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Title:Transformations of additivity in measurement error models PDF Logo
Authors:Eckert, R. Stephen
Carroll, Raymond J.
Wang, Naisyin
Issue Date:1996
Series/Report no.:Discussion Papers, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes 1997,8
Abstract: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 which 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 of selecting a transformation which 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.
Subjects:Errors-in-Variables
Nonlinear Models
Power Transformations
Regression Calibration
SIMEX
Spline Transformations
Transform-Both-Sides
Persistent Identifier of the first edition:urn:nbn:de:kobv:11-10063684
Document Type:Working Paper
Appears in Collections:Discussion Papers, SFB 373, HU Berlin

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