shortIRT (version 0.1.3)

uip: Unequal interval procedure

Description

Create a Short Test Form (STF) using the \(\theta\)-target procedure based on the unequal segmentation of the latent trait (Unequal Interval Procedure, EIP)

Usage

uip(data, item_par = NULL, seed = 999, starting_theta = NULL, num_item = NULL)

Value

A list of length 5:

- item_stf: data.frame, contains the items included in the STF. The number of rows is equal to the number of items included in the STF. The \(\theta\)-targets and the item information functions of the optimal item for each \(\theta\)-target are reported as well

- summary: data.frame, contains the list of items included in the STF and the test information on both the full-length test and the STF

- info_stf: list, contains the item information functions of the STF

- info_full: list, contains the item information functions of the full-length test

- theta: data.frame, contains the starting \(\theta\) and the \(\theta\) estimated with the STF

Arguments

data

data.frame, subject \(\times\) item matrix containing the accuracy responses

item_par

matrix, two-column matrix containing the item parameters. The first column must contain the difficulty parameters \(b_i\), the second column must contain the discrimination parameters \(a_i\).

seed

integer, define the random seed. Default is 999

starting_theta

vector, define the starting \(\theta\) of the subjects. If empty, the \(\theta\) values will be estimated from the data

num_item

integer, the number of items to include in the short test form

Examples

# set a seed to replicate the results
set.seed(999)
# Simulate person and item parameters
true_theta <- rnorm(1000)
b <- runif(30, -3, 3)
a <- runif(30, 0.6, 2)
parameters <- data.frame(b, a)
# simulate data
data <- sirt::sim.raschtype(true_theta, b = b, fixed.a = a)
stf_uip = uip(data, starting_theta = true_theta, item_par = parameters, num_item = 10)
# check the obtained short test form
stf_uip$item_stf
# check the comparison between the short test form and the full-length test
stf_uip$summary