Computes equivalence table for the Rasch and partial credit model

Function provides the equivalence table for unidimensional 1pl models, specifying the individual competence level for each possible total score of the test.

simEquiTable  ( anchor, item = NULL, cat = NULL, value = NULL, mRef,
       sdRef, addConst = 500, multConst = 100, cutScores)

Arguments

anchor: A data frame with anchor parameters on the logit scale, transformed to the metric of the reference population. Data frame must have at least two columns: The first column contains the names of all anchored items. The second column contains anchor parameters. If the equivalence table is to be generated for a partial credit model, an additional column for the respective item category must be specified in the data.frame. The data.frame will then have three columns. In this case, the additional arguments item, cat, and value must be specified. The various item parameters for a partial credit item must therefore be listed one below the other in the data.frame. See the second example for further details.
item: Optional: Give the number or name of the item identifier column in anchor. Only necessary for partial credit models.
cat: Optional: Give the number or name of the category column in anchor. Only necessary for partial credit models.
value: Optional: Give the number or name of the parameter column in anchor. Only necessary for partial credit models.
mRef: Scalar: mean of the reference population.
sdRef: Scalar: Standard deviation of the reference population.
addConst: Additive constant for parameter transformation.
multConst: Multiplicative constant for parameter transformation.
cutScores: Named list of one or two elements. "values" is a numeric vector of cut scores (increasing), "labels" is an optional character vector of cut score labels. Note that "labels" (if specified) has to be of one more length than "values".

Value

A list of two data frames, including the complete table and the reduced table with the following 5 columns.

score: Students raw score
est: Estimated individual WLE according to the raw score.
bista: Transformed WLE
ks: competence level

Author

Johannes Schult, Sebastian Weirich

Examples

### Example 1: equivalence table for Rasch models
# read anchor parameter
file <- system.file("extdata", "results.rda", package = "eatModel")
if (nzchar(file)) {
load(file)

# use domain 'reading'
prm  <- subset(itemFromRes(res), model == "komplesen")

# use bista cut scores
cuts   <- list ( values = 390+0:3*75, labels = c("I", "II", "III", "IV", "V") )

# create the equivalence table
ret <- simEquiTable( anchor = prm[,c("item", "est")], cutScores = cuts , mRef = 0.039, sdRef = 1.071)
}

### Example 2: equivalence table for partial credit model
if (FALSE) { # \dontrun{
# This example estimates a partial-credit model. R CMD check skips it by default,
# but it can still be run locally via run_dontrun = TRUE.
# load partial credit data
data(reading)

# To speed up the process, the tests will be administered only for Test
# Booklet 8. This booklet contains questions with some partial credit items.
d   <- subset(reading, bookletID == "TH08")
dw  <- reshape2::dcast(d, idstud~item, value.var = "valueSum")
defT<- defineModel(dat = dw, items = -1, id = "idstud",  irtmodel = "PCM",software="tam")
runT<- runModel(defT)
resT<- getResults(runT, omitPV=TRUE, Q3 = FALSE)
it  <- itemFromRes(resT)

# create equivalence table with arbitrary cuts and reference values
ret2<- simEquiTable( anchor = it, item = "item", cat="category", value = "est",
       cutScores = list ( values = c(400, 600)), mRef = 0.047, sdRef = 1.181)
} # }