responsesm4pl: Simulation of Response Patterns and Computation of the...
In irtProb: Utilities and Probability Distributions Related to Multidimensional Person Item Response Models

Description Usage Arguments Details Value Author(s) References See Also Examples

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 (Raiche et al., 2013).

 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)

`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.

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.

`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).

Gilles Raiche, Universite du Quebec a Montreal (UQAM),

Departement d'education et pedagogie

Raiche.Gilles@uqam.ca, http://www.er.uqam.ca/nobel/r17165/

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.

Raiche, G., Magis, D., Blais, J.-G., and Brochu, P. (2013). Taking atypical response patterns into account: a multidimensional measurement model from item response theory. In M. Simon, K. Ercikan, and M. Rousseau (Eds), Improving large-scale assessment in education. New York, New York: Routledge.

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.

gr4pl, ggr4pl, pggr4pl, ctt2irt, irt2ctt

## Not run: 
## ....................................................................
# 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)
## ....................................................................
 
## End(Not run)