Traditional notions of measurement error typically rely on a strong mean-zero assumption on the expectation of the errors conditional on an unobservable “true score” (classical measurement error) or on the data themselves (Berkson measurement error). Weakly calibrated measurements for an unobservable true quantity are defined based on a weaker mean-zero assumption, giving rise to a measurement model of differential error. Applications show it retains many attractive features of estimation and inference when performing a naive data analysis (i.e. when performing an analysis on the error-prone measurements themselves), and other interesting properties not present in the classical or Berkson cases. Applied researchers concerned with measurement error should consider weakly calibrated errors and rely on the stronger formulations only when both a stronger model's assumptions are justifiable and would result in appreciable inferential gains.
Kroc, E., & Zumbo, B. D. (2018). Calibration of measurements. Journal of Modern Applied Statistical Methods, 17(2), eP2780. doi: 10.22237/jmasm/1555355848