Re: Linear Regression question. Is this a Berkson Model situation?
- From: Richard Ulrich <Rich.Ulrich@xxxxxxxxxxx>
- Date: Tue, 25 Sep 2007 22:17:38 -0400
On Tue, 25 Sep 2007 18:40:16 -0700, elodie.gillain@xxxxxxxxx wrote:
In linear regression with one predictor, and when the predictor X is
measured with error (whose mean is null among other assumptions), the
estimate of the slope is biased. Specifically, the slope is
underestimated.
But there are situations when error in X is not a problem. Those can
be referred to as Berkson model situations. For instance, in an
experiment on the effect of room temperature on word processor
productivity, the temperature may be set at target levels of 68, 70
and 72 degrees F, according to the temperature on the thermostat. The
measured X is fixed in this situation, and the true temperature is a
random variable since the thermostat may not be accurate. In this
situation, it can be shown that the assumptions of linear regression
are satisfied, and consequently the estimator of the slope is
unbiased.
This assumes that the error is a FIXED amount, not random.
Not like the later example.
I am studying the following situation, and I would like to tell
whether it qualifies as "Bergsonian", or not. When studying the effect
of process time (X) on the hardness of a plastic piece (Y), suppose
that errors arise in X because the laboratory technician is instructed
to measure the hardness of the ith specimen (Yi) at a prerecorded
elapsed time (Xi). but the timing is imperfect so the true elapsed
time varies at random from the prerecorded elapsed time.
This looks Bergsonian to me, since the measured X* is fixed (by
experimental design) and the true X is random (due to human error of
the technician).
--
Rich Ulrich, wpilib@xxxxxxxx
http://www.pitt.edu/~wpilib/index.html
.
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