[From Bruce Abbott (950312.1410 EST)]
Bill Powers (950311.1540 MST) --
I've been trying out procedures to determine the switching lag and have come
up with two so far, neither of which I am completely satisfied with but
which give fairly comparable results. The first procedure looks at the data
immediately following a switch of SD until it finds the first deviation of
cursor from the old target position that is larger than some value and in
the direction of the new target. The second method computes the error as
error = h^[i] + d^[i] - ref
where "ref" is the current target position. Immediately after a switch this
becomes greater than 200 (the distance beween targest is 212); the procedure
uses the first point >= 200 as the start (switch) and the first point after
start < 200 as the end of the delay.
For run 008 I get the following results:
Mean SD
Method 1 31 30 33 27 34 34 27 27 30.38 3.11
Method 2 34 28 34 28 36 35 29 29 31.63 3.42
And these results for run 009 (no disturbance):
Mean SD
Method 1 21 14 18 11 14 18 16.00 3.63
Method 2 22 15 19 12 16 20 17.33 3.67
(There were fewer switches in run 009 because of the random selection of the
switch interval at the start of each run.)
As you may recall, the best-fit delay in the model was 30 for run 008 and 15
for run 009, so the delay estimates provided by either method are not too
far off the mark.
This is indeed interesting. Without the disturbance acting, the cursor
stops moving before the next SD. It's possible to select the next target by
looking at it or at least attending to it in peripheral vision. If you're
in the middle of tracking, perhaps you can't do this selecting of the off-
axis target at the same time. Maybe it takes 1/4 sec to locate an off-axis
target. It would be terribly nice to have an eye-position measurement
setup.
In military terms I think this would be referred to as "aquiring the
target." Perhaps one way to get at this would be to look at different target
separations to see what effect the separation has on the delay. (It would
also affect the cursor transit time, but that could be analyzed separately.)
We might also try allowing the unselected target to drift and see if that
affected the delay.
Note that on Mary's third run (011), the interval happened to be very
short, so the transient errors constituted a much larger proportion of the
total error. Also note (re remarks on age): I am 68, Mary is 64. On the
other hand, we all know that women are superior.
Yes, and don't forget that you have to transform her age from woman-years to
man-equivalent years. These days women live about 11 years to a man's 10.
Multiplying Mary's true age by 10/11 makes her only 58 man-years old. Then
you have to apply the fudge and diddle factors to this number, which
eventually gets her age down to 39, the absolute adjusted-age ceiling for
American women. This explains why Mary's delay is shorter than mine; I'm
49. Rick and Sam, what are your ages?
I agree that we should look into representing the physics of the external
part of the loop. The problem here is that there are really one or two
levels of control below the visual-motor loop we're concentrating on,
kinesthetic levels. These will greatly modify effects of inertia and slip-
stick friction (as seen from the visual level). What we need is the ability
to insert known mechanical disturbances, and that would take some equipment
and funds.
Funds? What are funds? Measurement would be best, but I suspect we could
get by with a few simple observations and some calculations. I don't want
to get involved in the details of those lowest-level systems at this point
if we can help it; perhaps it would be enough to apply some kind of inertial
control based on the effective mass of the arm/mouse system. The
accelerations involved could be deduced from the current data, I would think.
As interesting as these problems are, I don't want to loose sight of the
initial problem that got us started along this line--modeling stimulus
control. So I'm going to put my thinking cap on and try to develop a simple
model that will govern the switch of active target. It seems to me that
there are several possible ways to construct the model. When we were
modeling the inverted T situation I wanted to use the horizontal line length
as reference, but you noted that this length was a perception and should
properly enter the model as an input to the perceptual function, along with
the vertical line length. The reference then became a specified DIFFERENCE
between the lengths of the two lines (or, in the ratio model, a specified
RATIO). The same strategy can be followed here: the two target positions
are perceptions, as is the cursor color. The lower-level system could be
construed as controlling the difference between cursor and active target
position at zero. But I'm wondering whether it doesn't make sense to have a
POSITION control system at the bottom level rather than a DISTANCE control
system, which is what the first proposal amounts to. In this case the
reference is indeed the position of the currently active target. And this
position is, of course, a RELATIVE position whose frame of reference is the
screen. Is there a particular advantage of one conception over the other?
