MEI(itemBank, item, x, theta, it, method="BM", priorDist="norm",
priorPar=c(0,1), D=1, range=c(-4,4), parInt=c(-4,4,33),
infoType="observed")itBank, typically an output of the function createItemBank.it must be equal to the
"BM" (default), "ML" and "WL". See Details."norm" (default), "unif" and "Jeffreys".
Ignored if method is neither "BM" nor "EAP". See Details.c(0,1)) of the prior ability distribution. Ignored if method is neither "BM"
nor "EAP", or if priorDist="Jeffreys"D=1 (for logistic metric); D=1.702 yields approximately the normal metric (Haley, 1952).c(-4,4)).
Ignored if method=="EAP".lower, upper and nqp of the
eapEst command. Default vector is (-4, 4, 33). Ignor"observed" (default) for observed
information function, and "Fisher" for Fisher information function.nextItem function.
Let k be the number of administered items, and set $x_1, ..., x_k$ as the provisional response pattern. Set $\hat{\theta}_k$ as the
provisional ability estimate (with the first k responses) and let j be the item of interest (not previously administered). Set also $P_j(\theta)$
as the probability of answering item j correctly for a given ability level $\theta$, and set $Q_j(\theta)=1-P_j(\theta)$. Finally, set
$\hat{\theta}_{k+1}^0$ and $\hat{\theta}_{k+1}^1$ as the ability estimates computed under the condition that the response to item j is 0 or 1
respectively (that is, if the response pattern is updated by 0 or 1 for item j). Then, the MEI for item j equals
$$MEI_j = P_j(\hat{\theta}_k)\,I_j(\hat{\theta}_{k+1}^1) + Q_j(\hat{\theta}_k)\,I_j(\hat{\theta}_{k+1}^0)$$
where $I_j(\theta)$ is the information function for item j.
Two types of information functions are available. The first one is the observed information function, defined as
$$I_j(\theta) = -\frac{\partial^2}{\partial\,\theta^2} \,\log P_j(\theta).$$
(van der Linden, 1998). The second one is Fisher information function:
$$I_j(\theta) = -E\,\left[\frac{\partial^2}{\partial\,\theta^2} \,\log P_j(\theta)\right].$$
Under the 1PL and the 2PL models, these functions are identical (Veerkamp, 1996).
The observed and Fisher information functions are specified by the infoType argument, with respective values "observed" and "Fisher". By
default, the observed information function is considered (Choi and Swartz, 2009; van der Linden, 1998).
The estimator of provisional ability is defined by means of the arguments method, priorDist, priorPar, D, range and
parInt of the thetaEst function. See the corresponding help file for further details.
The item bank is provided through the argument itemBank. The provisional response pattern and the related item parameters are provided by the arguments
x and it respectively. The target item (for which the maximum information computed) is given by its number in the item bank, through the
item argument.Ii, OIi, nextItem, integrate.xy, thetaEst# Loading the 'tcals' parameters
data(tcals)
# Selecting item parameters only
tcals <- as.matrix(tcals[,1:4])
# Item bank creation with 'tcals' item parameters
bank <- createItemBank(tcals)
# Selection of two arbitrary items (15 and 20) of the
# 'tcals' data set
it <- bank$itemPar[c(15,20),]
# Creation of a response pattern
x <- c(0,1)
# MEI for item 1, provisional ability level 0
MEI(bank, 1, x, 0, it)
# With Fisher information instead
MEI(bank, 1, x, 0, it, infoType="Fisher")
# With WL estimator instead
MEI(bank, 1, x, 0, it, method="WL")Run the code above in your browser using DataLab