Select next item to be administered
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"
)A list with two elements
item the number o the selected item in item bank
name name of the selected item (row name)
matrix with item parameters (a, b, c)
may be 3PL or graded
current theta
vector with administered items, NULL if it is the first
item
item selection method: may be MFI, progressive
or random
CAT with variable or fixed length.
Necessary only for progressive method.
threshold for cat.type.
Necessary only for progressive method.
current standard error.
Necessary only for progressive method, with cat.type = "variable"
acceleration parameter. Necessary only for progressive method.
the procedure to calculate the progressive's weight in variable-length
CAT. It can be "magis" or "mcclarty" (default). See details.
maximum number of items to be administered.
Necessary only for progressive method, with cat.type = "variable"
vector with the contents of the test
desirable proportion of each content in test, in
the same order of content.names
vector indicating the content of each item
content balancing method: MCCAT (default), CCAT
or MMM. See content.balancing for more information.
Alexandre Jaloto
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.
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