Hello, I am working with others here on a tool that will help developing countries measure local poverty at lower cost by using a short scale. We calibrate a short scale to an established scale on an older national survey and then conduct new surveys with the short scale. To estimate the variances of estimates based on the short scale with the new surveys, I am using Rubin's formula for combining imputation variance (caused by not asking all scale items) with survey sampling variance (of survey 2 short scale). The estimates of imputation variance come from imputing the full scale based on the short scale report in the second survey and the calibration model fit on the first survey. Now I am looking for a rule of thumb for planning the size of the second survey. Some sort of design effect due to increased measurement variance at the household level. Anyone have any intuition on this or examples of similar work? If one can obtain an 80% R-square for the full scale based on the short scale, would that suggest an extra design effect on the order of 1.2 beyond design effects caused by any clustering and/or differential weighting?
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