xxIRT (version 2.0.0)

irt.model: Common IRT Computations and Operations

Description

irt.model is a function for creating irt.model objects

irt.model.3pl.init is a function for creating irt.model.3pl object using parameter vectors

irt.stats is a function for common IRT computations (e.g., probability, information, likelihood)

plot.irt.model draws the item/test characteristics curve, informaiton function, likelihood curve for an IRT object

irt.select selects data from an IRT object

irt.sample samples data from an IRT object

irt.rescale.3pl rescale 3PL parameters

Usage

irt.model(people = NULL, items = NULL, responses = NULL, model = "3pl")
irt.model.3pl.init(theta, a, b, c, responses = NULL)
irt.stats(x, stats = "probability", summary = NULL, fun = NULL, ...)
"print"(x, ...)
"plot"(x, ...)
irt.select(x, people.index = NULL, items.index = NULL)
irt.sample(x, n.people = 0, n.items = 0)
irt.rescale.3pl(x, parameter = "theta", mu = 0, sig = 1)

Arguments

people

a data frame of people parameters

items

a data frame of item parameters

responses

a data frame of responses

model

the name of IRT model

theta

a vector of theta parameters

a

a vector of a parameters

b

a vector of b parameters

c

a vector of b parameters

x

a irt.model object

stats

the statistic to be computed (e.g., probability, information, likelihood)

summary

the summarization dimension (e.g., people, items)

fun

the summarization function (e.g, sum or prod)

...

other optional arguments

people.index

the indices of people to select

items.index

the indices of items to select

n.people

the nubmer of people to sample

n.items

the number of items to sample

parameter

the rescaling parameter

mu

the mean of the new scale

sig

the standard deviation of the new scale

Value

irt.model returns a irt.mode objectirt.stats returns a vector/matrix of resulting computation valuesplot.irt.model returns a 'ggplot2' object

Details

A irt.model object contains people parameters, item parameters and responses. The irt.model also contains functions toprobability, informaiton and likelihood. In addtional, it has a gen.data function to generate data.

In plot.irt.model, use the stats argument to control what IRT statistics for drawing. Use total argument to control draw one summed line for the whole test or multiple line for indiviual items. When drawing stats="loglikelihood", make sure the irt.model object has only one person

irt.select subsets responses when it is not NULL. When people.index or items.index is NULL, keep all.

Examples

# create a 3PL model with manual inputs
people <- data.frame(theta=c(-1,0,1))
items <- data.frame(a=c(.5,1,1.5,1,1,1,1), b=c(0,0,0,-1,1,0,0), c=c(0,0,0,0,0,.1,.2))
responses <- data.frame(item1=c(0,0,1), item2=c(0,1,1), item3=c(0,1,1), 
item4=c(1,1,1), item5=c(0,0,1), item6=c(0,1,1), item7=c(1,1,1))
x <- irt.model(people, items, responses, "3PL")
x
x$probability(x)
x$information(x)
x$likelihood(x)
# create a 3PL model with generated data
x <- irt.model(model="3pl")$gen.data(20, 5)
x
x$probability(x)
x$information(x)
x$likelihood(x)
# Generate Rasch items
irt.model(model="3pl")$gen.data(20, 5, a.mu=0, a.sig=0, c.alpha=0, c.beta=0)
# Generate an 3PL item pool
irt.model(model="3pl")$gen.data(1, 100)$items
# Generate responses using given people and item parameters
irt.model(model="3pl")$gen.data(people=people, items=items)$responses
# create 3pl model using parameter vectors
irt.model.3pl.init(people$theta, items$a, items$b, items$c, responses)
irt.model.3pl.init(people$theta, .58, items$b, 0, NULL)
 
# compute probability, information, likelihood and loglikelihood
x <- irt.model(model="3pl")$gen.data(20, 5)
irt.stats(x, "probability")
irt.stats(x, "probability", "people", sum)
irt.stats(x, "information")
irt.stats(x, "information", "items", sum)
irt.stats(x, "likelihood")
irt.stats(x, "likelihood", "people", prod)
log(irt.stats(x, "likelihood", "people", prod))
irt.stats(x, "loglikelihood", "people", sum)
# plot probability, information and log-likelihood
x <- irt.model(model="3pl")$gen.data(20, 5)
plot(x, stats="probability")
plot(x, stats="probability", total=FALSE)
plot(x, stats="information")
plot(x, stats="information", total=FALSE)
plot(irt.sample(x, n.people=1), stats="loglikelihood")
# select from an IRT model
irt.select(x, people.index=c(1,3,5))
irt.select(x, items.index=c(1,3,5))
# sample wihtout replacement from an IRT model
irt.sample(x, n.people=3)
irt.sample(x, n.items=3)
# sample with replacement from an IRT model
irt.sample(x, n.people=30)
irt.sample(x, n.items=30)
# rescale theta
x <- irt.model(model="3pl")$gen.data(5,3)
c(mean(x$people$theta), sd(x$people$theta))
y <- irt.rescale.3pl(x, "theta", 0, 1)
c(mean(y$people$theta), sd(y$people$theta))
irt.stats(x, "probability")
irt.stats(y, "probability")
# rescale b
x <- irt.model(model="3pl")$gen.data(5,3)
c(mean(x$items$b), sd(x$items$b))
y <- irt.rescale.3pl(x, "b", 0, 1)
c(mean(y$items$b), sd(y$items$b))
irt.stats(x, "probability")
irt.stats(y, "probability")