xxIRT (version 2.0.0)

estimate.items: Estimation of Item Parameters

Description

estimate.items is a wrapper function for estimating item parameters

estimate.items.3pl.jmle calibrates item parameters with knwon thetas using joint maximum likelihood.

estimate.items.3pl.mmle calibrates item parameters without knowing people parameters using marginal maximum likelihood.

estimate.items.3pl.bme calibrates item parameters without knowing people parameters using bayesian maximum likelihood.

Usage

estimate.items(responses, model = "3pl", method = "jmle", ...)
estimate.items.3pl.jmle(responses, people, fix = list(), iter = 30, conv = 0.01, bound = list(a = 2, b = 3.5, c = 0.25), init = list(a = 1, b = 0, c = 0), debug = FALSE)
estimate.items.3pl.mmle(responses, fix = list(), iter = 30, conv = 0.01, bound = list(a = 2, b = 3.5, c = 0.25), init = list(a = 1, b = 0, c = 0), debug = FALSE)
estimate.items.3pl.bme(responses, fix = list(), iter = 30, conv = 0.01, prior = list(a.mu = 0, a.sig = 0.2, b.mu = 0, b.sig = 1, c.alpha = 5, c.beta  = 43), bound = list(a = 2, b = 3.5, c = 0.25), init = list(a = 1, b = 0, c  = 0.1), debug = FALSE)

Arguments

responses

a data frame of responses

model

the IRT model

method

the estimation method

...

further arguments

people

a data frame of people parameters

fix

a list of fixed item parameters

iter

the maximum iterations

conv

the convergence criterion

bound

the bounds of item parameters

init

a list of initial item parameters

debug

TRUE to turn on debug mode

prior

a list of parameters for a-, b-, c-parameter prior distributions

Value

a data frame of estimated item parametersestimated item parameters and diagnosis data if debug mode is on

Details

For the joint maximum likelihood estimation, refer to Baker and Kim (2004), pp. 46-54. To fixing item parameters, pass in a number or a vector (the same length with the items) to the fix argument. The debug mode prints convergence process and add diagnosis data to output

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. In estimate.items.3pl.bme, a parameters is assumed to have a lognormal prior distribution, b parameters a normal prior distribution, and c parameters a beta prior distribution.

Examples

## Not run: 
# # data generation
# data <- irt.model(model="3pl")$gen.data(2000, 50)
# # JMLE
# x <- estimate.items(data$responses, model="3pl", method="jmle", people=data$people, debug=TRUE)
# cor(data$items, x$items)
# plot(data$items$a, x$items$a, xlim=c(0, 2), ylim=c(0, 2), pch=16, 
# xlab="True", ylab="Est.", col=rgb(.8,.2,.2,.6))
# plot(data$items$b, x$items$b, xlim=c(-4, 4), ylim=c(-4, 4), pch=16, 
# xlab="True", ylab="Est.", col=rgb(.8,.2,.2,.6))
# plot(data$items$c, x$items$c, xlim=c(0, .3), ylim=c(0, .3), pch=16, 
# xlab="True", ylab="Est.", col=rgb(.8,.2,.2,.6))
# # MMLE
# x <- estimate.items(data$responses, model="3pl", method="mmle", debug=TRUE)
# cor(data$items, x$items)
# plot(data$items$a, x$items$a, xlim=c(0, 2), ylim=c(0, 2), pch=16, 
# xlab="True", ylab="Est.", col=rgb(.8,.2,.2,.6))
# plot(data$items$b, x$items$b, xlim=c(-4, 4), ylim=c(-4, 4), pch=16, 
# xlab="True", ylab="Est.", col=rgb(.8,.2,.2,.6))
# plot(data$items$c, x$items$c, xlim=c(0, .3), ylim=c(0, .3), pch=16, 
# xlab="True", ylab="Est.", col=rgb(.8,.2,.2,.6))
# # BME
# x <- estimate.items(data$responses, model="3pl", method="bme", debug=TRUE)
# cor(data$items, x$items)
# plot(data$items$a, x$items$a, xlim=c(0, 2), ylim=c(0, 2), pch=16, 
# xlab="True", ylab="Est.", col=rgb(.8,.2,.2,.6))
# plot(data$items$b, x$items$b, xlim=c(-4, 4), ylim=c(-4, 4), pch=16, 
# xlab="True", ylab="Est.", col=rgb(.8,.2,.2,.6))
# plot(data$items$c, x$items$c, xlim=c(0, .3), ylim=c(0, .3), pch=16, 
# xlab="True", ylab="Est.", col=rgb(.8,.2,.2,.6))
# ## End(Not run)
## Not run: 
# # data generation
# data <- irt.model(model="3pl")$gen.data(2000, 50)
# # JMLE
# x <- estimate.items.3pl.jmle(data$responses, data$people, debug=TRUE)
# cor(data$items, x$items)
# plot(data$items$a, x$items$a, xlim=c(0, 2), ylim=c(0, 2), pch=16, 
# xlab="True", ylab="Est.", col=rgb(.8,.2,.2,.6))
# plot(data$items$b, x$items$b, xlim=c(-4, 4), ylim=c(-4, 4), pch=16, 
# xlab="True", ylab="Est.", col=rgb(.8,.2,.2,.6))
# plot(data$items$c, x$items$c, xlim=c(0, .3), ylim=c(0, .3), pch=16, 
# xlab="True", ylab="Est.", col=rgb(.8,.2,.2,.6))
# # MMLE
# x <- estimate.items.3pl.mmle(data$responses, debug=TRUE)
# cor(data$items, x$items)
# plot(data$items$a, x$items$a, xlim=c(0, 2), ylim=c(0, 2), pch=16, 
# xlab="True", ylab="Est.", col=rgb(.8,.2,.2,.6))
# plot(data$items$b, x$items$b, xlim=c(-4, 4), ylim=c(-4, 4), pch=16, 
# xlab="True", ylab="Est.", col=rgb(.8,.2,.2,.6))
# plot(data$items$c, x$items$c, xlim=c(0, .3), ylim=c(0, .3), pch=16, 
# xlab="True", ylab="Est.", col=rgb(.8,.2,.2,.6))
# # BME
# x <- estimate.items.3pl.bme(data$responses, debug=TRUE)
# cor(data$items, x$items)
# plot(data$items$a, x$items$a, xlim=c(0, 2), ylim=c(0, 2), pch=16, 
# xlab="True", ylab="Est.", col=rgb(.8,.2,.2,.6))
# plot(data$items$b, x$items$b, xlim=c(-4, 4), ylim=c(-4, 4), pch=16, 
# xlab="True", ylab="Est.", col=rgb(.8,.2,.2,.6))
# plot(data$items$c, x$items$c, xlim=c(0, .3), ylim=c(0, .3), pch=16, 
# xlab="True", ylab="Est.", col=rgb(.8,.2,.2,.6))
# ## End(Not run)