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

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Differences in regression slopes |

Date |
Wed, 20 Feb 2008 18:11:42 +0000 (GMT) |

--- "E. Paul Wileyto" <epw@mail.med.upenn.edu> wrote: > Responses so far have sent you this way and that. Just look up > -test- in STATA help. > > To get to the point of using -test- for your purpose, you would need > to specify a model that has group-specific slopes, or combine two > regressions, one for each group, using -suest-. This is still the conventional approach. The reason why the responses have been so mixed is that there are real problems with it, as was discussed in the handout sent earlier and in this working paper: http://www.nd.edu/~rwilliam/oglm/RW_Hetero_Choice.pdf, but there hasn't evovled a concensus yet on the appropriate solution. Rich's -oglm- seems promising, but is somewhat sensitve to model misspecification. However, I expect that any model that tries to deal with this problem will be at least as sensitve, and -oglm- has the advantage of being implemented in Stata. Some time ago I sent some comments to Richard Williams on his handouts for his talk at the 2007 West Coast Stata Users' Group Meeting talk on -oglm- (I whish I could bring up the discipline to write such handouts...): http://ideas.repec.org/p/boc/wsug07/3.html . I copy the relevent section below (heterogeneous choice model is -oglm-): The heterogeneous choice model seems to me a very fragile model: you estimate a model for both the effect of the observed variables and the errors, and you use your model for the errors to correct the effects of the observed variables. Any fault in your model will mean the errors are off, leading to faults in your model for those errors, which in turn will feed back into the estimates of all other parameters. The simulation below shows this: if the model is correct you will reproduce the correct estimates. However, if you misspecify one of the effects, all estimates are off, and are actually worse than a normal logit. Also, less spectacular but more practical since it involves real data and real analysis, a lot the oomph in the analysis of Allison's biochemist data seems to be due to a misspecification of the effect of the number of articles (an economist wouldn't be surprised, and see decreasing marginal returns). See the example below the simulation. Do not mistake these comments to mean that I dislike your work, I like it very much. Best, Maarten *------------- begin simulation ---------------- set more off set seed 1234 capture program drop sim program define sim, rclass drop _all set obs 500 gen x1 = invnorm(uniform()) gen x2 = invnorm(uniform()) gen x1sq = x1^2 gen sigma = exp(x1) gen y = invlogit((-1 + x1 + x1sq + x2)/sigma) > uniform() oglm y x1 x2 x1sq, scale(x1) return scalar x1 = _b[x1] return scalar x2 = _b[x2] return scalar sx1 = [lnsigma]_b[x1] oglm y x1 x2, scale(x1) return scalar fx1 = _b[x1] return scalar fx2 = _b[x2] return scalar fsx1 = [lnsigma]_b[x1] logit y x1 x2 return scalar lx1 = _b[x1] return scalar lx2 = _b[x2] end simulate x1=r(x1) x2=r(x2) sx1=r(sx1) /* */ fx1=r(fx1) fx2=r(fx2) fsx1=r(fsx1) /* */ lx1=r(lx1) lx2=r(lx2), reps(1000): sim hist x1, name(x1, replace) hist x2, name(x2, replace) hist sx1, name(sx1, replace) hist fx1, name(fx1, replace) hist fx2, name(fx2, replace) hist fsx1, name(fsx1, replace) hist lx1, name(lx1, replace) hist lx2, name(lx2, replace) *---------------- end simulation ------------------- *------------- begin biochemist -------------------- use "http://www.indiana.edu/~jslsoc/stata/spex_data/tenure01.dta";, clear keep if pdasample oglm tenure female year yearsq select /// articles prestige , /// het(female) store(lin) mkspline art=articles, cubic displ oglm tenure female year yearsq select /// art1-art4 prestige , /// het(female) store(art) lrtest lin art, stats gen lodds = _b[art1]*art1 + _b[art2]*art2 + /// _b[art3]*art3 + _b[art4]*art4 twoway line lodds articles, sort *------------------ end biochemist ------------------- ----------------------------------------- Maarten L. Buis Department of Social Research Methodology Vrije Universiteit Amsterdam Boelelaan 1081 1081 HV Amsterdam The Netherlands visiting address: Buitenveldertselaan 3 (Metropolitan), room Z434 +31 20 5986715 http://home.fsw.vu.nl/m.buis/ ----------------------------------------- ___________________________________________________________ Support the World Aids Awareness campaign this month with Yahoo! For Good http://uk.promotions.yahoo.com/forgood/ * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: Differences in regression slopes***From:*Richard Williams <Richard.A.Williams.5@ND.edu>

**RE: st: Differences in regression slopes***From:*"Barth Riley" <BarthRiley@comcast.net>

**References**:**Re: st: Differences in regression slopes***From:*"E. Paul Wileyto" <epw@mail.med.upenn.edu>

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