CDM-package {CDM} | R Documentation |

## Cognitive Diagnosis Modeling

### Description

Functions for cognitive diagnosis modeling and multidimensional item response modeling for dichotomous and polytomous item responses. This package enables the estimation of the DINA and DINO model (Junker & Sijtsma, 2001, <doi:10.1177/01466210122032064>), the multiple group (polytomous) GDINA model (de la Torre, 2011, <doi:10.1007/s11336-011-9207-7>), the multiple choice DINA model (de la Torre, 2009, <doi:10.1177/0146621608320523>), the general diagnostic model (GDM; von Davier, 2008, <doi:10.1348/000711007X193957>), the structured latent class model (SLCA; Formann, 1992, <doi:10.1080/01621459.1992.10475229>) and regularized latent class analysis (Chen, Li, Liu, & Ying, 2017, <doi:10.1007/s11336-016-9545-6>). See George, Robitzsch, Kiefer, Gross, and Uenlue (2017) <doi:10.18637/jss.v074.i02> or Robitzsch and George (2019, <doi:10.1007/978-3-030-05584-4_26>) for further details on estimation and the package structure. For tutorials on how to use the CDM package see George and Robitzsch (2015, <doi:10.20982/tqmp.11.3.p189>) as well as Ravand and Robitzsch (2015).

### Details

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
DINA and DINO model (e.g.,de la Torre &
Douglas, 2004; Junker & Sijtsma, 2001; Templin &
Henson, 2006; the generalized DINA model for dichotomous attributes
(GDINA, de la Torre, 2011) and for polytomous attributes
(pGDINA, Chen & de la Torre, 2013);
the general diagnostic model (GDM, von Davier, 2008) and its extension
to the multidimensional latent class IRT model (Bartolucci, 2007),
the structure latent class model (Formann, 1992),
and tools for analyzing data under the 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 several external functions (functions the
package exports).
The package contains 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. 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`

).

See George et al. (2016) and Robitzsch and George (2019) for an overview and some computational details of the CDM package.

### Author(s)

Alexander Robitzsch [aut, cre], Thomas Kiefer [aut], Ann Cathrice George [aut], Ali Uenlue [aut]

Maintainer: Alexander Robitzsch <robitzsch@ipn.uni-kiel.de>

### References

Bartolucci, F. (2007). A class of multidimensional IRT models for testing
unidimensionality and clustering items. *Psychometrika, 72*, 141-157.

Chen, J., & de la Torre, J. (2013).
A general cognitive diagnosis model for expert-defined polytomous attributes.
*Applied Psychological Measurement, 37*, 419-437.

Chen, Y., Li, X., Liu, J., & Ying, Z. (2017).
Regularized latent class analysis with application in cognitive diagnosis.
*Psychometrika, 82*, 660-692.

de la Torre, J., & Douglas, J. (2004). Higher-order latent trait models
for cognitive diagnosis. *Psychometrika, 69*, 333–353.

de la Torre, J. (2009). A cognitive diagnosis model for cognitively based
multiple-choice options. *Applied Psychological Measurement,
33*, 163-183.

de la Torre, J. (2011). The generalized DINA model framework.
*Psychometrika, 76*, 179–199.

DiBello, L. V., Roussos, L. A., & 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.

Formann, A. K. (1992). Linear logistic latent class analysis for polytomous data.
*Journal of the American Statistical Association, 87*, 476-486.

George, A. C., & Robitzsch, A. (2015) Cognitive diagnosis models in R: A didactic.
*The Quantitative Methods for Psychology, 11*, 189-205.
doi:10.20982/tqmp.11.3.p189

George, A. C., Robitzsch, A., Kiefer, T., Gross, J., & Uenlue, A. (2016).
The R package CDM for cognitive diagnosis models.
*Journal of Statistical Software, 74*(2), 1-24.

Junker, B. W., & Sijtsma, K. (2001). Cognitive assessment models with few
assumptions, and connections with nonparametric item response theory.
*Applied Psychological Measurement, 25*, 258–272.

Ravand, H., & Robitzsch, A.(2015). Cognitive diagnostic modeling using R.
*Practical Assessment, Research & Evaluation, 20*(11).
Available online: http://pareonline.net/getvn.asp?v=20&n=11

Robitzsch, A., & George, A. C. (2019). The R package CDM.
In M. von Davier & Y.-S. Lee (Eds.). *Handbook of diagnostic
classification models* (pp. 549-572). Cham: Springer.
doi: 10.1007/978-3-030-05584-4_26

Rupp, A. A., & 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., & Henson, R. A. (2010). *Diagnostic
Measurement: Theory, Methods, and Applications*. New York: The Guilford
Press.

Templin, J., & Henson, R. (2006). Measurement of
psychological disorders using cognitive diagnosis
models. *Psychological Methods, 11*, 287–305.

von Davier, M. (2008). A general diagnostic model applied to
language testing data. *British Journal
of Mathematical and Statistical Psychology, 61*, 287-307.

### See Also

See the GDINA package for comprehensive functions for the GDINA model.

See also the ACTCD and NPCD packages for nonparametric cognitive diagnostic models.

See the dina package for estimating the DINA model with a Gibbs sampler.

### Examples

```
##
## **********************************
## ** CDM 2.5-16 (2013-11-29) **
## ** Cognitive Diagnostic Models **
## **********************************
##
```

*CDM*version 8.2-6 Index]