xxIRT (version 2.0.1)

estimate_items: Estimate Item Parameters

Description

Estimate item parameters

estimate_items_3pl_jmle is the joint maximum likelihood estimator (JML) of item parameters

estimate_items_3pl_mmle is the marginal maximum likelihood estimator (MMLE) of item parameters

estimate_items_3pl_bme is the bayesian estimator of item parameters

Usage

estimate_items(responses, model = c("3pl"), method = c("jmle", "mmle",
  "bme"), ...)
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.mean = 0, a.sd = 0.2, b.mean = 0, b.sd = 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 or matrix 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 debugging mode

prior

a list of prior distributions parameters

Value

a data frame of estimated item parameters

estimated item parameters and diagnosis data if debug mode is on

Details

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

For the Bayesian 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
library(ggplot2)
library(reshape2)
library(dplyr)
data <- irt_model("3pl")$gendata(2000, 50)

# Estimate item parameters: JMLE
x.jmle <- estimate_items(data$responses, "3pl", "jmle", people=data$people)
# Estimate item parameters: MMLE
x.mmle <- estimate_items(data$responses, "3pl", "mmle")
# Estimate item parameters: BME
x.bme <- estimate_items(data$responses, "3pl", "bme")
# Comparison with true parameters
sapply(list(jmle=x.jmle, mmle=x.mmle, bme=x.bme), function(x) diag(cor(x$items, data$items)))
sapply(list(jmle=x.jmle, mmle=x.mmle, bme=x.bme), function(x) rmse(x$items, data$items))
x <- rbind(data.frame(method="jmle", melt(x.jmle$items), true=melt(data$items)$value),
           data.frame(method="mmle", melt(x.mmle$items), true=melt(data$items)$value),
           data.frame(method="bme", melt(x.bme$items), true=melt(data$items)$value))
ggplot(data=x, aes(x=true, y=value, color=method)) + geom_point(pch=1) +
  facet_grid(variable ~ method, scales="free") + xlab("True") + ylab("Est.") +
  theme_bw() + theme(legend.key=element_blank())
# }