Package 'shortIRT'

Benchmark Procedure

Description

Create a Short Test Form (STF) using the typical IRT procedure for shortening test (Benchmark Procedure, BP)

Usage

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

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

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

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 <- bp(data, starting_theta = true_theta, item_par = parameters, num_item = 5)
# check the obtained short test form
stf$item_stf
# check the comparison between the short test form and the full-length test
stf$summary

---

Change column names

Description

Change the columns names of a data frame and stores the original column names

Usage

change_names(data)

Arguments

data	data.frame, A data frame

Value

A list of length two:

1. a data frame with the original column names and the corresponding new names

2. a data frame with the changed column names

Examples

# original data frame with 5 columns
data <- data.frame(matrix(1:20, nrow = 4, ncol = 5))
change_names(data)

---

Cut borders

Description

Extract the limits of the intervals obtained from sub setting a vector

Usage

cut_borders(x)

Arguments

x	numeric/integer vector

Value

A data frame with two columns. The first column contains the lower bounds of each interval. The second column contains the upper bound of each interval

Examples

x <- seq(-3, 3, length = 5)
groups <- cut(x, 5, include.lowest = TRUE)
boundaries <- cut_borders(groups)

---

Difference between $\theta$s

Description

Compute the difference between a starting value of $\theta$ and the $\theta$ estimated with the STF

Usage

diff_theta(results, starting_theta = NULL)

Arguments

results	The object obtained from the stf-generating functions
starting_theta	vector, optional vector of length equal to the number of rows in the original data frame with the true $\theta$ of the respondents. Default is NULL, such that the $\theta$ estimated with the full-length test will be considered as the starting $\theta$

Value

A data frame with number of rows equal to the number of respondents and 3 columns, one with the starting/true $\theta$, one with the $\theta$ estimated with the STF, and the difference between the estimated $\theta$ and the starting/true $\theta$

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(data, starting_theta = true_theta, item_par = parameters, num_item = 5)
# without starting theta
my_diff <- diff_theta(stf)
head(my_diff)

---

Equal Interval Procedure

Description

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

Usage

eip(
  data,
  item_par = NULL,
  seed = 999,
  starting_theta = NULL,
  num_item = NULL,
  theta_targets = NULL
)

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
theta_targets	vector, define the specific $\theta$ targets for the user defined procedure. Might also be the same $\theta$ target repeated for as many times as the number of items to be included in the short test form

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

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 <- eip(data, starting_theta = true_theta, item_par = parameters, num_item = 5)
# check the obtained short test form
stf$item_stf
# check the comparison between the short test form and the full-length test
stf$summary

# Short test form with cut off values
stf_cutoff <- eip(data, starting_theta = true_theta,
item_par = parameters, theta_targets = rep(2, 5))
stf_cutoff$item_stf

---

Plot the difference between $\theta$s

Description

Plot the difference or the absolute difference between the starting $\theta$ and the $\theta$ estimated with the STF as a function of different levels of the latent trait

Usage

plot_difference(difference, type = c("diff", "absolute_diff"), levels = 4)

Arguments

difference	data.frame, data frame obtained with the function [diff_theta()]
type	character, type of difference, either as is ("diff") or absolute ("absolute_diff"). Default is "diff".
levels	integer, number of levels of the starting $\theta$ Default is 4

Value

A ggplot object

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(data, starting_theta = true_theta, item_par = parameters, num_item = 5)
# compute the difference between starting theta and that estimated with the stf
my_diff <- diff_theta(stf)
# plot the difference with default number of levels
plot_difference(my_diff, type = "diff")
# plot the absolute difference with 10 levels
plot_difference(my_diff, type = "absolute_diff", levels = 10)

---

Plot Test Information Functions

Description

Plot the test information functions of the short test form (default), of the full length test or of both versions

Usage

plot_tif(results, tif = c("stf", "full", "both"))

Arguments

results	The object obtained from the stf-generating functions
tif	character, define the TIF to plot, either "stf" (TIF of the STF), "full", (TIF of the full-length test) or "both" (TIF of both STF and full-length test). Default is "stf"

Value

A ggplot object

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(data, starting_theta = true_theta, item_par = parameters, num_item = 5)
# plot the test information function of the full-length test
plot_tif(stf, tif = "full")
# plot the test information of the full-length test and of the short test form
plot_tif(stf, tif = "both")

---

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)

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

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

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

---