TAM: tam.ctt – R documentation

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TAM

tam.ctt

Classical Test Theory Based Statistics and Plots

Description

This function computes some item statistics based on classical test theory.

Usage

tam.ctt(resp, wlescore=NULL, pvscores=NULL, group=NULL, progress=TRUE)
tam.ctt2(resp, wlescore=NULL, group=NULL, allocate=30, progress=TRUE)
tam.ctt3(resp, wlescore=NULL, group=NULL, allocate=30, progress=TRUE, max_ncat=30,
          pweights=NULL)

plotctt( resp, theta, Ncuts=NULL, ask=FALSE, col.list=NULL,
       package="lattice", ... )

Arguments

`resp`	A data frame with unscored or scored item responses
`wlescore`	A vector with person parameter estimates, e.g. weighted likelihood estimates obtained from `tam.wle`. If `wlescore=NULL` is chosen in `tam.ctt2`, then only a frequency table of all items is produced.
`pvscores`	A matrix with plausible values, e.g. obtained from `tam.pv`
`group`	Vector of group identifiers if descriptive statistics shall be groupwise calculated
`progress`	An optional logical indicating whether computation progress should be displayed.
`allocate`	Average number of categories per item. This argument is just used for matrix size allocations. If an error is produced, use a sufficiently higher number.
`max_ncat`	Maximum number of categories of variables for which frequency tables should be computed
`pweights`	Optional vector of person weights
`theta`	A score to be conditioned
`Ncuts`	Number of break points for `theta`
`ask`	A logical which asks for changing the graphic from item to item. The default is `FALSE`.
`col.list`	Optional vector of colors for plotting
`package`	Package used for plotting. Can be `"lattice"` or `"graphics"`.
`...`	Further arguments to be passed.

Details

The functions tam.ctt2 and tam.ctt3 use Rcpp code and are slightly faster. However, only tam.ctt allows the input of wlescore and pvscores.

Value

A data frame with following columns:

`index`	Index variable in this data frame
`group`	Group identifier
`itemno`	Item number
`item`	Item
`N`	Number of students responding to this item
`Categ`	Category label
`AbsFreq`	Absolute frequency of category
`RelFreq`	Relative frequency of category
`rpb.WLE`	Point biserial correlation of an item category and the WLE
`M.WLE`	Mean of the WLE of students in this item category
`SD.WLE`	Standard deviation of the WLE of students in this item category
`rpb.PV`	Point biserial correlation of an item category and the PV
`M.PV`	Mean of the PV of students in this item category
`SD.PV`	Standard deviation of the PV of students in this item category

Note

For dichotomously scored data, rpb.WLE is the ordinary point biserial correlation of an item and a test score (here the WLE).

Examples

## Not run: 
#############################################################################
# EXAMPLE 1: Multiple choice data data.mc
#############################################################################

data(data.mc)
# estimate Rasch model for scored data.mc data
mod <- TAM::tam.mml( resp=data.mc$scored )
# estimate WLE
w1 <- TAM::tam.wle( mod )
# estimate plausible values
set.seed(789)
p1 <- TAM::tam.pv( mod, ntheta=500, normal.approx=TRUE )$pv

# CTT results for raw data
stat1 <- TAM::tam.ctt( resp=data.mc$raw, wlescore=w1$theta, pvscores=p1[,-1] )
stat1a <- TAM::tam.ctt2( resp=data.mc$raw, wlescore=w1$theta )  # faster
stat1b <- TAM::tam.ctt2( resp=data.mc$raw )  # only frequencies
stat1c <- TAM::tam.ctt3( resp=data.mc$raw, wlescore=w1$theta )  # faster

# plot empirical item response curves
plotctt( resp=data.mc$raw, theta=w1$theta, Ncuts=5, ask=TRUE)
# use graphics for plot
plotctt( resp=data.mc$raw, theta=w1$theta, Ncuts=5, ask=TRUE, package="graphics")
# change colors
col.list <- c( "darkred",  "darkslateblue", "springgreen4", "darkorange",
                "hotpink4", "navy" )
plotctt( resp=data.mc$raw, theta=w1$theta, Ncuts=5, ask=TRUE,
        package="graphics", col.list=col.list )

# CTT results for scored data
stat2 <- TAM::tam.ctt( resp=data.mc$scored, wlescore=w1$theta, pvscores=p1[,-1] )

# descriptive statistics for different groups
# define group identifier
group <- c( rep(1,70), rep(2,73) )
stat3 <- TAM::tam.ctt( resp=data.mc$raw, wlescore=w1$theta, pvscores=p1[,-1], group=group)
stat3a <- TAM::tam.ctt2( resp=data.mc$raw, wlescore=w1$theta,  group=group)

## End(Not run)

TAM

Test Analysis Modules

v3.6-45

GPL (>= 2)

Authors

Alexander Robitzsch [aut,cre] (<https://orcid.org/0000-0002-8226-3132>), Thomas Kiefer [aut], Margaret Wu [aut]

Initial release

2021-04-22 14:35:52