Dear List:
 
I am trying to figure out how to incorporate measurement error in an longitudinal educational data set using lme to create a "true score" model. As a by-product of the procedures used to scale educational tests, one can obtain a person-specific measurement error associated with each score, or a conditional standard error. For example, a score of 200 would have measurement error specific to that score that would be different than, say, a score of 250.
 
I have been rather successful in figuring out how to rescale the necessary components to create this "true score" model. This simply requires that the response variable, the intercept, and any other variables in the design matrix be multiplied by the reciprocal of the standard error of measurement for the associated score. There may be a better way to do this, but I manually create a vector of 1s for all observations and multiply this vector by 1/sem. This is the new intercept. I also multiply any other predictors in the design matrix by the same value.
 
In the R code, I remove the intercept included by default (-1) and include the newly created intercept (which is no longer a constant) as well as the new response variable and rescaled predictors.
 
However, I am confused regarding the within-group error term. Fitting this model requires that the variance be fixed at 1:  e ~ n(0,1).
 
Is it possible to constrain the variance for this model as such?
 
I would appreciate any comments or suggestions regarding this model.
 
HCD
 
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Harold C. Doran
Director of Research and Evaluation
New American Schools
675 N. Washington Street, Suite 220
Alexandria, Virginia 22314
703.647.1628
 <http://www.edperform.net/>  
 
 
 

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