\(\hat V = \sum_r (\hat\theta_r - \hat\theta)^2 / (R(1-k)^2)\).
Usage
morie_brr_variance(estimates, full_estimate = NULL, fay_k = 0)
Arguments
- estimates
replicate estimates.
- full_estimate
the full-sample estimate; the replicate mean is
used when NULL.
- fay_k
the Fay factor used to build the replicates.
Value
list with variance, se, n_replicates,
estimate, cv.
Details
The replicate estimates must come from re-running the WHOLE
procedure – weighting, calibration, imputation and all – not just
the final formula on reweighted data. A variance that ignores the
weighting steps understates the uncertainty those steps introduced.
The \((1-k)^2\) divisor is mandatory under a Fay adjustment.
Omitting it inflates the variance by \(1/(1-k)^2\), which at
k = 0.3 is a 104% overstatement.
References
Wolter, K. M. (2007). Introduction to Variance
Estimation, 2nd ed., Ch. 3. Springer.
Examples
round(morie_brr_variance(c(1.9, 2.1, 2.2, 1.8), full_estimate = 2)$se, 4)
#> [1] 0.1581
