Document Detail

Transformations to additivity in measurement error models.
MedLine Citation:
PMID:  9147595     Owner:  NLM     Status:  MEDLINE    
In many problems, one wants to model the relationship between a response Y and a covariate X. Sometimes it is difficult, expensive, or even impossible to observe X directly, but one can instead observe a substitute variable W that is easier to obtain. By far, the most common model for the relationship between the actual covariate of interest X and the substitute W is W = X + U, where the variable U represents measurement error. This assumption of additive measurement error may be unreasonable for certain data sets. We propose a new model, namely h(W) = h(X) + U, where h(.) is a monotone transformation function selected from some family H of monotone functions. The idea of the new model is that, in the correct scale, measurement error is additive. We propose two possible transformation families H. One is based on selecting a transformation that makes the within-sample mean and standard deviation of replicated W's uncorrelated. The second is based on selecting the transformation so that the errors (U's) fit a prespecified distribution. Transformation families used are the parametric power transformations and a cubic spline family. Several data examples are presented to illustrate the methods.
R S Eckert; R J Carroll; N Wang
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Publication Detail:
Type:  Journal Article; Research Support, U.S. Gov't, P.H.S.    
Journal Detail:
Title:  Biometrics     Volume:  53     ISSN:  0006-341X     ISO Abbreviation:  Biometrics     Publication Date:  1997 Mar 
Date Detail:
Created Date:  1997-05-12     Completed Date:  1997-05-12     Revised Date:  2007-11-14    
Medline Journal Info:
Nlm Unique ID:  0370625     Medline TA:  Biometrics     Country:  UNITED STATES    
Other Details:
Languages:  eng     Pagination:  262-72     Citation Subset:  IM    
Lilly Research Laboratories, Eli Lilly and Company, Indianapolis, Indiana 46285, USA.
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MeSH Terms
Coronary Disease / etiology
Middle Aged
Models, Statistical*
Sodium Chloride / urine
Grant Support
Reg. No./Substance:
7647-14-5/Sodium Chloride

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