tam.linking: Linking of Fitted Unidimensional Item Response Models in TAM

Description

Performs linking of fitted unidimensional item response models in TAM according to the Stocking-Lord and the Haebara method (Kolen & Brennan, 2014; Gonzales & Wiberg, 2017). Several studies are linking by a chain of linkings of two studies. The linking of two studies is implemented in the tam_linking_2studies function.

Usage

tam.linking(tamobj_list, type="SL", theta=NULL, wgt=NULL, fix.slope=FALSE,
   verbose=TRUE)
# S3 method for tam.linking
summary(object, file=NULL, …)
# S3 method for tam.linking
print(x, …)
tam_linking_2studies( B1, AXsi1, guess1, B2, AXsi2, guess2, theta, wgt, type,
    M1=0, SD1=1, M2=0, SD2=1, fix.slope=FALSE)
# S3 method for tam_linking_2studies
summary(object, file=NULL, …)
# S3 method for tam_linking_2studies
print(x, …)

Arguments

tamobj_list

List of fitted objects in TAM

type

Type of linking method: "SL" (Stocking-Lord) or "Hae" (Haebara). The default is the Stocking-Lord method.

theta

Grid of $θ$ points. The default is seq(-6,6,len=101).

wgt

Weights defined for the theta grid. The default is tam_normalize_vector( stats::dnorm( theta, sd=2 )).

fix.slope

Logical indicating whether the slope transformation constant is fixed to 1.

verbose

Logical indicating progress of linking computation

object

Object of class tam.linking or tam_linking_2studies.

file

A file name in which the summary output will be written

…

Further arguments to be passed

Array $B$ for first study

AXsi1

Matrix $A ξ$ for first study

guess1

Guessing parameter for first study

Array $B$ for second study

AXsi2

Matrix $A ξ$ for second study

guess2

Guessing parameter for second study

Mean of first study

SD1

Standard deviation of first study

Mean of second study

SD2

Standard deviation of second study

Value

List containing entries

parameters_list

List containing transformed item parameters

linking_list

List containing results of each linking in the linking chain

M_SD

Mean and standard deviation for each study after linking

trafo_items

Transformation constants for item parameters

trafo_persons

Transformation constants for person parameters

References

Battauz, M. (2015). equateIRT: An R package for IRT test equating. Journal of Statistical Software, 68(7), 1-22.

Gonzalez, J., & Wiberg, M. (2017). Applying test equating methods: Using R. New York, Springer.

Kolen, M. J., & Brennan, R. L. (2014). Test equating, scaling, and linking: Methods and practices. New York, Springer.

Weeks, J. P. (2010). plink: An R package for linking mixed-format tests using IRT-based methods. Journal of Statistical Software, 35(12), 1-33.

Examples

Run this code

# NOT RUN {
#############################################################################
# EXAMPLE 1: Linking dichotomous data with the 2PL model
#############################################################################

data(data.ex16)
dat <- data.ex16
items <- colnames(dat)[-c(1,2)]

# fit grade 1
rdat1 <- TAM::tam_remove_missings( dat[ dat$grade==1, ], items=items )
mod1 <- TAM::tam.mml.2pl( resp=rdat1$resp[, rdat1$items], pid=rdat1$dat$idstud )
summary(mod1)

# fit grade 2
rdat2 <- TAM::tam_remove_missings( dat[ dat$grade==2, ], items=items )
mod2 <- TAM::tam.mml.2pl( resp=rdat2$resp[, rdat2$items], pid=rdat2$dat$idstud )
summary(mod2)

# fit grade 3
rdat3 <- TAM::tam_remove_missings( dat[ dat$grade==3, ], items=items )
mod3 <- TAM::tam.mml.2pl( resp=rdat3$resp[, rdat3$items], pid=rdat3$dat$idstud )
summary(mod3)

# define list of fitted models
tamobj_list <- list( mod1, mod2, mod3 )

#-- link item response models
lmod <- TAM::tam.linking( tamobj_list)
summary(lmod)

# estimate WLEs based on transformed item parameters
parm_list <- lmod$parameters_list

# WLE grade 1
arglist <- list( resp=mod1$resp, B=parm_list[[1]]$B, AXsi=parm_list[[1]]$AXsi )
wle1 <- TAM::tam.mml.wle(tamobj=arglist)

# WLE grade 2
arglist <- list( resp=mod2$resp, B=parm_list[[2]]$B, AXsi=parm_list[[2]]$AXsi )
wle2 <- TAM::tam.mml.wle(tamobj=arglist)

# WLE grade 3
arglist <- list( resp=mod3$resp, B=parm_list[[3]]$B, AXsi=parm_list[[3]]$AXsi )
wle3 <- TAM::tam.mml.wle(tamobj=arglist)

