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 computes linking errors based on the 1pl linking procedure according to equating.rasch from the sirt package for three measurement occasions.

Usage

multiEquatError (x1, x2, x3, difBound = 1, dependentDIF =FALSE, testletStr = NULL, verbose = TRUE )

Arguments

x1	The object returned by getResults for the first measurement occasion. Alternatively, a data.frame with two columns. First column: item identifier. Second column: item difficulty parameter.
x2	The object returned by getResults for the second measurement occasion. Alternatively, a data.frame with two columns. First column: item identifier. Second column: item difficulty parameter.
x3	The object returned by getResults for the third measurement occasion. Alternatively, a data.frame with two columns. First column: item identifier. Second column: item difficulty parameter.
difBound	Defines the boundary. Items with absolute linking DIF greater than the boundary will be removed from the linking procedure.
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.
testletStr	Optional: A data.frame with two columns. First column: testlet identifier, should be named unit. Second column: item identifier, should be named item. Only necessary if linking errors should be estimated via jackknife procedure. If items are nested in testlets, Monseur & Berezner, 2007 recommend jackknife procedures for linking error estimation in order to avoid bias.
verbose	Logical: print linking informations to console?

Value

description needed

Author(s)

Karoline Sachse, with code borrowed from the sirt package

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)
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)})
lErrors <- multiEquatError(results[[1]], results[[2]], results[[3]], difBound = 0.64)

# dependent DIF
lErrDif <- multiEquatError(results[[1]], results[[2]], results[[3]], difBound = 0.64, 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)
it1     <- itemFromRes(results[[1]])
eq1.vs.3<- equat1pl(results[[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=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)})
lErrors2<- multiEquatError(results2[[1]], results2[[2]], results2[[3]], difBound = 0.64)

# dependent DIF
lErrDif2<- multiEquatError(results2[[1]], results2[[2]], results2[[3]], difBound = 0.64, 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
allItems<- rbind(itemFromRes(results2[[1]]), itemFromRes(results2[[2]]), itemFromRes(results2[[3]]))
allItems<- unique(allItems[,"item"])
tl.frame<- data.frame (testlet = substr(allItems,1,3), item = allItems, stringsAsFactors = FALSE)

# repeat the linking from example 2
jkErr2  <- multiEquatError(results2[[1]], results2[[2]], results2[[3]], difBound = 0.64, testletStr = tl.frame)


################################################################################
###            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")]
multiEquatError(e1, e2, e3)

weirichs/eatModel documentation built on Jan. 26, 2025, 4:01 p.m.