Adjusting for Unsystematic Measurement Error
Unsystematic measurement error relates to the reliability of the predictor in the model. Many constructs of interest in consumer research cannot be perfectly observed; consequently measurement of these constructs includes some degree of measurement error. Unsystematic measurement error bias attenuates the effect on the outcome in a simple regression model. However, when there are control variables in the model that correlate with the predictor, the size and direction of the bias is less obvious (Angrist and Pischke 2009). Unsystematic measurement error in the outcome does not bias the estimated effect because it is absorbed in the error term of the model, and not an endogeneity issue as long as it is not systematic (i.e., the measurement error in the outcome is not related to the predictor).
Unsystematic measurement error in the predictor can addressed by explicitly considering the reliability of the predictor, either in structural equation modeling (MacKenzie 2001) or with errors-in-variables regression analysis. The advantage of the latter is that the errors-in-variables approach does not have the computational difficulties, restrictive assumptions, and sample size requirements inherent to structural equation modeling, and it is particularly suited for predictors that are measured using a single item or an index. The eivtools package in R (https://cran.r-project.org/web/packages/eivtools/index.html) or the eivreg command in Stata (https://www.stata.com/manuals/reivreg.pdf) enable errors-in-variables regression analysis. For multi-item predictors, the reliability of the measure can be obtained by using Cronbach’s alpha; alternatively, if reliability is not measurable, measurement error can be derived theoretically or based on past empirical research.
References
Angrist, Joshua D., and Jörn-Steffen Pischke, (2009). Mostly Harmless Econometrics: An Empiricist’s Companion. Princeton University Press.
MacKenzie, Scott B. (2001), “Opportunities for Improving Consumer Research through Latent Variable Structural Equation Modeling,” Journal of Consumer Research, 28(1), 159-166.