mcmc.2pno: MCMC Estimation of the Two-Parameter Normal Ogive Item...

In alexanderrobitzsch/sirt: Supplementary Item Response Theory Models

MCMC Estimation of the Two-Parameter Normal Ogive Item Response Model

Description

This function estimates the Two-Parameter normal ogive item response model by MCMC sampling (Johnson & Albert, 1999, p. 195ff.).

Usage

mcmc.2pno(dat, weights=NULL, burnin=500, iter=1000, N.sampvalues=1000,
      progress.iter=50, save.theta=FALSE)

Arguments

dat	Data frame with dichotomous item responses
weights	An optional vector with student sample weights
burnin	Number of burnin iterations
iter	Total number of iterations
N.sampvalues	Maximum number of sampled values to save
progress.iter	Display progress every progress.iter-th iteration. If no progress display is wanted, then choose progress.iter larger than iter.
save.theta	Should theta values be saved?

Details

The two-parameter normal ogive item response model with a probit link function is defined by

P(X_{pi}=1 | \theta_p )=\Phi ( a_i \theta_p - b_i ) \quad, \quad \theta_p \sim N(0,1)

Note that in this implementation non-informative priors for the item parameters are chosen (Johnson & Albert, 1999, p. 195ff.).

Value

A list of class mcmc.sirt with following entries:

mcmcobj	Object of class mcmc.list
summary.mcmcobj	Summary of the mcmcobj object. In this summary the Rhat statistic and the mode estimate MAP is included. The variable PercSEratio indicates the proportion of the Monte Carlo standard error in relation to the total standard deviation of the posterior distribution.
burnin	Number of burnin iterations
iter	Total number of iterations
a.chain	Sampled values of a_i parameters
b.chain	Sampled values of b_i parameters
theta.chain	Sampled values of \theta_p parameters
deviance.chain	Sampled values of Deviance values
EAP.rel	EAP reliability
person	Data frame with EAP person parameter estimates for \theta_p and their corresponding posterior standard deviations
dat	Used data frame
weights	Used student weights
...	Further values

References

Johnson, V. E., & Albert, J. H. (1999). Ordinal Data Modeling. New York: Springer.

See Also

S3 methods: summary.mcmc.sirt, plot.mcmc.sirt

For estimating the 2PL model with marginal maximum likelihood see rasch.mml2 or smirt.

A hierarchical version of this model can be estimated with mcmc.2pnoh.

Examples

## Not run: 
#############################################################################
# EXAMPLE 1: Dataset Reading
#############################################################################
data(data.read)
# estimate 2PNO with MCMC with 3000 iterations and 500 burn-in iterations
mod <- sirt::mcmc.2pno( dat=data.read, iter=3000, burnin=500 )
# plot MCMC chains
plot( mod$mcmcobj, ask=TRUE )
# write sampled chains into codafile
mcmclist2coda( mod$mcmcobj, name="dataread_2pno" )
# summary
summary(mod)

#############################################################################
# EXAMPLE 2
#############################################################################
# simulate data
N <- 1000
I <- 10
b <- seq( -1.5, 1.5, len=I )
a <- rep( c(1,2), I/2 )
theta1 <- stats::rnorm(N)
dat <- sirt::sim.raschtype( theta=theta1, fixed.a=a, b=b )

#***
# Model 1: estimate model without weights
mod1 <- sirt::mcmc.2pno( dat, iter=1500, burnin=500)
mod1$summary.mcmcobj
plot( mod1$mcmcobj, ask=TRUE )

#***
# Model 2: estimate model with weights
# define weights
weights <- c( rep( 5, N/4 ), rep( .2, 3/4*N ) )
mod2 <- sirt::mcmc.2pno( dat, weights=weights, iter=1500, burnin=500)
mod1$summary.mcmcobj

## End(Not run)

alexanderrobitzsch/sirt documentation built on Dec. 1, 2024, 2:18 a.m.