select.item {simCAT}

Select next item

Description

Select next item to be administered

Usage

select.item(
  bank,
  model = "3PL",
  theta,
  administered = NULL,
  sel.method = "MFI",
  cat.type = "variable",
  threshold = 0.3,
  SE,
  acceleration = 1,
  met.weight = "mcclarty",
  max.items = 45,
  content.names = NULL,
  content.props = NULL,
  content.items = NULL,
  met.content = "MCCAT"
)

Arguments

bank

matrix with item parameters (a, b, c)

model

may be ⁠3PL⁠ or graded

theta

current theta

administered

vector with administered items, NULL if it is the first item

sel.method

item selection method: may be MFI, progressive or random

cat.type

CAT with variable or fixed length. Necessary only for progressive method.

threshold

threshold for cat.type. Necessary only for progressive method.

SE

current standard error. Necessary only for progressive method, with cat.type = "variable"

acceleration

acceleration parameter. Necessary only for progressive method.

met.weight

the procedure to calculate the progressive's weight in variable-length CAT. It can be "magis" or "mcclarty" (default). See details.

max.items

maximum number of items to be administered. Necessary only for progressive method, with cat.type = "variable"

content.names

vector with the contents of the test

content.props

desirable proportion of each content in test, in the same order of content.names

content.items

vector indicating the content of each item

met.content

content balancing method: MCCAT (default), CCAT or MMM. See content.balancing for more information.

Details

In the progressive (Revuelta & Ponsoda, 1998), the administered item is the one that has the highest weight. The weight of the item i is calculated as following:

W_i = (1-s)R_i+sI_i

where R is a random number between zero and the maximum information of an item in the bank for the current theta, I is the item information and s is the importance of the component. As the application progresses, the random component loses importance. There are some ways to calculate s. For fixed-length CAT, Barrada et al. (2008) uses

s = 0

if it is the first item of the test. For the other administering items,

s = \frac{\sum_{f=1}^{q}{(f-1)^k}}{\sum_{f=1}^{Q}{(f-1)^k}}

where q is the number of the item position in the test, Q is the test length and k is the acceleration parameter. simCAT package uses these two equations for fixed-length CAT. For variable-length, simCAT package can use "magis" (Magis & Barrada, 2017):

s = max [ \frac{I(\theta)}{I_{stop}},\frac{q}{M-1}]^k

where I(\theta) is the item information for the current theta, I_{stop} is the information corresponding to the stopping error value, and M is the maximum length of the test. simCAT package uses as default "mcclarty" (adapted from McClarty et al., 2006):

s = (\frac{SE_{stop}}{SE})^k

where SE is the standard error for the current theta, SE_{stop} is the stopping error value.

Value

A list with two elements

• item the number o the selected item in item bank

• name name of the selected item (row name)

Author(s)

Alexandre Jaloto

References

Barrada, J. R., Olea, J., Ponsoda, V., & Abad, F. J. (2008). Incorporating randomness in the Fisher information for improving item-exposure control in CATs. British Journal of Mathematical and Statistical Psychology, 61(2), 493–513. 10.1348/000711007X230937

Leroux, A. J., & Dodd, B. G. (2016). A comparison of exposure control procedures in CATs using the GPC model. The Journal of Experimental Education, 84(4), 666–685. 10.1080/00220973.2015.1099511

Magis, D., & Barrada, J. R. (2017). Computerized adaptive testing with R: recent updates of the package catR. Journal of Statistical Software, 76(Code Snippet 1). 10.18637/jss.v076.c01

McClarty, K. L., Sperling, R. A., & Dodd, B. G. (2006). A variant of the progressive-restricted item exposure control procedure in computerized adaptive testing. Annual Meeting of the American Educational Research Association, San Francisco

Revuelta, J., & Ponsoda, V. (1998). A comparison of item exposure control methods in computerized adaptive testing. Journal of Educational Measurement, 35(4), 311–327. http://www.jstor.org/stable/1435308