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"[email protected]" <[email protected]> |

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

Date |
Tue, 5 Oct 2010 09:16:33 +0200 (CEST) |

Thanks Marteen and Kit for the very helpful replies. Andrea >----Messaggio originale---- >Da: [email protected] >Data: 4-ott-2010 21.44 >A: <[email protected]> >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 >-------------------------- > > > > > > >* >* For searches and help try: >* http://www.stata.com/help.cgi?search >* http://www.stata.com/support/statalist/faq >* http://www.ats.ucla.edu/stat/stata/ > * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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