R: Functions to Convert from and to CTT and IRT Models
conversion
R Documentation
Functions to Convert from and to CTT and IRT Models
Description
ctt2irt and irt2ctt are converter functions to change the parametrization of item parameters
from and to classical test theory (difficulty and discrimination parameters) and item response theory (difficulty
and discrimination parameters). Consequently, the conversion is only valid between ctt and 2 parameters logistic or normal models.
Usage
ctt2irt(rpbis = 0.7071068, difficulty = 0.5)
irt2ctt(a = 1, b = 0, c = 0, d = 1, model = "LOGISTIC")
Arguments
rpbis
numeric; vector of discrimination parameters: point biserial correlation between the item response and the total score.
difficulty
vector of difficulty parameters: proportion of corrected responses.
a
numeric; vector of discrimination parameters.
b
numeric; vector of difficulty parameters.
c
numeric; vector of pseudo-guessing parameters (not used for the moment).
d
numeric; vector of inattention parameters (not used for the moment).
model
character; if NORMAL the constant D (1.702) is used. Default to LOGISTIC with constant D=1.
Details
Eventually the 3 and 4 parameters logistic and normal models will be taken in account according to Urry approximation (1974).
Value
For ctt2irt
...................................
note
character; warnings about the use of the c and d item parameters.
normal.parameters
numeric; vector returning difficulty b and discrimination a parameters from the normal model.
irt.parameters
numeric; vector returning difficulty b and discrimination a parameters from the logistic model.
For irt2ctt
...................................
parameters
numeric; vector returning difficulty p and discrimination rpbis parameters from the normal model.
Author(s)
Gilles Raiche, Universite du Quebec a Montreal (UQAM),
Bartholomiew, D. J. (1987). Latent variable models and factor analysis. London, U. K.: Charles Griffin and Company.
Lord, F. M. (1980). Applications of item response theory to practical testing problems. Mahwah, New Jersey: LEA.
Lord, F. M. and Novick, M. R. (1968). Statistical theories of mental test scores, 2nd edition. Reading, Massacusett: Addison-Wesley.
Urry, V. W. (1974). Approximations to item parameters of mental tests models and their uses.
Educational and psychological measurement, 34, 253-269.
See Also
gr4pl, ggr4pl, ctt2irt, irt2ctt
Examples
## ....................................................................
# Values of p and rbis according to de a, b, c and d values
# MODEL means that item parameters are from a NORMAL or LOGISTIC model
# type
irt2ctt()
nItems <- 5
b <- seq(-3, 3, length=nItems)
a <- rep(1, nItems)
c <- rep(0, nItems)
d <- rep(1, nItems)
# Difference between classical item parameters and IRT ones
irt2ctt(b=b,a=a,c=c,d=d,model="LOGISTIC")
irt2ctt(b=b,a=a,c=c,d=d,model="NORMAL")
# Default values of a and b according p and rpbis
ctt2irt()
# Verification of the recovery of original ctt item parameters
nItems <- 5
p <- seq(0.10, 0.90, length=nItems)
rpbis <- seq(0.50, 0.95, length=nItems)
irt <- ctt2irt(dif=p, rpbis=rpbis)
clas <- irt2ctt(b=irt$irt[6:10], a=irt$irt[1:5], model="LOGISTIC")
data.frame(NORMAL=irt$normal, IRT=irt$irt, CTT=clas,ORIGINAL=c(rpbis,p))
clas <- irt2ctt(b=irt$normal[6:10], a=irt$normal[1:5], model="NORMAL")
data.frame(NORMAL=irt$normal, IRT=irt$irt, CTT=clas,ORIGINAL=c(rpbis,p))
## ....................................................................