CDM-package: Cognitive Diagnosis Modeling: The R Package CDM
Description
Cognitive diagnosis modeling (CDM) is restricted latent class modeling for
inferring from respondents' item answers fine-grained and individualized
diagnostic information about multiple latent attributes or competencies
(e.g., reading or mathematical comprehension skills). The package
CDM provides functions and example data for cognitive diagnosis
modeling with the deterministic-input, noisy-and-gate (DINA) and
deterministic-input, noisy-or-gate (DINO) models in R.concept
cognitive diagnosis modelingDetails
ll{
Package: CDM
Type: Package
Version: 0.0-4
Date: 2011-03-22
License: GPL (>= 2)
}
Cognitive diagnosis models (CDMs) are restricted latent class models.
They represent model-based classification approaches, which aim at
assigning respondents to different attribute profile groups. The latent
classes correspond to the possible attribute profiles, and the
conditional item parameters model atypical response behavior in the sense
of slipping and guessing errors. The core CDMs in particular differ in
the utilized condensation rule, conjunctive / non-compensatory versus
disjunctive / compensatory, where in the model structure these two
types of response error parameters enter and what restrictions are
imposed on them. The confirmatory character of CDMs is apparent in the
Q-matrix, which can be seen as an operationalization of the latent
concepts of an underlying theory. The Q-matrix allows incorporating
qualitative prior knowledge and typically has as its rows the items and
as the columns the attributes, with entries 1 or 0, depending on whether
an attribute is measured by an item or not, respectively.
CDMs as compared to common psychometric models (e.g., IRT) contain
categorical instead of continuous latent variables. The results of
analyses using CDMs differ from the results obtained under continuous
latent variable models. CDMs estimate in a direct manner the
probabilistic attribute profile of a respondent, that is, the
multivariate vector of the conditional probabilities for possessing the
individual attributes, given her / his response pattern. Based on these
probabilities, simplified deterministic attribute profiles can be
derived, showing whether an individual attribute is essentially possessed
or not by a respondent. As compared to alternative two-step
discretization approaches, which estimate continuous scores and discretize
the continua based on cut scores, with CDMs the classification error can
generally be reduced.
The package CDM implements parameter estimation procedures for the
two core CDMs DINA and DINO (e.g.,de la Torre and
Douglas, 2004, Junker and Sijtsma, 2001 and Templin and
Henson, 2006), and tools for analyzing data under the
two models. These and related concepts are explained in detail in the
book about diagnostic measurement and CDMs by
Rupp, Templin, and Henson (2010), and in such survey articles as
DiBello, Roussos, and Stout (2007) and
Rupp and Templin (2008).
The package CDM is implemented based on the S3 system. It comes
with a namespace and consists of one external function (a function the
package exports): the main function of this package, din. The
package obtains a utility method for the simulation of artificial data based
on a CDM model (sim.din). It also contains seven internal functions
(functions not exported by the package): this are plot, print, and
summary methods for objects of the class din (plot.din,
print.din, summary.din), a print method for
objects of the class summary.din (print.summary.din),
and three functions for checking the input format and computing intermediate
information (CDM-internal). The features of the package CDM are
illustrated with an accompanying real dataset and Q-matrix
(fraction.subtraction.data and fraction.subtraction.qmatrix)
and artificial examples (Data-sim).References
de la Torre, J. and Douglas, J. (2004) Higher-order latent trait models
for cognitive diagnosis. Psychometrika, 69, 333--353.
DiBello, L. V., Roussos, L. A. and Stout, W. F. (2007) Review of
cognitively diagnostic assessment and a summary of psychometric models.
In C. R. Rao and S. Sinharay (Eds.), Handbook of Statistics,
Vol. 26 (pp. 979--1030). Amsterdam: Elsevier.
Junker, B. W. and Sijtsma, K. (2001) Cognitive assessment models with few
assumptions, and connections with nonparametric item response theory.
Applied Psychological Measurement, 25, 258--272.
Rupp, A. A. and Templin, J. (2008) Unique characteristics of
diagnostic classification models: A comprehensive review of the current
state-of-the-art. Measurement: Interdisciplinary Research and
Perspectives, 6, 219--262.
Rupp, A. A., Templin, J. and Henson, R. A. (2010) Diagnostic
Measurement: Theory, Methods, and Applications. New York: The Guilford
Press.
Templin, J. and Henson, R. (2006) Measurement of
psychological disorders using cognitive diagnosis
models. Psychological Methods, 11, 287--305.