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APPENDIX 2 REPLICATE WEIGHTS TECHNIQUE
DERIVATION OF REPLICATE WEIGHTS
The delete-a-group jackknife method of replicate weighting was used to derive weights, through the following process:
APPLICATION OF REPLICATE WEIGHTS
As noted above, replicate weights enable variances of estimates to be calculated relatively simply. They also enable unit records analyses such as chi-square and logistic regression to be conducted, which take into account the sample design. Replicate weights for any variable of interest can be calculated from the 60 replicate groups, giving 60 replicate estimates. The distribution of this set of replicate estimates, in conjunction with the full sample estimate (based on the general weight) is then used to approximate the variance of the full sample.
The formula for calculating the Standard error (SE) and relative standard error (RSE) of an estimate using this method is shown below.
This method can also be used when modelling relationships from unit record data, regardless of the modelling technique used. In modelling, the full sample would be used to estimate the parameter being studied, such as a regression co-efficient, the 60 replicate groups used to provide 60 replicate estimates of the survey parameter. The variance of the estimate of the parameter from the full sample is then approximated, as above, by the variability of the replicate estimates.
USE OF REPLICATE WEIGHTS WITH STATISTICAL PACKAGES
Not all statistical computer packages may allow direct calculation of SEs using the delete-a-group jackknife replicate weights. However, those packages that allow the direct use of Balanced Repeated Replication (BRR) methodology generally include the option of an adjustment factor. This factor can be incorporated to overcome the difference between the variance formulae.
AVAILABILITY OF RSES CALCULATED USING REPLICATE WEIGHTS
Actual RSEs were used in the summary publication released from this survey. The RSEs for estimates published in the National Survey of Mental Health and Wellbeing: Summary of Results, 2007 (cat. no. 4326.0) are available from the ABS website <www.abs.gov.au> in spreadsheet format. The RSEs in the spreadsheets were calculated using the replicate weights methodology. Other RSEs for survey estimates are available on request. For more information see 'Survey products' in Chapter 11.
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