Linking Two Groups — linking

This function performs (robust) Haebara linking or Stocking-Lord for two groups in the 2PL model. There is also an option for simultaneous estimation in which joint item parameters should also be estimated.

Usage

linking_2groups(pars, method, type="asymm", pow=2, eps=0.001, simultan=FALSE,
     Theta=seq(-6, 6, len=101), wgt=NULL, par_init=NULL, optimizer="nlminb",
     control_optimizer=list())

Arguments

pars: Matrix containing item parameters that must have columns with names a1, b1, a2, and b2.
method: Linking method. Can be SL (Stocking-Lord) or Hae (Haebara).
type: Type of linking function. Can be "asymm" or "symm" for asymmetric or symmetric linking, respectively.
pow: Power used in the loss function. The values should be larger than or equal than zero. The default values is 2.
eps: Tuning parameter in numerical differentiation
simultan: Logical indicating whether joint item parameters should be simultaneously estimated
Theta: Theta grid
wgt: Weights for theta grid
par_init: Initial vector for parameters
optimizer: Chosen optimizer. Can be "nlminb" or "optim".
control_optimizer: Control arguments for optimizer

Value

List with following entries

par: Estimated linking parameters
$...$: More values

Examples

if (FALSE) {
#############################################################################
# EXAMPLE 1: data.ex16 from TAM package
#############################################################################

#- extract dataset
data(data.ex16, package="TAM")
dat <- data.ex16
items <- colnames(dat)[-c(1,2)]

# fit grade 1
rdat1 <- TAM::tam_remove_missings( dat[ dat$grade==1, ], items=items )
mod1 <- sirt::rasch.mml2( dat=rdat1$resp[, rdat1$items], est.a=1:length(rdat1$items) )

# fit grade 2
rdat2 <- TAM::tam_remove_missings( dat[ dat$grade==2, ], items=items )
mod2 <- sirt::rasch.mml2( dat=rdat2$resp[, rdat2$items], est.a=1:length(rdat2$items) )

# merge item parameters of separate scalings
item1 <- mod1$item[, c("item", "a","b") ]
colnames(item1)[2:3] <- c("a1","b1")
item2 <- mod2$item[, c("item", "a","b") ]
colnames(item2)[2:3] <- c("a2","b2")
pars <- merge(x=item1, y=item2, by="item")

# choose theta grid
Theta <- seq(-6,6, len=101)
wgt <- sirt::sirt_dnorm_discrete(x=Theta, mean=0, sd=2)

#- robust Haebara linking with powers 0.5 or 0 and different types
res1 <- sirt::linking_2groups(pars=pars, method="Hae", type="asymm",
              Theta=Theta, wgt=wgt, pow=0.5, eps=0.001 )
res2 <- sirt::linking_2groups(pars=pars, method="Hae", type="symm",
              Theta=Theta, wgt=wgt, pow=0, eps=0.01 )
res1$par  # linking parameter estimate
res2$par
}