Handling nonignorable nonresponse for mixture distribution survey data: application to Swiss Statistics on Income and Living Conditions (SILC) survey data
摘要
Income is a key variable in many surveys. Nonresponse rates are increasing in surveys conducted by national statistical institutes and income is no exception. Ignoring nonresponse can lead to two major problems, namely an increase in variability and bias in the estimators. Dealing with nonresponse regarding income is particularly challenging because the likelihood of responding depends on income (non-ignorable nonresponse). In addition, the empirical distribution of income may be complicated, with multiple bumps, asymmetry, and long tails. We propose an income mean estimator that can be used when income can be modeled using a mixture distribution. Our approach is inspired by the distribution of income collected from the Swiss Statistics on Income and Living Conditions (SLIC) survey data of 2009 (Federal Statistical Office, Survey on Income and Living Conditions in Switzerland. Data set of the 2009 survey, 2009). The proposed procedure combines two ingredients: a model-based estimation and a nonresponse weight adjustment. The values of the income (the variable of interest) are predicted on the basis of a fitted mixture distribution on the respondents’ set. The response probabilities are estimated using generalized calibration with the collected income as a response model variable. The inverse estimated response probabilities provide a nonresponse weight adjustment that accounts for nonignorable nonresponse. We incorporate both the predicted values of the variable of interest and the estimated response probabilities into a Hájek-type mean estimator, and provide an estimator of its variance by parametric bootstrap. We conduct a simulation study to check the behavior of the proposed estimator and its variance estimator. Finally, we show that the proposed estimator outperforms some competitors used to estimate the mean population income for the SILC data.