[From Rick Marken (950124.0845)]

Ok. The horse is dead but I can't resist one more small beat.

This whole c=d+h thing started because Bruce was using regression analysis to

determine the relationship between handle, h, and disturbance, d, in a

tracking task. The regression equation is:

h = r + kd

Bruce found that the intercept of this regression equation (r) is almost

exactly equal (in screen units) to the reference position at which the

subject is trying to maintain the cursor. That is, if the subject is trying

to keep the cursor at screen position 319 (the middle) then the value of r

that results from the regression analysis is almost exactly 319. But (as

Bruce discovered) this is only true if the predictor variable (d) is properly

reconstructed. If it is, then d will have an average value of 0. Since h is

stored in screen units, then r will be the value of h when d is 0, which is

the reference value of the controlled variable in screen units.

My last beat on the dead horse is just a caveat regarding the use of

regression analysis to estimate the reference state, r, of a controlled

variable. The intercept of the regression equation gives an estimate of r

only under (at least) the following special circumstances:

1. The average of the predictor (d) must be 0.

2. The dependent variable, h, must be measured in units of the controlled

variable, c. In the THREECV1 experiments, h = c, where c is the displayed

position of the cursor.

3. The subject must keep the cursor in one position (fixed reference). In

this case, the average position of the handle corresponds to the fixed

position where c is maintained (assuming the average disturbance is 0).

If any one of these conditions is not met then the r of the regression

equation is not an estimate of the reference position of the controlled

variable.

Best

Rick