This article describes a two-step calibration-weighting scheme for a stratified simple random sample of hospital emergency departments. The first step adjusts for unit nonresponse. The second increases the statistical efficiency of most estimators of interest. Both use a measure of emergency-department size and other useful auxiliary variables contained in the sampling frame. Although many survey variables are roughly a linear function of the measure of size, response is better modeled as a function of the log of that measure. Consequently the log of size is a calibration variable in the nonresponse-adjustment step, while the measure of size itself is a calibration variable in the second calibration step. Nonlinear calibration procedures are employed in both steps. We show with 2010 DAWN data that estimating variances as if a one-step calibration weighting routine had been used when there were in fact two steps can, after appropriately adjusting the finite-population correct in some sense, produce standard-error estimates that tend to be slightly conservative.
Folsom, R.E. 1991. “Exponential and Logistic Weight Adjustments for Sampling and Nonresponse Error Reduction.” In Proceedings of the American Statistical Association, Social Statistics Section, 197-202.
Folsom, R.E. and A.C. Singh. 2000. “The Generalized Exponential Model for Sampling Weight Calibration for Extreme Values, Nonresponse, and Poststratification.” In Proceedings of the American Statistical Association, Survey Research Methods Section, 598-603. Available at: https://www.amstat.org/sections/srms/Proceedings/papers/2000_099.pdf (accessed July 1, 2014).
Kim, J.K. and M. Riddles. 2012. “Some Theory for Propensity Scoring Adjustment Estimator.” Survey Methodology 38: 157-165.
Kott, P.S. 2011. “A Nearly Pseudo-optimal Method for Keeping Calibration Weights from Falling Below Unity in the Absence of Nonresponse or Frame Errors.” Pakistan Journal of Statistics 27: 391-396.
Kott, P.S. 2006. “Using Calibration Weighting to Adjust for Nonresponse and Coverage Errors.” Survey Methodology 32: 133-142.
Kott, P.S. and D. Liao. 2012. “One Step or Two? Calibration Weighting from a Complete List Frame with Nonresponse.” Under review by Survey Methodology (presented at the Symposium on the Analysis of Survey Data and Small Area Estimation, in honour of the 75th Birthday of Professor J. N. K. Rao).
RTI International 2012. SUDAAN Language Manual, Release 11.0. Research Triangle Park, NC: RTI International.
Substance Abuse and Mental Health Services Administration 2012. Drug Abuse Warning Network (DAWN). Available at: http://www.samhsa.gov/data/DAWN.aspx (accessed July 1, 2014).
US Census Bureau 2012. ZIP Codee Tabulation Areas (ZCTAse). Available at: https://www.census.gov/geo/reference/zctas.html (accessed July 1, 2014).