I'll put in one last 2 cents here.
From my looking on the internet, the hierarchical model approach specifically addresses the problem that Beverly put before this list.serve, but is based on a Bayesian model and is, from what I looked at, difficult to implement. The measurement error in X could be important, but, for simple linear regression, an easily implemented approach to taking into account the error in X can be found in the work of Wayne Fuller (who was my major professor, although I never worked with him on measurement error theory), given that there is available a good estimator of the variance of X, which Beverly has. The presence of measurement error in X biases down the estimate for beta when simple regression is done. However, according to Fuller, even in the presence of measurement error in X, for simple regression, the t test for beta equal to zero is valid, just not as powerful as the test could be.
Margot
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Margot Tollefson
Owner
Vanward Statistical Consulting
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Original Message:
Sent: 04-27-2011 10:30
From: J. Dobbins
Subject: Correlation between X and Y, where each Y has multiple X values
I think it is very interesting and appreciate the sharing and exchanges.-------------------------------------------
J. Dobbins
Delmarva Foudation
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