tam.ctt: Classical Test Theory Based Statistics and Plots

Description

The functions 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)
tam.cb( dat, wlescore=NULL, group=NULL, max_ncat=30, progress=TRUE,
             pweights=NULL, digits_freq=5)
plotctt( resp, theta, Ncuts=NULL, ask=FALSE, col.list=NULL,
       package="lattice", ... )

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

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
dat: Data frame
digits_freq: Number of digits for rounding in frequency table
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.

Examples

Run this code

if (FALSE) {
#############################################################################
# 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)
}