🚀 go-pugleaf

I'd greatly appreciate feedback concerning the following arguments
concerning the terms "measurement error" and "bias".  In particular,
references supporting or refuting these arguments would be helpful.
 
Say one is following the typical steps in prediction (1) determining a
variable list, (2) collecting a sample, (3) modeling the sample, and (4)
applying the model to new data.  In the sample of step (2), the values
of the predictor variables do not correspond appropriately with the
values of the response variable.  This would be called measurement
error, which may occur due to misunderstood questions, approximations,
incorrect observations, etc.  If the values of the response variable are
inappropriate (e.g., sample mean does not equal population mean), bias
has occurred.  Another example of bias is if the observed distribution
of the response variable does not follow the true distribution of the
response variable.
 
[So basically the argument here is that X problems are due to
measurement error, and Y problems are due to bias -- is this a
reasonable interpretation of the terms "measurement error" and
"bias"?]
 
 
 
Now consider application of a regression model to new data [step (4)
from above].  The betas have already been estimated.  If it is not con-
venient to measure the predictor variables from step (1), and one measures
surrogate variables perfectly, measurement error (rather than bias) has
occurred, even though the surrogate variables were measured perfectly.
In fact, when making a single prediction with a regression equation, if
the wrong values for the predictor variables are used, the predicted
value for the response variable would be incorrect due to measurement
error -- bias has no meaning in this context.
 
[When making a single prediction with a regression equation, bias
cannot occur in the *new* data (not the original sample data from which
the regression coefficients were estimated) -- only measurement error
could occur.  Is this interpretation reasonable?]
 
References for or against these interpretations would be most helpful.
Should I receive many e-mail response, I'll post a summary.  Thanks in
advance.
--
Mike Kattan  / Decision and Information Sciences  / University of Houston
Houston, TX 77204-6282 / 713-743-4734 / Fax x4693 / kattan@uhupvm1.uh.edu
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