Nick et al.--
The Poisson model really only needs E(y|x)=exp(xb) to get consistent
estimates of b, which is why it is the model of choice with a
nonnegative dependent variable (esp. one that is sometimes zero, and
is theoretically unbounded above). See Wooldridge
(http://www.stata.com/bookstore/cspd.html) p.651 and surrounding text:
"A nice property of the Poisson QMLE is that it retains some
efficiency for certain departures from the Poisson assumption," etc.
This addresses why one would use a "count model" for non-count data,
but it does not address why one would use Poisson for an outcome
variable that is an ordinal scale, which I would think is crying out
for an ordered logit, or the like:
http://www.nd.edu/~rwilliam/gologit2
And just because the ordinal scale corresponds to an underlying
measure of the number of events, does not justify using Poisson here
Response options:
0-never; 1-once or twice; 2-three or four times; 3-five or more times
Clearly y is bounded above, so we would not want to use a model that
predicts y greater than 3 for big x, i.e. the E(y|x) should not exceed
3.
On 10/11/06, Nick Cox <n.j.cox@durham.ac.uk> wrote:
I don't follow the example here from your posting,
but I have no quarrel with the late great James
S. Coleman and his wonderful book (from 1964,
in my memory) and I am sure he understood the
Poisson better than I do.
I am attacking the application of count models
to non-count data, which I understood Timothy Mak to be
defending, and I don't see my dimensional arguments being
addressed here.
At some point this thread may have got
detached from the original question....
Nick
n.j.cox@durham.ac.uk
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