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
of corn and available nitrogen
in the soil. A common
approach is to assume that
depends upon
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
, but rather an estimate of
. Therefore,
we represent the observed nitrogen by
, also called the surrogate of
.
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.
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