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# Re: st: glm for binomial regression with

 From Nick Cox To statalist@hsphsun2.harvard.edu Subject Re: st: glm for binomial regression with Date Thu, 21 Apr 2011 01:07:54 +0100

I guess this was a puzzling question because as David clearly
indicates it depends on how the experiment was conducted and we don't
know what he doesn't tell us.

My take is simple. If replicates mean that you should reach for -xt-
analyses then the same argument goes for any ties observed on
predictors. That is, if the argument is that values that are similar
on predictors should be grouped then it applies also to those that
arise by chance and not just by design. In experimental practice the
intention is clearly to give the same dose, or whatever, but in
practice the received dose will not be identical even if what is
recorded is the same number, so experimental set-ups don't differ so
much from observational set-ups as is sometimes implied.

Otherwise, the key point with -xt- is that there is other information,
typically in categorical variable form, indicating that observations
should be grouped. A simple example would be if data came from
different laboratories, so that even if everyone was trying to follow
the same protocol, there could still be all sorts of differences.

An even simpler argument is that is this is how the analysis should be
done, should not be most applications of -anova- be revisited?

Nick
On Wed, Apr 20, 2011 at 7:46 PM, Airey, David C
<david.airey@vanderbilt.edu> wrote:
> .
>
> I see the cloglog link in xtgee, and I have just one level of clustering, so this is a possibility.
>
>> I have questions about binomial regression.
>>
>> On page 527 of the Stata 11 -glm- help in the [R] base reference PDF manual is described in Example 2 a binomial data set which describes the death of beetles for a dose response experiment (ldose = log dose, n = total number of beetles, r = number dead):
>>
>> . list , clean
>>
>>        ldose    n    r
>>  1.   1.6907   59    6
>>  2.   1.7242   60   13
>>  3.   1.7552   62   18
>>  4.   1.7842   56   28
>>  5.   1.8113   63   52
>>  6.   1.8369   59   53
>>  7.    1.861   62   61
>>  8.   1.8839   60   60
>>
>> The data is modeled by:
>>
>> glm r ldose, family(binomial n) link(logit)
>>
>> or
>>
>> glm r ldose, family(binomial n) link(cloglog)
>>
>> where the cloglog links allows the dose curve to be asymmetric. In these data the cloglog link fits better than the logit link.
>>
>> I have data like the above, except with replications at each dose.
>>
>> The manual also says the data could be analyzed by expanding the data and using -logit- (if the logit link was the better fit).
>>
>> I have two questions.
>>
>> Unlike the data above, I have replications for each dose. Is this -xt- or clustered data?
>>
>> The data above are already grouped and beetles are replicates, but we have:
>>
>> . list , clean
>>
>>        ldose    n    r
>>  1.   1.6907   59    6
>>  2.   1.6907   62    5
>>  3.   1.6907   62   10
>>  4.   1.6907   59    3
>>  etc.
>>
>> I could ignore the potential clustering and simply model n = 59+62+62+59 and r = 6+5+10+3. I guess it depends on how the experiment is actually done, and I could test for clustering too.
>>
>> My second question, however, is if I were to expand the data above that included a replication by dose (with appropriate replicate id variable included as the cluster id), I could analyze this using xtlogit or xtmelogit---but how do you do this if you want asymmetry, like you get with glm and the cloglog link? Is that available in glm but not xt models in Stata?
>>

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