3. Errors-in-Variables Models

Hua Liang
18 November 2003

Errors-in-variables (EIV) models are regression models in which the regressors are observed with errors. These models include the linear EIV models, the nonlinear EIV models, and the partially linear EIV models. Suppose that we want to investigate the relationship between the yield $ (Y)$ of corn and available nitrogen $ (X)$ in the soil. A common approach is to assume that $ Y$ depends upon $ X$ linearly. To evaluate the degree of dependence, it's necessary to sample the soil of the experimental plot and to perform an analysis. We can not observe $ X$, but rather an estimate of $ X$. Therefore, we represent the observed nitrogen by $ W$, also called the surrogate of $ X$. The model thus studied is an errors-in-variables model.

This chapter surveys the basic results and explains how errors-in-variables models are implemented in XploRe . The first part covers the class of ordinary linear errors-in-variables models, which has been studied in detail by Fuller (1987). The second part focuses on the nonlinear errors-in-variables or measurement error models surveyed in Carroll, Ruppert, and Stefanski (1995). In the third part, we give an overview of partially linear errors-in-variables models. All chapters contain practical examples. The corresponding quantlets are contained in the quantlib eiv .