sirt: mcmc.2pno – R documentation

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mcmc.2pno

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 | θ_p )=Φ ( a_i θ_p - b_i ) \quad, \quad θ_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 θ_p parameters
`deviance.chain`	Sampled values of Deviance values
`EAP.rel`	EAP reliability
`person`	Data frame with EAP person parameter estimates for θ_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.

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)

sirt

Supplementary Item Response Theory Models

v3.10-118

GPL (>= 2)

Authors

Alexander Robitzsch [aut,cre] (<https://orcid.org/0000-0002-8226-3132>)

Initial release

2021-09-22 17:45:34