Criteria for choosing between calibration weighting and survey weighting
Section 1. Introduction
When estimating population parameters, adjustment techniques are often used to reduce variance or correct non-response. When there is auxiliary information, calibration is an adjustment technique often used in practice. The weight of the calibration estimator is used to adjust the sample so that it reflects the known population totals for a set of auxiliary variables (Deville and Särndal, 1992). The improved accuracy by the calibration estimator depends on the auxiliary variables used in calibration. The variance of the calibration estimator is low when the calibration variables are strongly linked to the variable of interest.
In practice, once the calibration weights are calculated, they replace the survey weights for the production of parameter estimates of all survey variables of interest. However, using calibration weighting can lead to an increase in the mean square error (MSE) for some variables of interest, particularly those not linked to calibration variables. Therefore, calibration weights cannot be used systematically to estimate population parameters for any variable of interest, particularly in the case of multi-purpose surveys covering different subjects. That is why it is necessary to develop a criterion to assess the impact of calibration weighting on the precision of estimates for each variable of interest.
To develop this type of criterion, we can refer to a comparison of the precision of calibration estimators with the Horvitz-Thompson (HT) estimator. Several inferential approaches can be used to measure the precision of these estimators. In this paper, we will consider a sample design- and model-based approach. This approach was chosen because it is the only one with which we can develop a measurement of the MSE of the calibration estimator in order to account for bias due to the use of calibration weights, as well as variance, which depends on the quality of the model. In other approaches (design-based or model-assisted), it is extremely difficult to calculate the MSE of the calibration estimator, and the estimates do not take into account the bias introduced by the use of calibration weights.
Using the design- and model-based approach allows us to develop a criterion with the advantage of approaching a situation where the loss in bias increase for the calibration estimator exceeds the gain in the reduction of variance obtained when there is a link between the variable of interest and the calibration variables. This is a case where the calibration estimator must not be used.
In this paper, we propose a new criterion that measures the impact of using calibration weighting. The proposed criterion takes into account the degree of the existing link between the variable of interest and the calibration variables. Furthermore, it is simple to calculate for each survey variable of interest so that the best sets of weights to use can be identified.
It should be noted that the impact of using calibration weights was studied previously, but only in the context of measuring the design effect (Deff) used to assess the relative increase or decrease in the variance of an estimator compared with simple random sampling. For example, in the model-assisted approach, Henry and Valliant (2015) proposed a Deff measurement that translated the joint impact of an unequal probability sample design and an adjustment of sampling weights compared with simple random sampling.
Following the introduction, which identifies the issue examined in this paper, Section 2 presents the inferential approach adopted in this paper and the criterion used to measure the precision of estimators, while determining its expression for a calibration estimator and an HT estimator. In Section 3, we present the proposed new criterion for assessing the impact of using calibration weights. Section 4 evaluates the proposed criterion using simulations. The purpose of this evaluation is to verify that this criterion identifies situations where a set of calibration weights should be used. In Section 5, we conclude with a discussion of the advantages of the proposed criterion.
- Date modified: