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. A 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 rich 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 parametric and the other semiparametric. In addition, two criteria for selecting the correct transformation are discussed. One criterion assumes a specified distribution for the measurement error U and selects the transformation which best fits the data. A second criterion assumes only that the measurement error has a symmetric distribution, and selects the transformation which best fits the symmetric model. Several data examples are presented to illustrate the methods.
Eckert, Robert Stephen (1995). Transformations to additivity in measurement error models. Texas A&M University. Texas A&M University. Libraries. Available electronically from
https : / /hdl .handle .net /1969 .1 /DISSERTATIONS -1574683.