Summary:
When the sample design of a survey is complex, design-based analysis should be
performed. This kind of analysis takes into account the stages of the complex
design and the survey weights. In order to deal with unit nonresponse, the
survey weights are properly adjusted so that the respondent weighted sample
is representative of the population. To perform such a correction the
researcher must collect data for non responders. Then, using the available
information, weighting classes are created. Within these classes response
probabilities are considered constant. The corresponding adjusted weight is the
product of the inverse of the estimated response probability and the survey
weight. Subsequent adjustments can be performed in order to conform the
respondent sample distribution to distributions from an external source, such
as population census.
The second type of non response we dealt with, is item non response. Two broad
categories of methods are usually employed to address this issue. Inverse
probability weighting and multiple imputation.
Standard multiple imputation methods can be modified to incorporate design
features. We used the fully adjusted weights to incorporate design features
into the imputation model first by weighting the imputation model, and second
by including them as a predictor in the imputation model. Alternative
approaches that we did not implement are stratified imputations and multilevel
imputation models.
Inverse probability weighting method and doubly robust estimator are easily
implemented using statistical software, and yielded similar estimates as
multiple imputation. The main drawback, is that variance estimates and
confidence intervals were computed using bootstrap methods, thus they were not
as precise as the ones obtained using multiple imputation. Moreover, the
structure of the missing data in a survey setting, do not allow the use of
these methods.
To conclude, when handling item non response in a survey setting, a good
practice is to perform multiple imputation using the fully adjusted weights as
a covariate. This practice is both theoretically sound and easily implemented
using statistical software such as Stata.
Keywords:
Survey data, Nonresponse, Missing data, Inverse probability weighting, Multiple imputation
