Sage Journals: Discover world-class research

Abstract

The deterministic-input, noisy “and” gate (DINA) model can judge whether an individual examinee has mastered each skill that is needed to answer an item correctly. This information is useful for students to know their deficits and for teachers to teach effectively. The DINA model is a statistical model for binary (correct or incorrect) data. However, recently a DINA model for multiple-choice items was developed by de la Torre. The model is aimed at obtaining information about students’ skills from incorrect answers. In the present study, new DINA models for multiple-choice items are developed that need many fewer parameters while still being able to express various answering probabilities without any restrictions on the form of the Q-matrix. Simulations using a Markov chain Monte Carlo method are performed to demonstrate the efficacies of the proposed models compared with the DINA model for binary data and the model of de la Torre for multiple-choice items, if appropriate starting values are set.

Keywords

diagnostic testing MCMC multiple-choice item

Get full access to this article

View all access options for this article.

References

Baker

F. B.

(1992). Item response theory: Parameter estimation techniques. New York, NY: Dekker.

Birenbaum

Tatsuoka

Xin

(2005). Large-scale diagnostic assessment: Comparison of eighth graders’ mathematics performance in the United States, Singapore and Israel. Assessment in Education Principles Policy and Practice, 12, 167-181.

Bock

R. D.

(1972). Estimating item parameters and latent ability when responses are scored in two or more nominal categories. Psychometrika, 37, 29-51.

DeCarlo

L. T.

(2011). On the analysis of fraction subtraction data: The DINA model, classification, latent class sizes, and the Q-matrix. Applied Psychological Measurement, 35, 8-26.

de la Torre

(2009a). A cognitive diagnosis model for cognitively based multiple-choice options. Applied Psychological Measurement, 33, 163-183.

de la Torre

(2009b). DINA model and parameter estimation: A didactic. Journal of Educational and Behavioral Statistics, 34, 115-130.

de la Torre

(2011). The generalized DINA model framework. Psychometrika, 76, 179-199.

de la Torre

Douglas

(2004). Higher-order latent trait models for cognitive diagnosis. Psychometrika, 69, 333-353.

Embretson

(1984). A general latent trait model for response processes. Psychometrika, 49, 175-186.

10.

Gelman

Rubin

D.B.

(1992). Inference from Iterative Simulation using Multiple Sequences. Statistical Science, 7, 457-511.

11.

Hartz

(2002). A Bayesian framework for the unified model for assessing cognitive abilities: Blending theory with practicality (Doctoral dissertation). University of Illinois at Urbana–Champaign.

12.

Junker

B. W.

Sijtsma

(2001). Cognitive assessment models with few assumptions, and connections with nonparametric item response theory. Applied Psychological Measurement, 25, 258-272.

13.

Maris

(1999). Estimating multiple classification latent class models. Psychometrika, 64, 187-212.

14.

Patz

R. J.

Junker

B. W.

(1999). A straightforward approach to Markov chain Monte Carlo methods for item response models. Journal of Educational Measurement, 24, 146-178.

15.

R Development Core Team. (2005). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing.

16.

Tatsuoka

K. K.

(1983). Rule-space: An approach for dealing with misconceptions based on item response theory. Journal of Educational Measurement, 20, 345-354.

17.

Tatsuoka

K. K.

(1990). Toward an integration of item-response theory and cognitive error diagnosis. In Frederiksen

Glaser

Lesgold

Shafto

(Eds.), Diagnostic monitoring of skill and knowledge acquisition (pp. 453-488). Hillsdale, NJ: Lawrence Erlbaum.

18.

Tatsuoka

K. K.

(2009). Cognitive assessment: An introduction to the rule space method. New York, NY: Routledge Academic.

19.

Tatsuoka

K. K.

Corter

Tatsuoka

(2004). Patterns to diagnosed mathematical content and process skills in TIMSS-R across a sample of 20 countries. American Educational Research Journal, 41, 901-906.

20.

Templin

Henson

(2006). Measurement of psychological disorders using cognitive diagnosis models. Psychological Methods, 11, 287-305.

Supplementary Material

Please find the following supplemental material available below.

For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.

For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.

0.00 MB

0.15 MB

DINA Models for Multiple-Choice Items With Few Parameters

Abstract

Keywords

Get full access to this article

References

Supplementary Material