Historically, the taxonomy of measurement error models has been based upon two major defining characteristics. The first is the structure of the error model relatingW to X, and the second is the type and amount of additional data available to assess the important features of this error model, for example, replicate measurements as in the Framingham data or second measurements as in the NHANES study. These two factors, error structure and data structure, are clearly related, since more sophisticated error models can be entertained only if sufficient data are available for estimation. We take up the issue of error models in detail in Section 2.2, although it is a recurrent theme throughout the book.