Abstract:
Applied researchers often analyze ordered categories that discretize continuous quantities (income, time frequencies, biomarkers, exposures). Treating such indices as continuous or imputing bin midpoints are convenient but misleading strategies to estimate marginal effects in regression analyses. This paper characterizes a form of measurement error that arises in those strategies by design, from the sampling mechanism, which induces biased and inconsistent estimations that are model-dependent and a priori unpredictable. I provide a solution to this problem, a calibration method - regularized interval regression - that treats responses as intervals of a latent distribution, and predicts calibrated proxies robust to measurement error biases in downstream linear regressions. Monte Carlo evidence shows that, relative to midpoint imputation and “ordinal-as-continuous,” the calibrated proxy yields unbiased linear estimates, especially in the presence of right-censoring/top-coding. An example based on survey income data illustrates the source of this measurement error but the approach generalizes to any grouped-continuous ordinal variables and has direct implications for observational and experimental designs that rely on ordinal treatment measurements.
Ramses is a Ph.D. candidate in the department of Political Science, and research assistant at the CS&SS consulting service. His research interests are in political economy and methodology.
