IRT.simulate(object, ...)

## S3 method for class 'tam.mml'
IRT.simulate(object, iIndex=NULL, theta=NULL, nobs=NULL, ...)

## S3 method for class 'tam.mml.2pl'
IRT.simulate(object, iIndex=NULL, theta=NULL, nobs=NULL, ...)

## S3 method for class 'tam.mml.mfr'
IRT.simulate(object, iIndex=NULL, theta=NULL, nobs=NULL, ...)

## S3 method for class 'tam.mml.3pl'
IRT.simulate(object, iIndex=NULL, theta=NULL, nobs=NULL, ...)

#############################################################################
# EXAMPLE 1: Simulating Rasch model
#############################################################################

data(data.sim.rasch)

#** (1) estimate model
mod1 <- TAM::tam.mml(resp=data.sim.rasch )

#** (2) simulate data
sim.dat <- TAM::IRT.simulate(mod1)

## Not run: 
#** (3) use a subset of items with the argument iIndex
set.seed(976)
iIndex <- sort(sample(ncol(data.sim.rasch), 15))  # randomly select 15 items
sim.dat <- TAM::IRT.simulate(mod1, iIndex=iIndex)
mod.sim.dat <- TAM::tam.mml(sim.dat)

#** (4) specify number of persons in addition
sim.dat <- TAM::IRT.simulate(mod1, nobs=1500, iIndex=iIndex)

# Rasch - constraint="items" ----
mod1 <- TAM::tam.mml(resp=data.sim.rasch,  constraint="items",
                control=list( xsi.start0=1, fac.oldxsi=.5) )

# provide abilities
theta0 <- matrix( rnorm(1500, mean=0.5, sd=sqrt(mod1$variance)), ncol=1 )
# simulate data
data <- TAM::IRT.simulate(mod1, theta=theta0 )
# estimate model based on simulated data
xsi.fixed <- cbind(1:nrow(mod1$item), mod1$item$xsi.item)
mod2 <- TAM::tam.mml(data, xsi.fixed=xsi.fixed )
summary(mod2)

#############################################################################
# EXAMPLE 2: Simulating 2PL model
#############################################################################

data(data.sim.rasch)
# estimate 2PL
mod2 <- TAM::tam.mml.2pl(resp=data.sim.rasch, irtmodel="2PL")
# simulate 2PL
sim.dat <- TAM::IRT.simulate(mod2)
mod.sim.dat <- TAM::tam.mml.2pl(resp=sim.dat, irtmodel="2PL")

#############################################################################
# EXAMPLE 3: Simulate multiple group model
#############################################################################

# Multi-Group ----
set.seed(6778)
N <- 3000
theta <- c( stats::rnorm(N/2,mean=0,sd=1.5), stats::rnorm(N/2,mean=.5,sd=1)  )
I <- 20
p1 <- stats::plogis( outer( theta, seq( -2, 2, len=I ), "-" ) )
resp <- 1 * ( p1 > matrix( stats::runif( N*I ), nrow=N, ncol=I ) )
colnames(resp) <- paste("I", 1:I, sep="")
group <- rep(1:2, each=N/2 )
mod3 <- TAM::tam.mml(resp, group=group)

# simulate data
sim.dat.g1 <- TAM::IRT.simulate(mod3,
                   theta=matrix( stats::rnorm(N/2, mean=0, sd=1.5), ncol=1) )
sim.dat.g2 <- TAM::IRT.simulate(mod3,
                   theta=matrix( stats::rnorm(N/2, mean=.5, sd=1), ncol=1) )
sim.dat <- rbind( sim.dat.g1, sim.dat.g2)
# estimate model
mod3s <- TAM::tam.mml( sim.dat, group=group)

#############################################################################
# EXAMPLE 4: Multidimensional model and latent regression
#############################################################################

set.seed(6778)
N <- 2000
Y <- cbind( stats::rnorm(N), stats::rnorm(N))
theta <- mvtnorm::rmvnorm(N, mean=c(0,0), sigma=matrix(c(1,.5,.5,1), 2, 2))
theta[,1] <- theta[,1] + .4 * Y[,1] + .2 * Y[,2]  # latent regression model
theta[,2] <- theta[,2] + .8 * Y[,1] + .5 * Y[,2]  # latent regression model
I <- 20
p1 <- stats::plogis(outer(theta[, 1], seq(-2, 2, len=I), "-"))
resp1 <- 1 * (p1 > matrix(stats::runif(N * I), nrow=N, ncol=I))
p1 <- stats::plogis(outer(theta[, 2], seq(-2, 2, len=I ), "-" ))
resp2 <- 1 * (p1 > matrix(stats::runif(N * I), nrow=N, ncol=I))
resp <- cbind(resp1, resp2)
colnames(resp) <- paste("I", 1 : (2 * I), sep="")

# (2) define loading Matrix
Q <- array(0, dim=c(2 * I, 2))
Q[cbind(1:(2*I), c(rep(1, I), rep(2, I)))] <- 1
Q

# (3) estimate models
mod4 <- TAM::tam.mml(resp=resp, Q=Q, Y=Y, control=list(  maxiter=15))

# simulate new item responses
theta <- mvtnorm::rmvnorm(N, mean=c(0,0), sigma=matrix(c(1,.5,.5,1), 2, 2))
theta[,1] <- theta[,1] + .4 * Y[,1] + .2 * Y[,2]  # latent regression model
theta[,2] <- theta[,2] + .8 * Y[,1] + .5 * Y[,2]  # latent regression model

sim.dat <- TAM::IRT.simulate(mod4, theta=theta)
mod.sim.dat <- TAM::tam.mml(resp=sim.dat, Q=Q, Y=Y, control=list( maxiter=15))

## End(Not run)