More Data Analysis

CSGnet Archive CSG1995
1

[From Rick Marken (950118.2135)]

Boy, the net is OUT TO LUNCH. I hope this shows up sometime
in the next couple of weeks.

Bruce Abbott (950117.0930 EST) --

Do the PCT-analysis programs you have written estimate the
reference value from the data?

No, I don't. But I think that figuring out ways to do this merits a
research program all its own -- one that I would really like to pursue.
It's not trivial to estimate the actual (probably varying) reference a
person establishes for the value of a controlled variale -- even when
that reference is ostensibly being set at a fixed value; see Powers
"Quantitative measurement of volition: A pilot study" in Hershberger
(Ed) Volitional Action (North Holland, 1989).

When the data set contains only cursor and handle positions, (i.e.,
lacks the disturbance tables), the disturbance values can be calculated
exactly only if the reference values are known.

This is not true. In the tracking tasks you are analyzing, it is precisely
the case that c = d+h. The reference value doesn't enter into the picture
at all; the equation for c describes a physical fact. So, if you know the
cursor positions, c, and the corresponding handle positions, h, then
you know d because d=c-h, regardless of the reference for c. In fact, the
reference for c can be wandering all over the place and it will still be
true that d=c-h.

Rick, the way Minitab has been set up on our LAN, it does not get
enough workspace to handle multiple regression with three
predictors on an 1800 row dataset.

I don't understand. Once Minitab has the correlation matrix (which
you posted) it has all it needs for the regression analysis; the number of
cases that went into obtaining that matrix can be dumped from memory
as soon as the matrix elements are computed. Don't tell me these statistics
experts at MINITAB need a statistics-bashing control theorist to help
them out;-).

On a related nite, I finally got the SPSS regression analysis to work
using a correlation matrix as input. I used the following matrix as input,
which is the one Bruce posted where the correlations are all based on
1800 data pairs.

     C1 C2 C3
C2 .105
C3 .177 .039
H .527 .783 .035

I did a stepwise regression, which adds predictor variables to the
regression equation one at a time;the predictor that picks up the most
variance is added first, the one that picks up the next most is added
second, etc. This procedure provides a nice way to see how much variance
in the dependent variable, H, is accounted for by each predictor variable,
C1, C2 and C3.

The first variable added to the regression equation was C2 which, all by
itself, accounts for 61% of the variance in H. The next variable added
was C1 which accounts for an extra 20% of the variance in H. So C1 and
C2 together account for 81% of the variance in H. Finally, C3 is added,
which accounts for less than 1% of the variance. So C1, C2 and C3 together
account for 82% of the variance in H.

The results of the SPSS analysis lead to the conclusion that C1 and C2
have the most to do with the subject's behavior (variations in H); C3,
the controlled variable, is seen as unimportant in the subject's behavior
because it makes virtually no contribution at all to variations in H. So
a conventional statistical analysis of a very simple behavioral situation
identifies two irrelevant side effects of a subject's behavior (variations
in C1 and C2) as the variables that are most relevant to behavior.

Are we having fun yet? :slight_smile:

Best

Rick

2

[From Bruce Abbott (950119.1515 EST)]

Rick Marken (950118.2135) --

Bruce Abbott (950117.0930 EST)

Do the PCT-analysis programs you have written estimate the
reference value from the data?

No, I don't. But I think that figuring out ways to do this merits a
research program all its own -- one that I would really like to pursue.
It's not trivial to estimate the actual (probably varying) reference a
person establishes for the value of a controlled variale -- even when
that reference is ostensibly being set at a fixed value; see Powers
"Quantitative measurement of volition: A pilot study" in Hershberger
(Ed) Volitional Action (North Holland, 1989).

I agree, but the mean cursor position seemed to do a good job in this task.
The mean closely agreed with the target position we had asked the
participant (me) to maintain.

When the data set contains only cursor and handle positions, (i.e.,
lacks the disturbance tables), the disturbance values can be calculated
exactly only if the reference values are known.

This is not true. In the tracking tasks you are analyzing, it is precisely
the case that c = d+h. The reference value doesn't enter into the picture
at all; the equation for c describes a physical fact. So, if you know the
cursor positions, c, and the corresponding handle positions, h, then
you know d because d=c-h, regardless of the reference for c. In fact, the
reference for c can be wandering all over the place and it will still be
true that d=c-h.

Perhaps I should have said "target" instead of reference, where the target
is the X-position in pixels of the stationary red lines. Here the target
position and the reference we ask the participant to use have the same
value. Now d = c - [a + bh] + t, where a is the offset (where the cursor is
on the screen when the mouse position is zero, in the absence of
disturbance), b is the constant of proportionality between c and h (i.e.,
how much the cursor moves per unit of mouse movement), and t is the target
position. The parameters (a+t) and b can be estimated from the data. If
you don't factor in the target position, your computed disturbance is off by
a constant equal to the location of the target. In the program, a = 0 and b
= 1, so c = h + d + t. Leaving t out does not affect the correlations or
regression weights, but does change the constant in the linear equation for
predicting h. When left out of Bill's analysis routine, it causes all
disturbance values (computed as c - h) to be 319 units too large. The sum of
these values then exceeds the maximum permitted size of an integer value,
and the program fails (using longint variables would cure this). Minitab
can digest these numbers and thus allows you to estimate t (since a = 0),
assuming that t = r. However, estimates are just that--estimates.

I took a look at step-wise regression on the data comprising every fifth
observation using Minitab's default criterion for excluding variables; the
result was that only C1 and C2 remained. The full regression that includes
all three cursor positions, which I reported in my earlier post, gave raw
regression weights of .426, .501, and .456, respectively. Strangely,
Minitab does not give the standardized weights, but I have computed these to
be .496, .557, and .040. The low standardized weight given C3 reflects its
small contribution to variance in handle position. In these data, including
C1 and C2 account for 69.70% of the variance; adding C3 brings it up to
69.86%, and increase of 0.16%.

Are we having fun yet? :slight_smile:

You bet! It's always fun to visit the [statistical] zoo! You never know
what strange beasties you will meet. (Look, there goes a three-horned
Suppressor Variable! Look out for those Beta Weights!)

Regards,

Bruce