Linearly transform a set of IRT parameters to bring them
to the scale of another set of parameters. Four methods
are implemented: Mean/Mean, Mean/Sigma, Lord-Stocking,
and Haebara.
A set of parameters that are already on the
desired scale
new.ip
A set of parameters that must be placed on
the same scale as old.ip
old.items
A vector of indexes pointing to those
items in old.ip that are common to both sets of
parameters
new.items
The indexes of the same items in
new.ip
old.qu
A quadrature object for old.ip,
typically produced by the same program that estimated
old.ip. Only needed if method="LS" or
method="HB"
new.qu
A quadrature object for new.ip,
typically produced by the same program that estimated
new.ip. Only needed if method="HB"
method
One of "MM" (Mean/Mean), "MS" (Mean/Sigma),
"SL" (Stocking-Lord), or "HB" (Haebara). Default is "MS"
bec
Use back-equating correction? When TRUE, the
Stocking-Lord or Hebaera procedures will be adjusted for
back-equating (see Hebaera, 1980). Ignored when method is
MM or MS. Default is FALSE.
Value
A list of:
slope
The slope of the linear
transformation
intercept
The intercept of the
linear transformation
scaled.ip
The parameters in
new.ip tranformed to a scale that is compatible
with old.ip
Author(s)
Ivailo Partchev and Tamaki Hattori
References
Kolen, M.J. & R.L. Brennan (1995) Test Equating: Methods
and Practices. Springer.
Haebara, T. (1980) Equating logistic ability scales by a
weighted lest squares method. Japanese Psychological
Research, 22, p.144–149
Examples
## Not run:
# a small simulation to demonstrate transformation to a common scale
# fake 50 2PL items
pa <- cbind(runif(50,.8,2), runif(50,-2.4,2.4), rep(0,50))
# simulate responses with two samples of different ability levels
r.1 <- sim(ip=pa[1:30,], x=rnorm(1000,-.5))
r.2 <- sim(ip=pa[21:50,], x=rnorm(1000,.5))
# estimate item parameters
p.1 <- est(r.1, engine="ltm")
p.2 <- est(r.2, engine="ltm")
# plot difficulties to show difference in scale
plot(c(-3,3), c(-3,3), ty="n", xlab="True",ylab="Estimated",
main="Achieving common scale")
text(pa[1:30,2], p.1$est[,2], 1:30)
text(pa[21:50,2], p.2$est[,2], 21:50, co=2)
# scale with the default Mean/Sigma method
pa.sc = sca(old.ip=p.1$est, new.ip=p.2$est, old.items=21:30, new.items=1:10)
# add difficulties of scaled items to plot
text(pa[21:50,2], pa.sc$scaled.ip[,2], 21:50, co=3)
## End(Not run)