xxIRT (version 1.1.0)

estimate.theta.mle: Estimation of Ability Parameters

Description

estimate.theta.mle estimates thetas with known item parameters using maximum likelihood.

estimate.theta.map estimates thetas with known item parameters using maximum a posterior.

estimate.theta.eap estimates thetas with known item parameters using expected a posterior.

Usage

estimate.theta.mle(u, a, b, c, init = NULL, iteration = 15, delta = 0.005, bound = 3.5)
estimate.theta.map(u, a, b, c, init = NULL, prior.mu = 0, prior.sig = 1, iteration = 15, delta = 0.005, bound = 3.5)
estimate.theta.eap(u, a, b, c)

Arguments

u

a response matrix, with people in rows and items in columns

a

a vector of item discrimination parameters

b

a vector of item difficulty parameters

c

a vector of item pseudo-guesing parameters

init

a vectoro of initial value for theta parmaeters

iteration

the maximum iterations of Newton-Raphson procedure

delta

convergence criterion used to terminate Newton-Raphson procedure

bound

the maximum absolute values of estimated theta parameters

prior.mu

the mean of the prior theta distribuiton

prior.sig

the standard deviation of the prior theta distribution

Value

a vector of estimated thetas

Details

For the maximum likelihood estimation, refer to Baker and Kim (2004), pp. 66-69.

For the maximum a posteriori estimation, refer to Baker and Kim (2004), pp. 192.

For the expected a posteriori, refer to Baker and Kim (2004), pp. 193.

See Also

Other estimation: estimate.item.jmle

Other estimation: estimate.item.jmle

Other estimation: estimate.item.jmle

Examples

# MLE
x <- gen.rsp(gen.irt(100, 20))
y <- estimate.theta.mle(x$rsp, x$items$a, x$items$b, x$items$c)
cor(x$thetas, y)
plot(x$thetas, y, xlim=c(-4, 4), ylim=c(-4, 4), col=rgb(.8,.2,.2,.5), pch=16)
abline(a=0, b=1)
# MAP
x <- gen.rsp(gen.irt(100, 20))
y <- estimate.theta.map(x$rsp, x$items$a, x$items$b, x$items$c)
cor(x$thetas, y)
plot(x$thetas, y, xlim=c(-3, 3), ylim=c(-3, 3), col=rgb(.8,.2,.2,.5), pch=16)
abline(a=0, b=1)
# EAP
x <- gen.rsp(gen.irt(100, 20))
y <- estimate.theta.eap(x$rsp, x$items$a, x$items$b, x$items$c)
cor(x$thetas, y)
plot(x$thetas, y, xlim=c(-3, 3), ylim=c(-3, 3), col=rgb(.8,.2,.2,.5), pch=16)
abline(a=0, b=1)