gendataIRT {lazy.irt}

R Documentation

Generation of Simulated Item Response Data

Description

Generation of Simulated Item Response Data

Usage

gendataIRT(
  Ntot,
  param,
  DinP = 1,
  Nmat = NULL,
  zero = 1,
  theta = NULL,
  npoints = 31,
  thmin = -3,
  thmax = 3,
  thd = NULL,
  thdist = "NORMAL",
  thmean = 0,
  thstd = 1,
  nomiss = 0,
  compress = 0,
  sort = 1,
  thetaname = NULL
)

Arguments

Ntot	# of total observations to be generated If Ntot == 1, one observation per each theta point will be generated, otherwize, the # of observations per each theta point is proportional to round(Ntot*thd) where thd is the npoint x 1 vector of theta distribution. Therefore, Ntot must be large enough.
param	Item Parameter Data Frame
DinP	= 1 to include D=1.7 in logistic function
Nmat	npoints x nitems matrix consisting of # of trials, or NULL. This will be used only when Ntot=1 and compress=0.
zero	= 0 to exclude zero-th category when not compressed.
theta	Discrete theta values
npoints	# of discrete points for theta, or # of random variables
thmin	Minimum value of discrete thata value
thmax	Maximum value of discrete thata value
thd	theta distribution probability vector
thdist	= "NORMAL" or "UNIFORM" or "rnorm" or "runif" When "NORMAL" or "rnorm", thmean and thstd will be used to generate thd. When "UNIFORM" or "runif", thmin and thmax will be used to generate thd. When "rnorm" or "runif", theta will be generated using npoints random numbers and thd and Ntot is set equal to 1.
thmean	mean of theta distribution
thstd	std of theta distribution
nomiss	= 1 to exclude those theta points with N = 0.
compress	= 1 to compress the data when Ntot = 1.
sort	= 1 to sort the result according to theta.
thetaname	= Name of the variable which will contain theta value or NULL.

Value

A list of
U, N, npoints, theta, thd, Ntot, fromP, toP, type, ncat, thmean, thstd , compress, sort

where

If compress = 0 and Ntot is large,
U is npoints x sum of ncat[j]
U[,fromP[j]:toP[j]] is npoints x ncat[j]
U[,fromP[j]:toP[j]][i,k] contains # of responses to
the k-th category (k=0,1,...,ncat[j]) at theta[i]
to which N[i]=round(Ntot*thd[i]) observations belong.


If compress = 1 and Ntot = 1,
U is npoints x nitems
U[i,j] contains the response to the j-th item at theta[i]
where 0 <= U[i,j] <= ncat[j]-1.
In this case, fromP and toP are not compressed.

(theta, thd, N) are npoints x 1
N[i] is the # of observations at theta[i]

Examples

# 10 observations with theta from N( 0, 1 ): not compressed
set.seed(1702)
res1 <- gendataIRT( 1, paramS1, npoints=10, thdist="rnorm" )
Print(res1$N,res1$U,res1$theta)
#
# 10 observations with theta from N( 0, 1 ): compressed
set.seed(1702)
res1 <- gendataIRT( 1, paramS1, npoints=10, thdist="rnorm", compress=1 )
Print(res1$N,res1$U,res1$theta)
#
# 10 observations with theta from N( 0, 1 ): no zero category
set.seed(1702)
res1 <- gendataIRT( 1, paramS1, npoints=10, thdist="rnorm", zero=0 )
Print(res1$N,res1$U,res1$theta)
#
#
#
# seven theta points in [-3,3]
set.seed(1701)
res1 <- gendataIRT( 1, paramS1, npoints=7, thmin=-3, thmax=3 )
Print(res1$N,res1$U,res1$theta)
#
# seven theta points in [-3,3] and compressed
set.seed(1701)
res1 <- gendataIRT( 1, paramS1, npoints=7, thmin=-3, thmax=3, compress=1 )
Print(res1$N,res1$U,res1$theta)
#
set.seed(1701)
# 100 observations tabulated at seven theta points in [-3,3]
res1 <- gendataIRT( 1000, paramS1, npoints=7, thmin=-3, thmax=3 )
Print(res1$N,res1$U,res1$theta)
#
#
# Using Nmat argument
set.seed(1701)
npoints=20
param=paramS1
nitems=nrow(param)
Nmat=matrix(100,npoints,nitems)
res1 <- gendataIRT( 1, param, Nmat=Nmat, npoints=npoints
                  , thdist="rnorm", compress=1 )
Print(res1$N,res1$U,res1$theta)

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