Maarten - But suppose I told you I had two types of coins - one that
came up 45% heads, the other 53% heads. Does the probability of a head
depend on the type of coin? If you knew the number of trials that
produced those proportions you could do the inference. If all you were
given were the two numbers 45 and 53, you could do nothing useful. On
the other hand if you were given N1 sample proportions from Coin 1 and
N2 proportions from Coin 2, you could do inference even if you did not
know the number of flips per proportion, but you would also have to
assume the numbers of flips were the same for each proportion otherwise
the sample proportions would not be identically distributed. Even in
this case, unless you had a large number of proportions per coin, you
would sacrifice a lot in power compared to knowing the actual number of
flips.
Al
-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Maarten buis
Sent: Friday, March 03, 2006 3:07 PM
To: statalist@hsphsun2.harvard.edu
Subject: RE: st: Multinomial logit in stata
Alan and Albert
Inference could be done if the unit of analysis is cities (in Alberts
example), e.g. proportion of city budget spent on categories 1, 2, 3, 4,
and 5. If you wanted to do the inference on lower level units
(individuals/companies/dogs who choose to buy/eat hotdog brand 1, 2, 3,
4, or 5 within
cities) than the problem is even more severe than Alan's remark suggest:
than you also have the ecological inference problem. See for example:
http://www.stat.columbia.edu/~cook/movabletype/archives/2006/03/the_ecol
ogical.html . Note that the Papke and Wooldridge paper I reccomended
falls in the ecological inference trap.
HTH,
Maarten
--- "Feiveson, Alan H. (JSC-SK311)" <alan.h.feiveson@nasa.gov> wrote:
> Unless you had repeated observations for the same covariate pattern, I
> don't see how proportions alone would be enough information to do
> proper inference. Those same proportions could have arisen from 100,
> 1000 or 100000 observations. Clearly the inference would be different
> for those situations.
-----------------------------------------
between 1/2/2006 and 31/3/2006 I will be visiting the UCLA, during this
time the best way to reach me is by email
Maarten L. Buis
Department of Social Research Methodology Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands
visiting adress:
Buitenveldertselaan 3 (Metropolitan), room Z214
+31 20 5986715
http://home.fsw.vu.nl/m.buis/
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