Please use this identifier to cite or link to this item:
Eckert, R. Stephen
Carroll, Raymond J.
Wang, Naisyin
Year of Publication: 
Series/Report no.: 
Discussion Papers, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes 1997,8
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.
Nonlinear Models
Power Transformations
Regression Calibration
Spline Transformations
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

Files in This Item:
177.97 kB

Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.