Item Calibration

Description

estimate.item.jmle calibrates item parameters with knwon thetas using joint maximum likelihood.

estimate.item.mmle calibrates item parameters using marginal maximum likelihood.

estimate.item.bme calibrates item parameters using bayesian maximum likelihood.

Usage

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estimate.item.jmle(u, theta, model = "3PL", iteration = 100, delta = 0.01,
  a.bound = 2, b.bound = 3.5, c.bound = 0.25, diagnose = FALSE)

estimate.item.mmle(u, model = "3PL", iteration = 100, delta = 0.01,
  a.bound = 2, b.bound = 3.5, c.bound = 0.25, diagnose = FALSE)

estimate.item.bme(u, model = "3PL", a.mu = 0, a.sig = 0.2, b.mu = 0,
  b.sig = 1, c.alpha = 5, c.beta = 43, iteration = 100, delta = 0.01,
  a.bound = 2, b.bound = 3.5, c.bound = 0.25, diagnose = FALSE)

Arguments

u

a response matrix

theta

a vector of theta parameters

model

an IRT model used for calibration, taking values of "3PL", "2PL", "1PL", and "Rasch"

iteration

the maximum iterations in Newton-Raphson procedure

delta

the convergence criterion to terminate the Newton-Raphson procedure

a.bound

the maximum value of estimated a parameters

b.bound

the maximum absolute value of estimated b parameters

c.bound

the maximum value of estimated c parameters

diagnose

TRUE to return diangosis information

a.mu

the log mean of the lognormal prior distribution for a pameters

a.sig

the log sd of the lognormal prior distribution of a parmaeters

b.mu

the mean of the normal prior distribution for b pameters

b.sig

the sd of the normal prior distribution of b parmaeters

c.alpha

alpah of the prior beta distribution for c pameters

c.beta

beta of the prior beta distribution of c parmaeters

Details

Diagnosis information contains the average changes and values of a-, b-, c-parameters over the Newton-Raphson procedure.
For the joint maximum likelihood estimation, refer to Baker and Kim (2004), pp. 46-54.

For the marginal maximum likelihood estimation, refer to Baker and Kim (2004), pp.166-174.

For the Bayesian maximum likelihood estimation, refer to Baker and Kim (2004), pp.183-191.

Value

estimated item parameters and diagnosis information if required

See Also

Other estimation: estimate.theta.mle

Other estimation: estimate.theta.mle

Other estimation: estimate.theta.mle

Examples

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## Not run: 
# JMLE
x <- gen.rsp(gen.irt(3000, 30, a.sig=.4))
y <- estimate.item.jmle(x$rsp, x$thetas, model="3PL", diagnose=TRUE)
plot(x$items$a, y$parameters$a, xlim=c(0, 3), ylim=c(0, 3), pch=16, col=rgb(.8,.2,.2,.5))
abline(a=0, b=1, lty=2)
plot(x$items$b, y$parameters$b, xlim=c(-3, 3), ylim=c(-3, 3), pch=16, col=rgb(.8,.2,.2,.5))
abline(a=0, b=1, lty=2)
plot(x$items$c, y$parameters$c, xlim=c(0, .5), ylim=c(0, .5), pch=16, col=rgb(.8,.2,.2,.5))
abline(a=0, b=1, lty=2)

## End(Not run)
## Not run: 
# MMLE
x <- gen.rsp(gen.irt(3000, 30, a.sig=.4))
y <- estimate.item.mmle(x$rsp, model="3PL", diagnose=TRUE)
plot(x$items$a, y$parameters$a, xlim=c(0, 3), ylim=c(0, 3), pch=16, col=rgb(.8,.2,.2,.5),)
abline(a=0, b=1, lty=2)
plot(x$items$b, y$parameters$b, xlim=c(-3, 3), ylim=c(-3, 3), pch=16, col=rgb(.8,.2,.2,.5))
abline(a=0, b=1, lty=2)
plot(x$items$c, y$parameters$c, xlim=c(0, .5), ylim=c(0, .5), pch=16, col=rgb(.8,.2,.2,.5))
abline(a=0, b=1, lty=2)
y$diagnosis$h
z <- estimate.theta.mle(x$rsp, y$parameters$a, y$parameters$b, y$parameters$c)
plot(x$thetas, z, xlim=c(-5, 5), ylim=c(-5, 5), pch=16, col=rgb(.8,.2,.2,.5))
abline(a=0, b=1, lty=2)

## End(Not run)
## Not run: 
# BME
x <- gen.rsp(gen.irt(3000, 30, a.sig=.4))
y <- estimate.item.bme(x$rsp, model="3PL", diagnose=TRUE, a.mu=0, a.sig=.4, c.alpha=5, c.beta=30)
plot(x$items$a, y$parameters$a, xlim=c(0, 3), ylim=c(0, 3), pch=16, col=rgb(.8,.2,.2,.5))
abline(a=0, b=1, lty=2)
plot(x$items$b, y$parameters$b, xlim=c(-3, 3), ylim=c(-3, 3), pch=16, col=rgb(.8,.2,.2,.5))
abline(a=0, b=1, lty=2)
plot(x$items$c, y$parameters$c, xlim=c(0, .5), ylim=c(0, .5), pch=16, col=rgb(.8,.2,.2,.5))
abline(a=0, b=1, lty=2)
y$diagnosis$h
z <- estimate.theta.mle(x$rsp, y$parameters$a, y$parameters$b, y$parameters$c)
plot(x$thetas, z, xlim=c(-5, 5), ylim=c(-5, 5), pch=16, col=rgb(.8,.2,.2,.5))
abline(a=0, b=1, lty=2)

## End(Not run)