Can Calibration Be Used to Adjust for “Nonignorable” Nonresponse?
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Calibration can be used to adjust for unit nonresponse when the model
variables on which the response/nonresponse mechanism depends do
not coincide with the benchmark variables in the calibration equation.
As a result, model-variable values need only known for the
respondents. This allows the treatment of what is usually considered
nonignorable nonresponse. Although one can invoke either quasirandomization
or prediction-model-based theory to justify the
calibration, both frameworks rely on unverifiable model assumptions,
and both require large samples to produce nearly unbiased estimators
even when those assumptions hold. We will explore these issues
theoretically and with an empirical study.