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
Actually, there is an added wrinkle in the original problem: ordinal
variables were summed to create composite scales. That summing and
subsequent use of count models would still seem to be
problematic. On the other hand, suppose the responses had been
worded 0 = never, 1 = a few times, 2 = a moderate amount, and 3 = a
lot. Would the summation seem more questionable then, or less
so? And what method would be better - a count model or plain old
OLS? It is not inconceivable to me that a case could be made for a
count model, but it seems like you ought to be able (or forced) to
justify it rather than just do it!