with classical VCE and apply robust
>> on -suest- if desired.
>>
>> It might be interesting to do some simulations of
>> the two approaches to see where they will agree or differ
>
>That is true. So I made a first stab at such a simulation.
>In particular whether my "pooled regression" approach will
>work when the residual variance actually differs across the
>sub-populations. In the simulation below there is virtually
>no difference in the point estimates. That is no surprise 
>for robust and non-robust, that is build in the program, 
>but as far as I understand it, this did not have to be true
>for -suest- (though this does not really surprise me either). 
>
>The area where I expected the method might matter was the test
>statistic. The simulation returns the p-values of the test
>of a true null-hypothesis. These p-values should be uniformly
>distributed. That way if we choose a significance level of 
>.05 we will find a p-value less than .05 in 5% of the 
>simulations, and if we choose a significance value .10 we
>will find a p-value less than .10 in 10% of the simulations,
>etc. In other words, we would than get the correct coverage
>regarless of what significance level we have chosen. I 
>checked this with the -hangroot- program, which can be 
>downloaded from SSC by typing in Stata:
>-ssc install hangroot-. The confidence intervals shown in the
>graphs now have an interpretation as the area where we might 
>expect the simulations to occur due to the randomness inherrit 
>in simulation.
>
>What surprised me is that in this simulation the regular 
>regression without the robust standard errors seems to do
>best. A possible reason is the sample size: I choose 200
>as in that case there might be some random variation
>resulting in more interesting pictures, but robust 
>standard errors and -suest- rely on asymptotic arguments
>and 200 may not be large enough.
>
>*------------------------- begin simulation ----------------------
>set seed 12345
>set more off
>program drop _all
>program define sim, rclass
>	drop _all
>	set obs 200
>	gen d = _n <=100
>	gen x = rnormal()
>	gen y = d + x + x*d + .25*(d + 1)*rnormal()
>
>	reg y x if d
>	est store a
>	reg y x if !d
>	est store b
>	suest a b
>	test _b[a_mean:x] - _b[b_mean:x] = 1
>	return scalar dif_suest = _b[a_mean:x] - _b[b_mean:x]
>	return scalar p_suest = r(p)
>	
>	reg y c.x##i.d
>	test _b[1.d#c.x] = 1
>	return scalar dif_reg = _b[1.d#c.x]
>	return scalar p_reg = r(p)
>	
>	reg y c.x##i.d, vce(robust)
>	test _b[1.d#c.x] = 1
>	return scalar dif_rob = _b[1.d#c.x]
>	return scalar p_rob = r(p)
>end
>
>simulate dif_suest=r(dif_suest) p_suest=r(p_suest) ///
>         dif_reg  =r(dif_reg)   p_reg  =r(p_reg)   ///
>         dif_rob  =r(dif_rob)   p_rob  =r(p_rob),  ///
>         rep(10000) : sim
>		 
>sum dif*
>hangroot p_suest, susp notheor ci dist(uniform) name(suest, replace)
>hangroot p_reg, susp notheor ci dist(uniform) name(reg, replace)
>hangroot p_rob, susp notheor ci dist(uniform) name(rob, replace)
>*----------------------- end simulation --------------------------	
>(For more on examples I sent to the Statalist see: 
>http://www.maartenbuis.nl/example_faq )
>
>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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