Analysis

In recent years, there has been a strong interest in indirect measures of nonresponse bias in surveys or other forms of data collection. This interest originates from gradually decreasing propensities to respond to surveys parallel to pressures on survey budgets. These developments led to a growing focus on the representativeness or balance of the responding sample units with respect to relevant auxiliary variables. One example of a measure is the representativeness indicator, or R-indicator. The R-indicator is based on the design-weighted sample variation of estimated response propensities. It pre-supposes linked auxiliary data. One of the criticisms of the indicator is that it cannot be used in settings where auxiliary information is available only at the population level. In this paper, we propose a new method for estimating response propensities that does not need auxiliary information for non-respondents to the survey and is based on population auxiliary information. These population-based response propensities can then be used to develop R-indicators that employ population contingency tables or population frequency counts. We discuss the statistical properties of the indicators, and evaluate their performance using an evaluation study based on real census data and an application from the Dutch Health Survey.

Propensity weighting is a procedure to adjust for unit nonresponse in surveys. A form of implementing this procedure consists of dividing the sampling weights by estimates of the probabilities that the sampled units respond to the survey. Typically, these estimates are obtained by fitting parametric models, such as logistic regression. The resulting adjusted estimators may become biased when the specified parametric models are incorrect. To avoid misspecifying such a model, we consider nonparametric estimation of the response probabilities by local polynomial regression. We study the asymptotic properties of the resulting estimator under quasi-randomization. The practical behavior of the proposed nonresponse adjustment approach is evaluated on NHANES data.

The weighting cell estimator corrects for unit nonresponse by dividing the sample into homogeneous groups (cells) and applying a ratio correction to the respondents within each cell. Previous studies of the statistical properties of weighting cell estimators have assumed that these cells correspond to known population cells with homogeneous characteristics. In this article, we study the properties of the weighting cell estimator under a response probability model that does not require correct specification of homogeneous population cells. Instead, we assume that the response probabilities are a smooth but otherwise unspecified function of a known auxiliary variable. Under this more general model, we study the robustness of the weighting cell estimator against model misspecification. We show that, even when the population cells are unknown, the estimator is consistent with respect to the sampling design and the response model. We describe the effect of the number of weighting cells on the asymptotic properties of the estimator. Simulation experiments explore the finite sample properties of the estimator. We conclude with some guidance on how to select the size and number of cells for practical implementation of weighting cell estimation when those cells cannot be specified a priori.

In recent years, there has been a strong interest in indirect measures of nonresponse bias in surveys or other forms of data collection. This interest originates from gradually decreasing propensities to respond to surveys parallel to pressures on survey budgets. These developments led to a growing focus on the representativeness or balance of the responding sample units with respect to relevant auxiliary variables. One example of a measure is the representativeness indicator, or R-indicator. The R-indicator is based on the design-weighted sample variation of estimated response propensities. It pre-supposes linked auxiliary data. One of the criticisms of the indicator is that it cannot be used in settings where auxiliary information is available only at the population level. In this paper, we propose a new method for estimating response propensities that does not need auxiliary information for non-respondents to the survey and is based on population auxiliary information. These population-based response propensities can then be used to develop R-indicators that employ population contingency tables or population frequency counts. We discuss the statistical properties of the indicators, and evaluate their performance using an evaluation study based on real census data and an application from the Dutch Health Survey.

Propensity weighting is a procedure to adjust for unit nonresponse in surveys. A form of implementing this procedure consists of dividing the sampling weights by estimates of the probabilities that the sampled units respond to the survey. Typically, these estimates are obtained by fitting parametric models, such as logistic regression. The resulting adjusted estimators may become biased when the specified parametric models are incorrect. To avoid misspecifying such a model, we consider nonparametric estimation of the response probabilities by local polynomial regression. We study the asymptotic properties of the resulting estimator under quasi-randomization. The practical behavior of the proposed nonresponse adjustment approach is evaluated on NHANES data.

The weighting cell estimator corrects for unit nonresponse by dividing the sample into homogeneous groups (cells) and applying a ratio correction to the respondents within each cell. Previous studies of the statistical properties of weighting cell estimators have assumed that these cells correspond to known population cells with homogeneous characteristics. In this article, we study the properties of the weighting cell estimator under a response probability model that does not require correct specification of homogeneous population cells. Instead, we assume that the response probabilities are a smooth but otherwise unspecified function of a known auxiliary variable. Under this more general model, we study the robustness of the weighting cell estimator against model misspecification. We show that, even when the population cells are unknown, the estimator is consistent with respect to the sampling design and the response model. We describe the effect of the number of weighting cells on the asymptotic properties of the estimator. Simulation experiments explore the finite sample properties of the estimator. We conclude with some guidance on how to select the size and number of cells for practical implementation of weighting cell estimation when those cells cannot be specified a priori.