[R] using a noisy variable in regression (not an R question)

[Jonathan Baron]

If you form categories, you add even more error, specifically, the
variation in the distance between each number and the category
boundary.

What's wrong with just including it in the regression?

Yes, the measure X1 will account for less variance than the underlying
variable of real interest (T1, each individual's mean, perhaps), but
X1 could still be useful in two ways.  One, it might be a significant
predictor of the dependent variable Y despite the error.  Two, it
might increase the sensitivity of the model to other predictors (X2,
X3...) by accounting for what would otherwise be error.

What you cannot conclude in this case (when you measure a predictor
with error) is that the effect of (say) X2 is not accounted for by its
correlation with T1.  Some people try to conclude this when X2 remains
a significant predictor of Y when X1 is included in the model.  The
trouble is that X1 is an error-prone measure of T1, so the full effect
of T1 is not removed by inclusion of X1.

Jon

On 03/07/09 12:49, Juliet Hannah wrote:
> Hi, This is not an R question, but I've seen opinions given on non R
> topics, so I wanted
> to give it a try. :)
> 
> How would one treat a variable that was measured once, but is known to
> fluctuate a lot?
> For example, I want to include a hormone in my regression as an
> explanatory variable. However, this
> hormone varies in its levels throughout a day. Nevertheless, its levels differ
> substantially between individuals so that there is information there to use.
> 
> One simple thing to try would be to form categories, but I assume
> there are better ways to handle this. Has anyone worked with such data, or could
> anyone suggest some keywords that may be helpful in searching for this
> topic. Thanks
> for your input.
> 
> Regards,
> 
> Juliet
> 
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-- 
Jonathan Baron, Professor of Psychology, University of Pennsylvania
Home page: http://www.sas.upenn.edu/~baron
Editor: Judgment and Decision Making (http://journal.sjdm.org)