# Ettinger and Staddon -- faulty analysis?

Good afternoon Bill,

(1) P = a*(Q - Qo) + Po, which is the form Staddon used, but with a
negative value of a (because he writes Ro - Rx instead of Rx - Ro .

From this you can see that Staddon's K is simply the value of the rate of
responding x when the food rate Rx is at its reference level Ro. It has
nothing to do with palatability. It is the rate of responding when the rat
is receiving exactly as much food as it wants -- and in fact is zero. The
definition of the reference level is that value of the input (Rx) at which
the output (x) is just zero. So when Rx = Ro, x = 0, and Staddon's K is
identically zero.

Yes, in a pure control model. But Ettinger and Staddon insist that K can
have some positive nonzero value, which would have to be subtracted from x,
the response rate, before you determined the true Ro or "set point" for food
rate. As I noted before, I think that including a nonzero K in this way is

As you say, the only problem here is that x is not a variable!

Well, actually, x is the average rate of responding, including the post-food
pauses (collection times). What didn't change was the rate of responding
within each ratio, and the length of the pause. x increased with the ratio
because pause-time became a smaller and smaller fraction of the inter-food
interval as the ratio size increased.

We're out of phase now, so I'll skip commenting on your comment on my

The more complicated the hypothesis gets, the less I'm interested. Every
new consideration introduces a new source of uncertainty, meaning you can
fit a curve to the data that proves anything you like.

We should be back in sync now. Unless I've overlooked something in my
analysis of the data I collected, I didn't find any strong evidence for
linear waiting either, at least over the ratios investigated on the cyclic
ratio schedule. But I'll have to review the data -- it's been long enough
that my memory of the results is rather vague. At any rate, the main point
I want to make in this talk is that the data do not support Staddon's
analysis (food _rate_ is not controlled), but that other control models are
possible which may account for these data. (Just because rate isn't
controlled doesn't mean that nothing is.)

Bruce

Hi, Bruce --

... the main point
I want to make in this talk is that the data do not support Staddon's
analysis (food _rate_ is not controlled), but that other control models are
possible which may account for these data. (Just because rate isn't
controlled doesn't mean that nothing is.)

Good enough. It would be nice to demonstrate how to derive model parameters
from raw data with the fewest possible assumptions, but that's not
something that could be done by Monday. I've always used, basically, trial
and error, but there must be some elegant statistical methods.

Bill