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From |
Maarten buis <maartenbuis@yahoo.co.uk> |

To |
statalist@hsphsun2.harvard.edu |

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

Date |
Mon, 4 Oct 2010 20:44:02 +0100 (BST) |

--- 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/

**References**:**re: Re: st: coefficient test in different regression models***From:*Christopher F Baum <baum@bc.edu>

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