Summary

Weighting is a statistical technique commonly used and applied in practice to compensate for nonresponse and coverage error. It is also used to make weighted sample estimates conform to known population external totals. In recent years a lot of theoretical work has been done in the area of weighting and there has been a rise in the use of these methods in many statistical surveys conducted by National Statistical Offices around the world. This module describes in detail calibration as a method of adjusting initial weights in surveys based on sampling in order to estimate known population totals of all auxiliary variables perfectly. This method can also be used in surveys as a possible solution for treatment of unit nonresponse and enables gain on efficiency in term of variance when strong correlation between the variable of interest and auxiliary variables exists. It is worth noting that this is one of many weighting methods which can be used in practice. Others include weighting, poststratification, raking, GREG weighting, logistic regression weighting, mixture approach and logit weighting. A review of the weighting method with examples can be found in Kalton and Flores-Cervantes (2003). More information can also be found in “Weighting and Estimation – Main Module”.

Calibration estimation, whereby sampling weights are adjusted to reproduce known population totals, is commonly used in survey sampling. The milestone was the article by Deville and Särndal (1992) in which calibration was described in details. Calibration can be treated as an important methodological instrument, especially in large-scale production of statistics. Many national statistical agencies have developed software designed to compute final weights, usually calibrated using auxiliary information available in administrative registers, censuses and other accurate sources. Calibration as a method of weighting has been described in detail in many articles. A full definition of calibration approach was formulated by Särndal (2007). According to Särndal, the calibration approach to estimation for finite populations consists of:
(a) the computation of weights that incorporate specified auxiliary information and are restrained by calibration equation(s);
(b) the use of these weights to compute linearly weighted estimates of totals and other finite population parameters: weight times variable value, summed over a set of observed units;
(c) satisfying an objective of obtaining nearly design unbiased estimates given that nonresponse and other non-sampling errors are absent.

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