[From Rick Marken (950725.2310)]

Bruce Abbott (950725.2110 EST) --

If we take the inverse of the reinforcement rates and convert, we get

seconds per reinforcement. This is the average time required to

complete one reinforcement "cycle": complete each response, collect

the pellet, and return to the lever.

OK.

As to the x-axis, the ratio value is the number of responses required to

complete one reinforcement cycle.

OK.

At the y intercept, no responses are required to complete one cycle.

Thus the value of the y intercept is the number of seconds required to

leave the lever, collect the reinforcer, and return to the lever.

OK.

The slope of the line for a given animal is the increase in time per

additional required response.

OK.

If you plot the seconds/cycle as a function of the number of responses

per cycle, you get four essentially straight lines

OK.

Minitab gives the following regression results for these four lines:

Rat intercept slope r r-sq

>C1 5.35 0.679 1.000 1.000

...

OK.

All of these equations and your interpretations of them are fine.

The problem is in what you did with them, which was an exercise in curve

fitting that was presented as the prediction of a model. You said

(Bruce Abbott (950721.1100 EST)):

The rate of reinforcement sustained would be estimated to be 73.4

rft/hr. The actual rate was 73.6 rft/hr.

Reinforcers/Hour: Predicted Vs. Observed

----C1---- ----C2---- ----C3---- ----C4----

Ratio Pred. Obs. Pred. Obs. Pred. Obs. Pred. Obs.

2 525 504 550 525 561 544 573 563

...

So what does it mean? The simplest interpretation is that

reinforcement rate is not being controlled.

This makes no sense for several reasons. The first is that the data you

present do not suggest that reinforcement rate is _not_ being controlled

becuase there is no evidence of _lack_ of disturbance resistance.

But the real problem is that the predicted values of reinforcers/hr are not

model-based predictions. They are predictions in the sense that the linear

regression line gives the predicted seconds /reinforcement at each

ratio. They are a result of curve fitting. The "predicted" reinforcers/hr

at each ratio are based on the same data (the observed reinforcers/hr

at each ratio) as the predicted seconds/reinforcement.

Seconds/reinforcement were derived from reinforcements/hr (by

dividing into 3600). Then you did the regression to find the linear fit to

the seconds/reinforcement. Then you get the predicted

reinforcements/hr by converting the predicted seconds/reinforcement

(based on the regression equation) back into reinforcements/hour (by

dividing into 3600 again).

Perhaps you could see that the "predictions" of reinforcement/hr are just

the predictions of a regression equation if you use the log of the ratio as

the predictor variable in a regression on reinforcements/hour. The fit to the

observed reinforcements/hour should be the same as what you report in

the table above.

Best

Rick