Returns the multiplier \(c\) in the replicate-variance formula
\(V = c \sum_r (\hat\theta_r - \hat\theta_0)^2\), for the common
large-scale-assessment replication designs.
Usage
rep_factor(method = c("BRR", "JK2", "JK1"), n_rep, fay = 0.5)
Arguments
- method
One of "BRR" (balanced repeated replication, the PISA
default), "JK2" (paired jackknife, used by TIMSS/PIRLS), or "JK1".
- n_rep
Number of replicate weights.
- fay
Fay's adjustment factor for BRR (PISA uses 0.5). Must lie in
\([0, 1)\). Ignored for jackknife methods.
Value
A single numeric multiplier.
Details
BRR/Fay: \(c = 1 / (R (1 - k)^2)\), where k is fay. With fay = 0
this is ordinary BRR (\(1/R\)); with fay = 0.5 (PISA) it is \(4/R\).
JK2 (IEA paired-zone construction): \(c = 1\).
JK1 (single-stratum / equal-zone): \(c = (R - 1) / R\).
References
OECD (2009). PISA Data Analysis Manual: SPSS and SAS, Second Edition.
OECD Publishing. (Replicate-weight variance estimation.)
Examples
rep_factor("BRR", n_rep = 80, fay = 0.5) # PISA: 1/20
#> [1] 0.05
rep_factor("JK2", n_rep = 75) # TIMSS/PIRLS: 1
#> [1] 1