I envision a component of the model that selects left-target when the cursor
is green and right-target when the cursor is red. In this case the identity
of the target is conferred by its relative position on the screen, but it
could just as well be conferred by some other property (say, shape). I
mention this because the idea of moving targets of different shapes makes
more apparent the problem of target acquisition: the output of the component
in this case is not a position directly, as it might be in the present
experiment. Unless the participant is able to accurately track all targets,
identifying the active target would have to be followed by a search, whose
result would be the target's position (and probably more, e.g., velocity,
angle of movement, etc.). Our current task with its stationary targets
simplifies the participant's job, but it would be well to develop a more
general model that would work in these other situations as well.
So, falling blissfully into the trap of thinking in terms of a computer
program, I see a system whose functional organization would follow these steps:
1. Keep cursor on the active target (compensatory tracking) while
attending to cursor color.
2. If cursor color changes, translate this into a change of target.
3. Acquire the target (identify the new target and find its position.)
4. Switch the compensatory tracking reference to the new target position.
or Switch the target location in the perceptual input function of the
compensatory tracking system to that of the new target.
I don't mean to imply by this that compensatory tracking is suspended while
the switch to the other target is being processed (it's an empirical
question). Steps 2-4 may very well be functions of a program- or
logic-level control system as Rick Marken proposed. There likely is a
comparison being made between cursor color and current cursor position
(alternatively, target selected?), but I'm wondering whether this system
doesn't begin to behave more like a switch once the associative pathway
between cursor color and target ID becomes habitual. This suggests that the
initial mechanism might be feedback regulated but that sufficient practice
might convert this into an automatic mechanism in which feedback plays a
minimum role (i.e., active only when errors occur elsewhere). For example,
it might become habitual to relate green to left target and red to right
target, so that perception of color converts directly into perception of
active target within a perceptual function. However, if the participant
perceives an error in points-accumulation (i.e., rate = zero when it should
be positive), this might trigger a recheck of the relationship (am I on the
correct target?), a reactivation of the control loop regulating the
cursor-color/target-selected relationship.
Well, have gone far enough afield? Just thinking aloud.... But note that
the switching lag appears to decrease (up to a point!) with practice. This
effect would be consistent with decreasing reliance on feedback regulation
of the cursor-color/target-selected relationship function (i.e.,
relationship control).
I think that you intended the intervals between switches to be randomized.
However, a new random interval is not selected after the count is reset. I
suggest it would be a good idea to put in that randomization; I think we
will want to study predictable switching separately. Your call.
Yes, I noticed that, too, but I didn't want to fix it just yet while we were
all trying the procedure and reporting results. I don't know when the bug
appeared; my initial procedure was working correctly but switches sometimes
occurred too quickly. In the interest of clean data the participant needs a
bit of time following a switch to settle down, so there should be a minimum
inter-switch time built into the procedure. Predictable switching times
provide an opportunity for even greater "automaticity" to set in, so they
should be somewhat variable (however, they have been variable BETWEEN runs;
in fact I didn't realize during the runs that the switching delays within
the run were constant; that only became apparent to me when I saw the plots.)
Oh, yes, I've been meaning to say that I changed the approximation
criterion from abs(delta) < 0.001 to abs(delta) < 0.0001. Seems to make a
slight improvement.
I'll make that change in SD3AN as well. Actually, I'm not too happy with
the current procedure as it wastes time "revisiting" k-values it has already
tried. It shouldn't be difficult to improve its efficiency.
Regards,
Bruce