#############################################################################
# EXAMPLE 2: Linking polytomous data with the partial credit model
#############################################################################

data(data.ex17)
dat <- data.ex17

items <- colnames(dat)[-c(1,2)]

# fit grade 1
rdat1 <- TAM::tam_remove_missings( dat[ dat$grade==1, ], items=items )
mod1 <- TAM::tam.mml.2pl( resp=rdat1$resp[, rdat1$items], pid=rdat1$dat$idstud )
summary(mod1)

# fit grade 2
rdat2 <- TAM::tam_remove_missings( dat[ dat$grade==2, ], items=items )
mod2 <- TAM::tam.mml.2pl( resp=rdat2$resp[, rdat2$items], pid=rdat2$dat$idstud )
summary(mod2)

# fit grade 3
rdat3 <- TAM::tam_remove_missings( dat[ dat$grade==3, ], items=items )
mod3 <- TAM::tam.mml.2pl( resp=rdat3$resp[, rdat3$items], pid=rdat3$dat$idstud )
summary(mod3)

# list of fitted TAM models
tamobj_list <- list( mod1, mod2, mod3 )

#-- linking: fix slope because partial credit model is fitted
lmod <- TAM::tam.linking( tamobj_list, fix.slope=TRUE)
summary(lmod)

# WLEs can be estimated in the same way as in Example 1.

#############################################################################
# EXAMPLE 3: Linking dichotomous data with the multiple group 2PL models
#############################################################################

data(data.ex16)
dat <- data.ex16
items <- colnames(dat)[-c(1,2)]

# fit grade 1
rdat1 <- TAM::tam_remove_missings( dat[ dat$grade==1, ], items=items )
# create some grouping variable
group <- ( seq( 1, nrow( rdat1$dat ) ) %% 3 ) + 1
mod1 <- TAM::tam.mml.2pl( resp=rdat1$resp[, rdat1$items], pid=rdat1$dat$idstud, group=group)
summary(mod1)

# fit grade 2
rdat2 <- TAM::tam_remove_missings( dat[ dat$grade==2, ], items=items )
group <- 1*(rdat2$dat$dat$idstud > 500)
mod2 <- TAM::tam.mml.2pl( resp=rdat2$resp[, rdat2$items], pid=rdat2$dat$dat$idstud, group=group)
summary(mod2)

# fit grade 3
rdat3 <- TAM::tam_remove_missings( dat[ dat$grade==3, ], items=items )
mod3 <- TAM::tam.mml.2pl( resp=rdat3$resp[, rdat3$items], pid=rdat3$dat$idstud )
summary(mod3)

# define list of fitted models
tamobj_list <- list( mod1, mod2, mod3 )

#-- link item response models
lmod <- TAM::tam.linking( tamobj_list)

#############################################################################
# EXAMPLE 4: Linking simulated dichotomous data with two groups
#############################################################################

library(sirt)

#*** simulate data
N <- 3000  # number of persons
I <- 30    # number of items
b <- seq(-2,2, length=I)
# data for group 1
dat1 <- sirt::sim.raschtype( rnorm(N, mean=0, sd=1), b=b )
# data for group 2
dat2 <- sirt::sim.raschtype( rnorm(N, mean=1, sd=.6), b=b )

# fit group 1
mod1 <- TAM::tam.mml.2pl( resp=dat1 )
summary(mod1)

# fit group 2
mod2 <- TAM::tam.mml.2pl( resp=dat2 )
summary(mod2)

# define list of fitted models
tamobj_list <- list( mod1, mod2 )

#-- link item response models
lmod <- TAM::tam.linking( tamobj_list)
summary(lmod)

# estimate WLEs based on transformed item parameters
parm_list <- lmod$parameters_list

# WLE grade 1
arglist <- list( resp=mod1$resp, B=parm_list[[1]]$B, AXsi=parm_list[[1]]$AXsi )
wle1 <- TAM::tam.mml.wle(tamobj=arglist)

# WLE grade 2
arglist <- list( resp=mod2$resp, B=parm_list[[2]]$B, AXsi=parm_list[[2]]$AXsi )
wle2 <- TAM::tam.mml.wle(tamobj=arglist)
summary(wle1)
summary(wle2)

# estimation with linked and fixed item parameters for group 2
B <- parm_list[[2]]$B
xsi.fixed <- cbind( 1:I, -parm_list[[2]]$AXsi[,2] )
mod2f <- TAM::tam.mml( resp=dat2, B=B, xsi.fixed=xsi.fixed )
summary(mod2f)
# }

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