Multidimensional Adaptive Testing (MAT)

Description

MAT is a package to simulate Multidimensional Adaptive Testing (MAT) for the Multidimensional 3-Parameter Logistic (M3PL) Model as described in Segall (1996), Reckase (2009), and Mulder & van der Linden (2009).

Author(s)

Seung W. Choi and David R. King

Maintainer: Seung W. Choi <s-choi@northwestern.edu>

References

1. Choi, S. W., & King, D. R. (2015). R Package MAT: Simulation of multidimensional adaptive testing for dichotomous IRT models. Applied Psychological Measurement, 39(3), 239-240.

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

3. 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.

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

5. Reckase, M. D. (2009). Multidimensional Item Response Theory. New York: Springer.

Examples

  #load sample item parameters containing 180 items measuring three dimensions
  data(sample.ipar)
  #create a variance-covariance (correlation) matrix
  vcv1<-diag(3); vcv1[lower.tri(vcv1,diag=FALSE)]<-c(.5,.6,.7)
  #simulate item responses
  resp1<-simM3PL(sample.ipar, vcv1, 3, n.simulee = 100)$resp
  #specify target content distributions
  target.content.dist1<-c(1/3,1/3,1/3)
  #content category designations for items
  content.cat1<-rep(1:3,rep(60,3))
  #simulate multidimensional adaptive testing
  MCAT.1<-MAT(sample.ipar,
              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)
	

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

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:

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)

internals

Description

internals

Details

internals

Value

none

Sample item parameters

Description

A sample item parameter file containing 180 Multidimensional 3-PL (M3PL) model.

Usage

data(sample.ipar)

Format

A data frame with item parameters for 180 items.

a1

the discrimination parameter for theta 1

a2

the discrimination parameter for theta 2

a3

the discrimination parameter for theta 3

d

the easiness parameter, d=-a*b

c

the guessing parameter

Details

First 60 items are primarily loaded on theta 1, second 60 on theta 2, and last 60 on theta 3.

Examples

  data(sample.ipar)

Simulate M3PL item responses

Description

Simulates item responses according to the Multidimensional 3-Parameter Logistic (M3PL) model

Usage

  simM3PL(ipar, cors, p, n.simulee = 100, D = 1, easiness = T, seed = NULL)

Arguments

Details

This function simulates item responses according to the Multidimensional 3-Parameter Logistic (M3PL) model using the item parameters input to the function. Thetas are drawn from the multivariate standard normal distribution with the population variance-covariance (correlation) matrix input to the function.

Value

Author(s)

Seung W. Choi

References

Reckase, M. D. (2009). Multidimensional Item Response Theory. New York: Springer.

Examples

  data(sample.ipar)
  vcv1<-diag(3)
  vcv1[lower.tri(vcv1,diag=FALSE)]<-c(.5,.6,.7)
  resp1<-simM3PL(sample.ipar, vcv1, 3, n.simulee = 100, seed = 1234)$resp