Ivan,

In reference to your part 2), in 1989 Li and Duan published a paper where
they examined the effect of using the "wrong" link function (
http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.aos/1176347254).
 The short version is that they found that in common models (lm and glm and
others) and when the x-variables meet certain conditions, then the
estimates of the slopes will change by a multiplicative constant as will
the variance co-variance matrix. Many of the tests are still well behaved
in this condition.  The link functions you mentioned are all very similar
to each other, so the impact of using a "wrong" one will be very minor.


On Fri, Feb 1, 2013 at 8:33 AM, Ivan-K <kia@ipae.uran.ru> wrote:

> Dear colleagues, I have 2 points: One opinion and one question.
>
> 1)
> In one paper in a peer-reviewed journal, I read about the idea of using a
> logit regression as a surrogate for the log-binomial, just adding the
> numerator to the denominator ...
> It’s tempting to immediately get the RR instead of OR ...
> I tried it and I think it's a bad idea, the confidence intervals
> dramatically inflated!
> Any opinions?
>
> 2)
> What would be the criteria for selection of link - functions for binary
> data?
> Usually I use the logit - just for simplest interpretation of parameters.
> Using logit, probit, log-log, and log-log, I get identical values of the
> maximum-likelihood, Pearson statistics, overdispersion parameter, etc.
> However, the regression coefficients and its standard errors are different
> (for logit b is the maximum, for the probit – min., for log-log & C-
> log-log
> are between them). LRs close, but the maximum has the log-log. Wald
> criterion - the maximum for the probit.
> ?What are the interpretations for regression parameters (except logit)???
>
> Ivan, IPAE RAS
>
>
>
>
> --
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>
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-- 
Gregory (Greg) L. Snow Ph.D.
538280@gmail.com

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