Abstract
In this chapter, we take a brief tour of the development of measurement error strategies so as to appreciate the challenges facing analysts hoping to address measurement error in applications. To conduct sensible analysis for real world data which are commonly error-corrupted, it is critical to understand the impact of measurement error effects and develop correction adjustments for measurement error effects accordingly. In the literature, research on measurement error models may be categorized into three areas: (1) measurement error in covariates, (2) measurement error in the response variable, and (3) measurement error in both covariate and response variables. The discussion in this chapter will focus on the first category. In particular, we are interested in addressing the following questions: (1) How has research in measurement error evolved over time, and what are some essential findings? (2) What has been the impact of the research addressing covariate measurement error in applications? (3) How can the impact be amplified?
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