irtProb (version 1.0)

responsesm4pl: Simulation of Response Patterns and Computation of the Probability of the Patterns from m4pl

Description

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

Usage

grm4pl(N = 10, theta = 0, S = 0, C = 0, D = 0, s = 1/1.702, b = 0, c = 0, d = 1)

 ggrm4pl(n=5,rep=1,theta=0,S=rep(0,length(theta)),C=rep(0,length(theta)),
         D=rep(0,length(theta)),s=rep(1/1.702,n),b=rep(0,n),c=rep(0,n),
         d=rep(1, n))
 
 pggrm4pl(x=ggrm4pl(rep=1),rep=1,n=dim(x)[2],N=dim(x)[1],theta=rep(0,N),
          S=0,C=0,D=0,s=rep(1/1.702,n),b=rep(0,n),c=rep(0,n),d=rep(1,n),
          log.p=FALSE, TCC=FALSE)

Arguments

x

integer 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

theta

numeric; vector of proficiency levels (z sscores).

S

numeric; person fluctuation parameter.

C

numeric; person pseud0-guessing parameter.

D

numeric; person inattention parameter.

s

numeric; item fluctuation 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

• grm4pl
  integer; vector of item responses (0 or 1).
• ggrm4pl
  integer data.frame; responses for n items.
• pggrm4pl
  graphic; if (TCC ==TRUE) return(list(prob=prob, tcc=tcc)). If (TCC==FALSE) return(prob).

Details

The function grm4pl generates N responses to an item according to the person parameters and the items parameters. The funcfion ggrm4pl 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 pggrm4pl will be applied.

References

Ferrando, P. J. (2004). Person reliability in personality measurement: an item response theory analysis. Applied Psychological Measurement, 28(2), 126-140. Hulin, C. L., Drasgow, F., and Parsons, C. K. (1983). Item response theory. Homewood, IL: Irwin. Levine, M. V., and Drasgow, F. (1983). Appropriateness measurement: validating studies and variable ability models. In D. J. Weiss (Ed.): New horizons in testing. New York, NJ: Academic Press. Magis, D. (2007). Enhanced estimation methods in IRT. In D. Magis (Ed.): Influence, information and item response theory in discrete data analysis. Doctoral dissertation, Liege, Belgium: University de Liege. Trabin, T. E., and Weiss, D. J. (1983). The person response curve: fit of individuals to item response theory models. In D. J. Weiss (Ed.): New horizons in testing. New York, NJ: Academic Press.

See Also

gr4pl, ggr4pl, pggr4pl, ctt2irt, irt2ctt

Examples

## ....................................................................
# Generation of response patterns (0,1) from r4pl() for N subjects (default value
# of N = 10)

# Generation of a response (0,1) from rm4pl for N subjects
 grm4pl(theta=0)
 grm4pl(N=5, theta=c(-4,4), c=0)

# Generation of n m4pl response patterns (0,1) for [rep * length(theta)] subjects
#  The subject number ia equal to [rep * length(theta)]
#  a,b,c et d are item parameters vectors
 nitems <- n <- 7; N <- 1
 s     <- rep(0,nitems); b <- seq(-4,4,length=nitems); c <- rep(0,nitems)
 d     <- rep(1,nitems)
 theta <- seq(-4,4,length=5)
 x     <- ggrm4pl(n=nitems, rep=N, theta=theta,s=s,b=b,c=c,d=d)
 x

# TO BE REWORKED - Probability of a response pattern and test caracteristic curve
# (TCC)
 nItems <- n <- 7; N <- 1
 s      <- rep(0,nItems); b <- seq(-4,4,length=nItems)
 c      <- rep(0,nItems); d <- rep(1,nItems)
 theta <- seq(-4,4,length=5);     S <- rep(1/1.702,length(theta));
 C     <- rep(0.3,length(theta)); D <- rep(0,length(theta))
 x <- ggrm4pl(n=nItems, rep=N, theta=theta, S=S, C=C, D=D, s=s, b=b, c=c, d=d)
 x
 res <- pggrm4pl(x=x, rep=N, theta=theta, S=1/1.702, C=0.3, D=0, s=s, c=c, d=d,
                 TCC=TRUE)
 res
 res <- pggrm4pl(x=x, rep=N, theta=rep(2,length(theta)), S=1/1.702, C=0, D=0,
                 s=s, c=c, d=d, TCC=FALSE)
 res
 pggrm4pl(theta=3)
 pggrm4pl(n=10, theta=seq(-4,4,length=5), x=ggrm4pl(rep=1), TCC=TRUE)
## ....................................................................