irtProb (version 1.0)

responses4pl: Simulation of Response Patterns and Computation of the Probability of the Patterns

Description

Simulation of response patterns and computation of the probability of the patterns according to the one, two, three and four parameters logistic item response models.~

Usage

gr4pl(N = 10, theta = 0, a = 1, b = 0, c = 0, d = 1)

 ggr4pl(n = 5, rep = 1, theta = 0, a = rep(1, n), b = rep(0, n),
        c = rep(0, n), d = rep(1, n))
       
 pggr4pl(x = ggr4pl(rep = 1), rep = 1, n = dim(x)[2], N = dim(x)[1],
         theta = rep(0, N), a = rep(1, n), b = rep(0, n), c = rep(0, n),
         d = rep(1, n), log.p=FALSE, TCC = FALSE)

Arguments

theta

numeric; vector of proficiency levels (z sscores).

x

numeric matrix; response patterns (0 or 1).

rep

numeric; number of replications of the simulation of the response patterns.

n

numeric; number of items.

N

numeric; number of response patterns

a

numeric; item discrimination parameters.

b

numeric; item difficulty parameters.

c

numeric; item pseudo-guessing parameters.

d

numeric; item inattention parameters.

log.p

logical; if TRUE, probabilities p are given as log(p).

TCC

logical; if TRUE generate the TCC figures for each response patterns. Default FALSE.

Value

• gr4pl
  numeric; vector of item responses (0 or 1).
• ggr4pl
  numeric; data.frame of responses at n items.
• pggr4pl
  logical; if (TCC ==TRUE) return(list(prob=prob, tcc=tcc)); if (TCC==FALSE) return(prob)

Details

The function gr4pl generates N responses to an item according to the theta parameter and the items parameters. The funcfion ggr4pl will be used to generate rep respose patterns at n items. To compute the probability of the response patterns, according to known person and item parameters, the function pggr4pl will be applied.

References

Hambleton, R. K. and Swaminathan, H. (1985). Item response theory - Principles and applications. Boston, Massachuset: Kluwer.

See Also

grm4pl, ggrm4pl, pggrm4pl, ctt2irt, irt2ctt

Examples

## ....................................................................
# Generation of reponses (0,1) from r4pl() for N subjects (default value of N= 10)
 gr4pl(c = 1)
 gr4pl(N = 5, theta = c(-4, 4), c = 0)

# Generation of a 7 responses pattern (0,1) for [rep * length(theta)] subjects
#  The subjects number is equal to [rep * length(theta)]]
#  a,b,c et d are item parameters vectors
 nitems <- 7
 N      <- 10
 a      <- rep(1, nitems)
 b      <- rnorm(nitems)
 c      <- rep(0, nitems)
 d      <- rep(1, nitems)
 theta  <- seq(-4,4,length=5)
 x      <- ggr4pl(n = nitems, rep = N, theta = theta, a = a, b = b, c = c, d = d)
 x

## Probability of a 10 responses pattern and test caracteristic curve (TCC)
 nitems <- 10
 a      <- rep(1,nitems)
 b      <- seq(-4,4,length=nitems)
 c      <- rep(0,nitems)
 d      <- rep(1,nitems)
 N      <- 3
 theta  <- seq(-1,1,length=12)
 # Generation of the response patterns
 x      <- ggr4pl(n = nitems, rep = N, theta = theta, a = a, b = b, c = c, d = d)
 x
 # Without TCC
 res    <- pggr4pl(x=x, rep=N, theta=theta,a=a,c=c,d=d,TCC=FALSE); res
 # With TCC for each response pattern
 res    <- pggr4pl(x=x, rep=N, theta=theta,a=a,c=c,d=d,TCC=TRUE); res
## ....................................................................