TAM (version 1.995-0)

IRT.simulate: Simulating Item Response Models

Description

Defines an S3 method for simulation of item response models.

Usage

IRT.simulate(object, ...)
"IRT.simulate"(object, iIndex=NULL, theta=NULL, nobs=NULL, ...)
"IRT.simulate"(object, iIndex=NULL, theta=NULL, nobs=NULL, ...)
"IRT.simulate"(object, iIndex=NULL, theta=NULL, nobs=NULL, ...)
"IRT.simulate"(object, iIndex=NULL, theta=NULL, nobs=NULL, ...)

Arguments

object

An object of class tam.mml, tam.mml.2pl, tam.mml.mfr or tam.mml.3pl.

iIndex

Optional vector of item indices

theta

Optional matrix of theta values

nobs

Optional numeric containing the number of observations to be simulated.

...

Further objects to be passed

Value

Data frame with simulated item responses

Examples

#############################################################################
# EXAMPLE 1: Simulating Rasch model
#############################################################################
	
data(data.sim.rasch)

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

#** (2) simulate data
sim.dat <- 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 <- IRT.simulate(mod1, iIndex = iIndex)
# mod.sim.dat <- tam.mml(sim.dat)
# 
# #** (4) specify number of persons in addition
# sim.dat <- IRT.simulate(mod1, nobs = 1500, iIndex = iIndex)
# 
# # Rasch - constraint = "items" ----
# mod1 <- 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$variance)) , ncol=1 )
# # simulate data
# data <- IRT.simulate(mod1, theta = theta0 )
# # estimate model based on simulated data
# xsi.fixed <- cbind(1:nrow(mod1$item), mod1$item$xsi.item)
# mod2 <- tam.mml(data , xsi.fixed=xsi.fixed )
# summary(mod2)
# 
# #############################################################################
# # EXAMPLE 2: Simulating 2PL model
# #############################################################################
# 
# data(data.sim.rasch)
# # estimate 2PL
# mod2 <- tam.mml.2pl(resp = data.sim.rasch, irtmodel = "2PL")
# # simulate 2PL
# sim.dat <- IRT.simulate(mod2)
# mod.sim.dat <- tam.mml.2pl(resp = sim.dat, irtmodel = "2PL") 
# 
# #############################################################################
# # SIMULATED 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.mml(resp, group = group)
# 
# # simulate data
# sim.dat.g1 <- IRT.simulate(mod3, theta = matrix( stats::rnorm(N/2, mean = 0, sd = 1.5) , ncol=1) )
# sim.dat.g2 <- 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.mml( sim.dat , group = group)
# 
# #############################################################################
# # SIMULATED 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.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 <- IRT.simulate(mod4, theta = theta)
# mod.sim.dat <- tam.mml(resp = sim.dat, Q = Q, Y = Y, control = list( maxiter = 15))
# ## End(Not run)