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Sonderforschungsbereich 373: Quantification and Simulation of Economic Processes, Humboldt-Universität Berlin >
Discussion Papers, SFB 373, HU Berlin >
Please use this identifier to cite or link to this item:
http://hdl.handle.net/10419/66247
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| Title: | | Transformations of additivity in measurement error models  |
| 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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