- Graf, Eric

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# Graf, Eric

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Graf, Eric

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- PublicationMÃ©tadonnÃ©es seulementImputation of Income Data with Generalized Calibration Procedure and GB2 distribution: Illustration with SILC data
Montrer plus In sample surveys of households and persons, questions about income are important variables and often sensitive and thus subject to a higher nonresponse rate. The distribution of such collected incomes is neither normal, nor log-normal. Hypotheses of classical regression models to explain the income (or their log) are not satisfied. Imputations using such models modify the original and true distribution of the data which is not. Empirical studies have shown that the generalized beta distribution of the second kind (GB2) it fits income data very well. We present a parametric method of imputation relying on weights obtained by generalized calibration. A GB2 distribution is fitted on the income distribution in order to assess that these weights can compensate for nonignorable nonresponse that affects the variable of interest. The success of the operation greatly depends on the choice of auxiliary and instrumental variables used for calibration, which we discuss. We validate our imputation system on data from the Swiss Survey on Income and Living Conditions (SILC) and compare it to imputations performed through the use of IVEware software running on SAS. We have made great efforts to estimate variances through linearization, taking all the steps of our procedure into account.Montrer plus - PublicationMÃ©tadonnÃ©es seulementVariance Estimation for Regression Imputed Quantiles and Inequality Indicators
Montrer plus This work is done in the framework of sampling theory. It is based on a scenario in which a sample survey has been carried out and only a sub-part of the selected sample has accepted to answer (total non-response). Moreover, some respondents did not answer all questions (partial non-response). This is common scenario in practice. We are particularly interested in income type variables. Generally, total non-response is treated by re-weighting and partial non-response through imputation. One further supposes here that the imputation is carried out by a regression model adjusted on the respondents. We then resume the idea presented by \citet{dev:sar:94} and tested afterwards by \citet{LeeRancSar:1994} which consists in constructing an unbiased estimator of the variance of a total based solely on the information at our disposal: the information known on the selected sample and the subset of respondents. While the two cited articles dealt with the exercise for a conventional total of an interest variable $y$, we reproduce here a similar development in the case where the considered total is one of the linearized variable of quantiles or of inequality indicators, and that, furthermore, it is computed from the imputed variable $y$. We show by means of simulations that regression imputation can have an important impact on the bias estimation as well as on the variance estimation of inequality indicators. This leads us to a method capable of taking into account the variance due to imputation in addition to the one due to the sampling design in the cases of quantiles. This method could be generalized to some of the inequality indicators.Montrer plus