Polynomial rank-score representations at several tuning values
Source:R/poly-ranks.R
riposte_poly_reps.RdReturns a named list of representation functions, one per value of zeta,
for riposte_test() or riposte_components(). Combining them gives a test
that responds to gains concentrated at the top of each block across several
weightings instead of one.
Arguments
- zeta
vector of tuning values, each
>= 1.- tail
"upper"(default) or"lower", passed toriposte_poly_scores().
Value
a named list of representation functions, named poly2, poly7, ...
for the upper tail and polylow2, polylow7, ... for the lower tail.
Details
The default, c(2, 7, 12, 17, 22), is the set in Bowers and Burton's
rank-score tables, chosen for blocks of 50 units with 25 treated. For other
designs, supply your own values; the vignette shows how to choose them. In
brief: the largest zeta near n_b / m - 1 targets gains confined to about
m units per block; and two scores at zeta and zeta' correlate at about
2 sqrt(u v) / (u + v) with u = 2 zeta - 1 and v = 2 zeta' - 1, so
values whose 2 zeta - 1 grow by a constant factor (for example zeta = 2, 5, 14, 41, where 2 zeta - 1 triples) are evenly spaced, while equal steps in
zeta give neighbours whose correlation approaches 1.
zeta = 2 is the rank rescaled. When it is added to
riposte_reps_default(), which already holds the rank, leave it out:
c(riposte_reps_default(), riposte_poly_reps(c(7, 12, 17, 22))).
With tail = "lower" the scores weight the bottom of each block, for a
treatment that lowers the outcomes of a few units; see
riposte_poly_scores() and vignette("harm").