xxIRT (version 2.0.0)

estimate.people: Estimation of People Parameters

Description

estimate.people is a wrapper function for estimating people parameters

estimate.people.3pl.mle estimates people parameters with known item parameters using maximum likelihood estimation.

estimate.people.3pl.map estimates people parameters with known item parameters using maximum a posterior.

estimate.3pl.theta.eap estimates people parameters with known item parameters using expected a posterior.

Usage

estimate.people(responses, items, model = "3pl", method = "mle", ...)
estimate.people.3pl.mle(responses, items, init = 0, iter = 30, conv = 0.01, bound = 3.5, debug = FALSE)
estimate.people.3pl.map(responses, items, prior.mu = 0, prior.sig = 1, init = 0, iter = 15, conv = 0.01, bound = 3.5, debug = FALSE)
estimate.people.3pl.eap(responses, items)

Arguments

responses

a data frame of responses

items

a data frame of item parameters

model

the IRT model

method

the estimation method

...

further arguments

init

initial values of people parameters, a number or a vector

iter

the maximum of iterations

conv

convergence criterion

bound

the bounds of resulting people parameters

debug

TRUE to turn on debug mode

prior.mu

the mean of the prior distribuiton

prior.sig

the standard deviation of the prior distribution

Value

a data frame of estimated people parameters

Details

The debug mode draws a convergence curve. 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.

Examples

## Not run: 
# # data generation
# data <- irt.model(model="3pl")$gen.data(500, 50)
# # MLE
# x <- estimate.people(data$responses, data$items, "3pl", "mle", debug=TRUE)
# cor(data$people$theta, x$people$theta)
# plot(data$people$theta, x$people$theta, xlim=c(-4,4), ylim=c(-4,4), 
# xlab="True", ylab="Est.", col=rgb(.8,.2,.2,.5), pch=16)
# # MAP
# x <- estimate.people(data$responses, data$items, "3pl", "map", debug=TRUE)
# cor(data$people$theta, x$people$theta)
# plot(data$people$theta, x$people$theta, xlim=c(-4,4), ylim=c(-4,4), 
# xlab="True", ylab="Est.", col=rgb(.8,.2,.2,.5), pch=16)
# # EAP
# x <- estimate.people(data$responses, data$items, "3pl", "eap")
# cor(data$people$theta, x$people$theta)
# plot(data$people$theta, x$people$theta, xlim=c(-4,4), ylim=c(-4,4), 
# xlab="True", ylab="Est.", col=rgb(.8,.2,.2,.5), pch=16)
# ## End(Not run)
## Not run: 
# # data generation
# data <- irt.model(model="3pl")$gen.data(500, 50)
# # MLE
# x <- estimate.people.3pl.mle(data$responses, data$items, debug=TRUE)
# cor(data$people$theta, x$people$theta)
# plot(data$people$theta, x$people$theta, xlim=c(-4,4), ylim=c(-4,4), 
# xlab="True", ylab="Est.", col=rgb(.8,.2,.2,.5), pch=16)
# # MAP
# x <- estimate.people.3pl.map(data$responses, data$items, debug=TRUE)
# cor(data$people$theta, x$people$theta)
# plot(data$people$theta, x$people$theta, xlim=c(-4,4), ylim=c(-4,4), 
# xlab="True", ylab="Est.", col=rgb(.8,.2,.2,.5), pch=16)
# # EAP
# x <- estimate.people.3pl.eap(data$responses, data$items)
# cor(data$people$theta, x$people$theta)
# plot(data$people$theta, x$people$theta, xlim=c(-4,4), ylim=c(-4,4), 
# xlab="True", ylab="Est.", col=rgb(.8,.2,.2,.5), pch=16)
# ## End(Not run)