Transformations of additivity in measurement error models

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: SFB 373 Discussion Paper ; No. 1997,8

Classification and Topics

• Classification: Wirtschaft
• Subject: Errors-in-Variables ; Nonlinear Models ; Power Transformations ; Regression Calibration ; SIMEX ; Spline Transformations ; Transform-Both-Sides

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Eckert, R. Stephen ; Carroll, Raymond J. ; Wang, Naisyin
• Event: Veröffentlichung
• (who): Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes
• (where): Berlin
• (when): 1996

Further information

• Handle: http://hdl.handle.net/10419/66247
• URN: urn:nbn:de:kobv:11-10063684
• Last update: 10.03.2025, 11:45 AM CET