| MAT {MAT} | R Documentation |
Multidimensional Adaptive Testing (MAT)
Description
MAT is a package to simulate multidimensional adaptive testing for the Multidimensional 3-Parameter Logistic (M3PL) model.
Usage
MAT(ipar, resp, cors,
target.content.dist = NULL, content.cat = NULL, ncc = 1,
content.order = NULL, p = stop("p is required"),
selectionMethod = c("D", "A", "C", "R"),
selectionType = c("FISHER", "BAYESIAN"), c.weights = NA,
stoppingCriterion = c("CONJUNCTIVE", "COMPENSATORY"),
topN = 1, minNI = 10, maxNI = 30, minSE = 0.3, D = 1,
maxIter = 30, conv = 0.001, minTheta = -4, maxTheta = 4,
plot.audit.trail = TRUE, theta.labels = NULL, easiness = TRUE)
Arguments
ipar |
a data frame containing M3PL item parameters, specifically a1, a2, ... , d, and c |
resp |
a data frame (that will be converted to a numeric matrix) of item responses, e.g., R1, R2, ..., R180 |
cors |
a square matrix of the lower diagonal elements of a variance-covariance (VCV) matrix, including 1's in the main diagonal |
target.content.dist |
an optional vector of target content distributions summed to 1.0, e.g., c(0.25,0.5,0.25) |
content.cat |
an optional vector specifying content designations |
ncc |
the number of content categories (default=1, i.e., no content balancing) |
content.order |
an optional vector specifying administration order of content categories, e.g., c(3,1,2) |
p |
the number of latent dimensions |
selectionMethod |
item selection criterion: "D"=D-optimality, "A"=A-optimality, "C"=C-optimality, "R"=Random (default="D") |
selectionType |
item selection method type: "FISHER"=Fisher information, "BAYESIAN"=adds inverse prior VCV |
c.weights |
an optional vector of weights of length p when selectionMethod="C" |
stoppingCriterion |
stopping criterion: "CONJUNCTIVE"=SEs for all dimensions must be met, "COMPENSATORY"=the generalized variance or SEs weighted by c-weights must be met |
topN |
Randomesque exposure control: selects an item randomly from the top N most informative items (default=1, no exposure control) |
minNI |
minimum number of items to administer (default=10) |
maxNI |
maximum number of items to administer (default=30) |
minSE |
minimum SE for stopping (default=0.3) |
D |
scaling constant: 1.7 or 1.0 (default=1.0) |
maxIter |
maximum number of Fisher scoring (default=30) |
conv |
convergence criterion for Fisher scoring (default=0.001) |
minTheta |
minimum theta value for plotting (default=-4) |
maxTheta |
maximum theta value for plotting (default=4) |
plot.audit.trail |
show CAT audit trail: T or F (default=T) |
theta.labels |
theta labels for plotting (default=c("Theta 1","Theta 2",...)) |
easiness |
logical, T if d is related to the easiness of items per Reckase, F otherwise |
Details
The purpose of this function is to simulate multidimensional adaptive testing based on the Multidimensional 3-Parameter Logistic (M3PL) model (Reckase, 2009):
P_i(\theta) \equiv P(U_i = 1|\boldsymbol{\theta}, \mathbf{a}_i, d_i, c_i) \equiv c_i + \frac{1-c_i}{1 + exp[-D(\mathbf{a}_i\cdot\boldsymbol{\theta} + d_i)]}
where \mathbf{a}_i is a vector of discrimination parameters of item i, \boldsymbol{\theta} is a vector of abilities, c_i is a scalar representing the
guessing parameter of item i, d_i is a scalar representing the easiness of item i.
Thetas are estimated using the Bayesian maximum a posteriori (MAP) estimator and the Fisher scoring method. Three item
selection criteria are available: D-optimality, A-optimality, and C-optimality (Segall, 1996; van der Linden, 1999;
Mulder & van der Linden, 2009). An option is provided to add the inverse of a prior variance-covariance
matrix to the multivariate information matrix (selectionType="BAYESIAN"). The stopping condition can be specified as a conjunctive criterion or a compensatory
criterion. Content balancing can be imposed by specifying target content distributions. An exposure control option is
provided via the randomesque technique.
Value
Returns a list of class "MAT" with the following components:
call |
function call stack |
items.used |
a matrix of items administered |
selected.item.resp |
a matrix containing item responses for selected items |
ni.administered |
a vector of the number of items administered |
theta.CAT |
a matrix of theta estimates from CAT |
se.CAT |
a matrix of SE estimates from CAT |
theta.history |
a matrix of theta history from CAT |
se.history |
a matrix of SE history from CAT |
theta.Full |
a matrix of theta estimates based on the full bank |
se.Full |
a matrix of SE estimates based on the full bank |
ipar |
a matrix of item parameters |
p |
the number of latent dimensions |
Note
The MAT function performs a number of checks to determine if the arguments for content balancing and content ordering have been specified correctly. If the arguments have not been specified correctly, content balancing and/or content ordering will not be used for the simulation. Additionally, a warning message will be printed to the console detailing the misspecification.
Content ordering is only available for fixed-length CAT. Namely, to invoke a particular content order, the user must set the minimum number of items equal to the maximum number of items (e.g., minNI=30 & maxNI=30).
Note
requires MASS
Author(s)
Seung W. Choi and David R. King
References
Segall, D. O. (1996). Multidimensional adaptive testing, Psychometrika, 61(2), 331-354
van der Linden, W. J. (1999). Multidimensional adaptive testing with a minimum error-variance criterion, Journal of Educational and Behavioral Statistics, 24(4), 398-412.
Mulder, J., & van der Linden, W. J. (2009). Multidimensional adaptive testing with optimal design criteria for item selection, Psychometrika, 74(2), 273-296.
Reckase, M. D. (2009). Multidimensional Item Response Theory. New York: Springer.
Examples
## Not run: MCAT.1<-MAT(ipar1,
resp1,
vcv1,
target.content.dist=target.content.dist1,
content.cat=content.cat1,
ncc=3,
p=3,
selectionMethod="A",
topN=1,
selectionType="FISHER",
stoppingCriterion="CONJUNCTIVE",
minNI=10,
maxNI=30)
## End(Not run)