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A Standard Estimation Approach that Adjusts for Non-Response
The rules for the choice of auxiliary variables to be included in the response modelling, along with how this choice interacts with strategies for making the predictions from the response modelling more robust, were examined. Firstly, the over-specification of the response propensity model can potentially cause an increase in the standard errors of the regression parameters, which can lead to inefficient estimates. One possible solution to overcome this problem is to use model selection methods to choose a parsimonious statistical model from a set of candidate statistical models (i.e. eliminate irrelevant explanatory variables in the response propensity model). Secondly, the mis-specification of the response propensity model can be a potential cause for extreme response propensity weight adjustments (i.e. inverse of estimated response propensity), which can lead to inefficient estimates, as well as potentially unreasonable estimates particularly for domains. One possible solution to overcome this problem is to trim the extreme response propensity weight adjustments.
The proposed modified boxplot method (based on Tukey's boxplot method for the identification of outliers) appeared to provide a suitable treatment for trimming extreme estimated response probability weight adjustments. The AIC selection method (an information criteria method based on the likelihood function of the model plus a penalty term) also appeared to provide a suitable semi-automated method for choosing auxiliary variables in the logistic regression. The proposed modified boxplot method and the AIC selection method performed well across various simulations and can be fully automated without the need for any user interaction.
The value of models that specifically incorporate the impact of follow-up strategies on the probability of unit response was also considered. Where different follow-up approaches are assigned randomly, an indicator of the follow-up strategy should not be included in estimation. However, where the follow-up is assigned deterministically, consideration should be given for inclusion in estimation, particularly where it identifies a particular type of unit that may have distinctive values for the study variables, so that that type of unit is appropriately represented in the estimates.
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