Calibration Used as a Nonresponse Adjustment
Adjusting for total nonresponse for household surveys carried out by INSEE is achieved at present by calibrating the respondents distribution of the characteristics against that of the French population according to k variables x 1,…, x k (like age, profession, sex, number of members in the household, kind of commune etc.) whose totals on the whole target population are known. The required values for x 1,…,x k for the French population are mostly supplied by the French annual Labour survey.
This way of reweighting the sample of respondents is supposed to handle both nonresponse and part of the sampling error when the nonresponse mechanism depends only on x 1,…, x k and when the variable y, which (total) is to be estimated, is correlated to x 1,…,x k . We shall refer to this way of correcting nonresponse and sampling error as method 1.
A natural way to handle both nonresponse and sampling error is to correct first for nonresponse using a nonresponse model and, correct secondly, for sampling error using calibration estimators. The nonresponse mechanism is considered as an additional phase of sampling so that the resulting weights for estimation after correcting for nonresponse are the inverse of the inclusion probability multiplied by the nonresponse probability. Then, the use of calibration estimators is equivalent to reweighting (see DEVILLE, SARNDAL 1992). We shall refer to this procedure as method 2. This method is more costly to implement, because it requires the estimation of the nonresponse model. This procedure also requires more information at the individual level: the values of the variables used in the nonresponse model are needed for both respondents and nonrespondents.
In section 1, we show that method 1 and method 2 coincide if and only if the nonresponse model and the calibration functions used are exponential and the variables x 1,…, x k used in the nonresponse model and in the calibration step being the same, or if the auxiliary variable consists of a unique qualitative variable. This last case corresponds to poststratification. In section 2, we compare the two procedures on an survey carried out by INSEE in 1989. We find surprisingly that for the survey on food consumption of 1989, the influence of method choice on individual weights is about the same as the influence of calibration function or response function choice. We also found that the influence of method choice is insignificant on the most aggregated results. Thus the use of method 1 instead of method 2 seems fairly acceptable.
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