multiEquatError: 1pl linking errors for three measurement occasions

In weirichs/eatModel: Educational Assessment Tools for IRT Modeling using Conquest or TAM

1pl linking errors for three measurement occasions

Description

Function combines linking errors based on the 1pl linking procedure according to equat1pl for three measurement occasions.

Usage

multiEquatError (eq.1_2, eq.2_3, eq.1_3, dependentDIF =FALSE, verbose=TRUE)

Arguments

eq.1_2	The object returned by equat1pl for linking the first and second measurement occasion.
eq.2_3	The object returned by equat1pl for linking the second and third measurement occasion.
eq.1_3	The object returned by equat1pl for linking the first and third measurement occasion.
dependentDIF	Logical. If DIF is assumed to be correlated between measurement occasions one and two versus two and three, this covariance will be taken into account. If the assumption of linear dependency does not seem reasonable, this option possibly results in overfitting and underestimation of the true linking error.
verbose	Logical: print linking informations to console?

Value

A list of data.frames with linking errors, according to the number of domains. The output is intended to be used as argument of the replaceLinkingError function.

Author(s)

Sebastian Weirich

References

Monseur, C., & Berezner, A. (2007). The Computation of Equating Errors in International Surveys in Education. Journal of Applied Measurement 8(3): 323-335.

Examples

data(trends)

################################################################################
###    Example 1: Linking for three measurement occasions and one domain     ###
################################################################################

# calibrate all three measurements, using a unidimensional model each
# (only reading, no testlets, no jackknife)
results <- by(data = trends, INDICES = trends[,"year"], FUN = function (y){
           dat <- reshape2::dcast(subset ( y, domain == "reading"), idstud~item, value.var="value")
           def <- defineModel(dat=dat, items= -1, id="idstud", software="tam")
           run <- runModel(def)
           res <- getResults(run)
           return(res)})
items   <- lapply(results, itemFromRes)
eq.1_2  <- equat1pl(items[[1]][,c("item", "est")], items[[2]][,c("item", "est")],difBound = 0.64, iterativ = TRUE)
eq.2_3  <- equat1pl(items[[2]][,c("item", "est")], items[[3]][,c("item", "est")],difBound = 0.64, iterativ = TRUE)
eq.1_3  <- equat1pl(items[[1]][,c("item", "est")], items[[3]][,c("item", "est")],difBound = 0.64, iterativ = TRUE)
lErrors <- multiEquatError(eq.1_2, eq.2_3, eq.1_3)

# dependent DIF
lErrDif <- multiEquatError(eq.1_2, eq.2_3, eq.1_3, dependentDIF =TRUE)

# Following code demonstrates the replacement of old linking error in the 'equatingList' object
# for further processing
# direct linking 1 to 3 (1 is reference)
eq1.vs.3<- equat1pl(results[[3]], prmNorm = items[[1]][,c("item", "est")], difBound = 0.64, iterativ = TRUE)

# replace 'direct' linking error with 'indirect' linking error from 'multiEquatError()'
eq1.vs.3<- replaceLinkingError (equatingList=eq1.vs.3, multiEquatError_output=lErrors)


################################################################################
###    Example 2: Linking for three measurement occasions and two domains    ###
################################################################################

# calibrate all three measurements, using a unidimensional model each
# reading and listening are handled subsequently, using the model split function
results2<- by(data = trends, INDICES = trends[,"year"], FUN = function (y){
           qmat<- unique(y[ ,c("item","domain")])
           qmat<- data.frame ( qmat[,"item", drop=FALSE], model.matrix(~domain-1, data = qmat))
           spl <- splitModels ( qMatrix = qmat,  nCores = 1)
           dat <- reshape2::dcast(y, idstud~item, value.var="value")
           def <- defineModel(dat=dat, splittedModels = spl, id="idstud", software="tam")
           run <- runModel(def)
           res <- getResults(run)
           return(res)})
eq.1_2  <- equat1pl(results2[[1]], itemFromRes(results2[[2]])[,c("item", "est")],difBound = 0.64, iterativ = TRUE)
eq.2_3  <- equat1pl(results2[[2]], itemFromRes(results2[[3]])[,c("item", "est")],difBound = 0.64, iterativ = TRUE)
eq.1_3  <- equat1pl(results2[[1]], itemFromRes(results2[[3]])[,c("item", "est")],difBound = 0.64, iterativ = TRUE)
lErrors2<- multiEquatError(eq.1_2, eq.2_3, eq.1_3, dependentDIF =TRUE)

# direct linking 1 to 3 (1 is reference)
it1     <- itemFromRes(results2[[1]])
eq1.vs.3<- equat1pl(results2[[3]], prmNorm = it1[,c("item", "est")], difBound = 0.64, iterativ = TRUE)

# replace 'direct' linking error with 'indirect' linking error from 'multiEquatError()'
eq1.vs.3<- replaceLinkingError (equatingList=eq1.vs.3, multiEquatError_output=lErrors2)


################################################################################
###    Example 3: Jackknife linking for three measurement and two domains    ###
################################################################################

# we reuse the previously created object 'results2' here
eq.1_2  <- equat1pl(results2[[1]], itemFromRes(results2[[2]])[,c("item", "est")] |> dplyr::mutate(testlet = substr(item,1,3)), item = "item", testlet = "testlet", value = "est", difBound = 0.64, iterativ = TRUE)
eq.2_3  <- equat1pl(results2[[2]], itemFromRes(results2[[3]])[,c("item", "est")] |> dplyr::mutate(testlet = substr(item,1,3)), item = "item", testlet = "testlet", value = "est", difBound = 0.64, iterativ = TRUE)
eq.1_3  <- equat1pl(results2[[1]], itemFromRes(results2[[3]])[,c("item", "est")] |> dplyr::mutate(testlet = substr(item,1,3)), item = "item", testlet = "testlet", value = "est", difBound = 0.64, iterativ = TRUE)
lErrors3<- multiEquatError(eq.1_2, eq.2_3, eq.1_3, dependentDIF =TRUE)


################################################################################
###            Example 4: Linking for three item parameter lists             ###
################################################################################

# use three item parameter lists for equating
# borrow item parameter data from the 'sirt' package
data(data.pars1.rasch, package="sirt")

# use the first three item parameter lists
e1 <- subset ( data.pars1.rasch, study == "study1")[,c("item", "b")]
e2 <- subset ( data.pars1.rasch, study == "study2")[,c("item", "b")]
e3 <- subset ( data.pars1.rasch, study == "study3")[,c("item", "b")]

# pairwise linking
eq.1_2 <- equat1pl(e1, e2,difBound = 0.64, iterativ = TRUE)
eq.2_3 <- equat1pl(e2, e3,difBound = 0.64, iterativ = TRUE)
eq.1_3 <- equat1pl(e1, e3,difBound = 0.64, iterativ = TRUE)
multiEquatError(eq.1_2, eq.2_3, eq.1_3)

weirichs/eatModel documentation built on June 11, 2025, 4:19 p.m.