Simulated Rasch data

Simulated Rasch data under unidimensional trait distribution

data(data.sim.rasch)
 data(data.sim.rasch.pweights)
 data(data.sim.rasch.missing)

Format

The format is:

num [1:2000, 1:40] 1 0 1 1 1 1 1 1 1 1 ...
- attr(*, "dimnames")=List of 2
..$ : NULL
..$ : chr [1:40] "I1" "I2" "I3" "I4" ...

Details

N <- 2000
# simulate predictors
Y <- cbind( stats::rnorm( N, sd=1.5), stats::rnorm(N, sd=.3 ) )
theta <- stats::rnorm( N ) + .4 * Y[,1] + .2 * Y[,2] # latent regression model
# simulate item responses with missing data
I <- 40
resp[ theta < 0, c(1,seq(I/2+1, I)) ] <- NA
# define person weights
pweights <- c( rep(3,N/2), rep( 1, N/2 ) )

Source

Simulated data (see Details)

Examples

if (FALSE) {
data(data.sim.rasch)
N <- 2000
Y <- cbind( stats::rnorm( N, sd=1.5), stats::rnorm(N, sd=.3 ) )

# Loading Matrix
# B <- array( 0, dim=c( I, 2, 1 )  )
# B[1:(nrow(B)), 2, 1] <- 1
B <- TAM::designMatrices(resp=data.sim.rasch)[["B"]]

# estimate Rasch model
mod1_1 <- TAM::tam.mml(resp=data.sim.rasch, Y=Y)

# standard errors
res1 <- TAM::tam.se(mod1_1)

# Compute fit statistics
tam.fit(mod1_1)

# plausible value imputation
# PV imputation has to be adpated for multidimensional case!
pv1 <- TAM::tam.pv( mod1_1, nplausible=7, # 7 plausible values
               samp.regr=TRUE       # sampling of regression coefficients
              )

# item parameter constraints
xsi.fixed <- matrix( c( 1, -2,5, -.22,10, 2 ), nrow=3, ncol=2, byrow=TRUE)
xsi.fixed
mod1_4 <- TAM::tam.mml( resp=data.sim.rasch, xsi.fixed=xsi.fixed )

# missing value handling
data(data.sim.rasch.missing)
mod1_2 <- TAM::tam.mml(data.sim.rasch.missing, Y=Y)

# handling of sample (person) weights
data(data.sim.rasch.pweights)
N <- 1000
pweights <- c(  rep(3,N/2), rep( 1, N/2 ) )
mod1_3 <- TAM::tam.mml( data.sim.rasch.pweights, control=list(conv=.001),
               pweights=pweights )
  }