irtProb (version 1.0)

conversion: 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.

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
  ...................................
• note
  character; warnings about the use of the c and d item parameters.
• normal.parameters
  numeric; vector returning difficulty p and discrimination rpbis parameters from the normal model.
• irt.parameters
  numeric; vector returning difficulty p and discrimination rpbis parameters from the logistic model.

Details

Eventually the 3 and 4 parameters logistic and normal models will be taken in account according to Urry approximation (1974).

References

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")

# 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$normal[2],a=irt$normal[1],model="NORMAL")
 round(c(NORMAL=irt$normal, IRT=irt$irt, CTT=clas$normal), 3)
## ....................................................................