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From |
"Austin Nichols" <austinnichols@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: logistic tranformation, proportion variables |

Date |
Thu, 13 Dec 2007 22:12:43 -0500 |

Marcello-- Yes, I did mean to include the denominator in the first term--thanks for the correction. Just to reiterate the main point, if the regression model logit(A/(A+B)) = Xb + e seems to fit the data better than A/(A+B) = Xb + e, then ln(A) - ln(B) = Xb + e is the same model, and has to fit just as well, as does the identical ln(A) = Xb + ln(B) + e so it must be the case that ln(A) = Xb + aln(B) + e must fit at least as well. A similar argument applies to a logit-transformed RHS var. It may make sense to constrain the elasticity of A w.r.t. B to be 1, i.e. constrain the regression coefficient a to be 1, but not on the grounds that the residuals are less heteroskedastic with a=1; it must be an appeal to theory, IMHO. In the case where A can be zero (mentioned by Marck Butler as the source of the problem), the nearly equivalent model A = exp[ Xb + aln(B) ]u can be estimated by -poisson- (including the obs where A=0). See also the help file for -ivpois- (on SSC). No help for the case where a RHS proportion is zero, though. On Dec 13, 2007 3:32 PM, Marcello Pagano <pagano@biostat.harvard.edu> wrote: > Surely you meant > > logit(a/(a+b))=ln(a/(a+b))-ln(b/(a+b)) = ln(a) - ln(b) > > m.p. > > On 12/13/2007 3:12 PM, Austin Nichols wrote: > > Yes, thanks. Should have been: > > > > logit(a/(a+b)) = ln(a)-ln(1-a/(a+b)) = ln(a)-ln(b) > > > > Read "other component of denominator" for "denominator" e.g. "all > > other bonds" in the example given. > > > > On Dec 13, 2007 2:51 PM, Steven Samuels <sjhsamuels@earthlink.net> wrote: > >> Austin, Did you mean to say: > >> > >> logit(a/(a+b))=ln(a)-ln(b) ? > >> > >> -Steve > >> * * 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/

**References**:**st: logistic tranformation, proportion variables***From:*Marck Bulter <177316mb@student.eur.nl>

**Re: st: logistic tranformation, proportion variables***From:*David Airey <david.airey@Vanderbilt.Edu>

**RE: st: logistic tranformation, proportion variables***From:*"Nick Cox" <n.j.cox@durham.ac.uk>

**Re: st: logistic tranformation, proportion variables***From:*Marck Bulter <177316mb@student.eur.nl>

**Re: st: logistic tranformation, proportion variables***From:*"Austin Nichols" <austinnichols@gmail.com>

**Re: st: logistic tranformation, proportion variables***From:*"Austin Nichols" <austinnichols@gmail.com>

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