[From Rick Marken (950724.1800)]

Me:

First convert a variable, y, to 3600/y; call that variable yc. Then do a

regression of x on yc. Then use the regression equation to find

predicted values of yc; call these yc". Then "predict" the values of y (y")

from 3600/yc". Since yc = 3600/y then y = 3600/yc, so it is not really

THAT surprising that y" (3600/yc") is as good a predictor of y (3600/yc)

as yc" is of yc.

Bruce Abbott (950724.1200 EST)--

If I did what you say I did above, you would be right to criticize it as

circular. Fortunately (or unfortunately, depending on your point of

view), you have completely misrepresented my approach.

Oops. It wasn't a satire. I am VERY sorry.

I suggest you go back to my posting and carefully reanalyze it.

Done. Comes out the same as above, with y = reinforcements/hr,

yc = seconds/reinforcement and x = ratio requirement. What you did was

equivalent to taking the square root of a variable (yc = y^1/2), finding

that yc is linearly related to another variable (x) and then showing the

you can recover y by squaring the predicted yc values (y = yc'^2). Since

we know that y = yc^2, it is not surprising that y = yc'^2 to the extent

that yc' is an accurate predictor of yc.

Surely at some point in your graduate education they taught you

about nonlinear transformations of data.

Yes they did. But, I don't think this is relevant to the problem with your

analysis. The problem with you prediction of rate of reinforcement has

nothing to do with non-linearities; the same problem would exist even

if both reinforcements/hr (y) and seconds/reinforcement (yc) were

linearly related to ratio requirement (x). The problem results from the

fact that you are applying the inverse of the function you used to get

yc from y to get the "prediction" of y from yc'.

As a starting point, try graphing the data as originally presented...

Next, replot the data, giving reinforcement rate as a function of ratio

requirement. Finally, plot seconds/reinforcement as a function of

ratio requirement. Let us know what you discover. I think you'll

find that the conclusion is far from trivial.

I found a non-linear relationship between ratio requirement and

reinforcements/hr and a linear relationship between ratio requirement

and seconds/reinforcement. This finding is (as I noted above) irrelevant

to the problem with your approach to predicting reinforcements/hr

from seconds/reinforcment.

Last I heard you were proposing to work on the operant PCT model at

the meeting. Did you make any progress?

Nah. We were just having a good time:-) Bill Powers did give a GREAT

talk on reinforcement theory (well, I thought it was great). I think

the operant PCT model already works awfully well; I think there is little

"progress" that can be made on it until someone starts collecting the

data we need in order to understand how organisms control their intake

of nourishment.

Is anyone planning to provide an overview on CSG-L?

I can provide an overview in one sentence:

"And I think it's gonna be a long, long time"

Best

Rick