MAT: Multidimensional Adaptive Testing (MAT)

In MAT: Multidimensional Adaptive Testing

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(θ) \equiv P(U_i = 1|\boldsymbol{θ}, \mathbf{a}_i, d_i, c_i) \equiv c_i + \frac{1-c_i}{1 + exp[-D(\mathbf{a}_i\cdot\boldsymbol{θ} + d_i)]}

where \mathbf{a}_i is a vector of discrimination parameters of item i, \boldsymbol{θ} 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

1. 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.

2. 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

1. Segall, D. O. (1996). Multidimensional adaptive testing, Psychometrika, 61(2), 331-354

2. 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.

3. Mulder, J., & van der Linden, W. J. (2009). Multidimensional adaptive testing with optimal design criteria for item selection, Psychometrika, 74(2), 273-296.

4. 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)

MAT documentation built on May 1, 2022, 5:07 p.m.