Estimation of Ability Parameters

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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

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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

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.

Value

a vector of estimated thetas

See Also

Other estimation: estimate.item.jmle

Other estimation: estimate.item.jmle

Other estimation: estimate.item.jmle

Examples

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# 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)