@conference {2655, title = {Computerized Adaptive Testing for Cognitive Diagnosis in Classroom: A Nonparametric Approach}, booktitle = {IACAT 2017 Conference}, year = {2017}, month = {08/2017}, publisher = {Niigata Seiryo University}, organization = {Niigata Seiryo University}, address = {Niigata, Japan}, abstract = {

In the past decade, CDMs of educational test performance have received increasing attention among educational researchers (for details, see Fu \& Li, 2007, and Rupp, Templin, \& Henson, 2010). CDMs of educational test performance decompose the ability domain of a given test into specific skills, called attributes, each of which an examinee may or may not have mastered. The resulting attribute profile documents the individual\’s strengths and weaknesses within the ability domain. The Cognitive Diagnostic Computerized Adaptive Testing (CD-CAT) has been suggested by researchers as a diagnostic tool for assessment and evaluation (e.g., Cheng \& Chang, 2007; Cheng, 2009; Liu, You, Wang, Ding, \& Chang, 2013; Tatsuoka \& Tatsuoka, 1997). While model-based CD-CAT is relatively well-researched in the context of large-scale assessments, this type of system has not received the same degree of development in small-scale settings, where it would be most useful. The main challenge is that the statistical estimation techniques successfully applied to the parametric CD-CAT require large samples to guarantee the reliable calibration of item parameters and accurate estimation of examinees\’ attribute profiles. In response to the challenge, a nonparametric approach that does not require any parameter calibration, and thus can be used in small educational programs, is proposed. The proposed nonparametric CD-CAT relies on the same principle as the regular CAT algorithm, but uses the nonparametric classification method (Chiu \& Douglas, 2013) to assess and update the student\’s ability state while the test proceeds. Based on a student\’s initial responses, 2 a neighborhood of candidate proficiency classes is identified, and items not characteristic of the chosen proficiency classes are precluded from being chosen next. The response to the next item then allows for an update of the skill profile, and the set of possible proficiency classes is further narrowed. In this manner, the nonparametric CD-CAT cycles through item administration and update stages until the most likely proficiency class has been pinpointed. The simulation results show that the proposed method outperformed the compared parametric CD-CAT algorithms and the differences were significant when the item parameter calibration was not optimal.

References

Cheng, Y. (2009). When cognitive diagnosis meets computerized adaptive testing: CD-CAT. Psychometrika, 74, 619-632.

Cheng, Y., \& Chang, H. (2007). The modified maximum global discrimination index method for cognitive diagnostic CAT. In D. Weiss (Ed.) Proceedings of the 2007 GMAC Computerized Adaptive Testing Conference.

Chiu, C.-Y., \& Douglas, J. A. (2013). A nonparametric approach to cognitive diagnosis by proximity to ideal response patterns. Journal of Classification, 30, 225-250.

Fu, J., \& Li, Y. (2007). An integrative review of cognitively diagnostic psychometric models. Paper presented at the Annual Meeting of the National Council on Measurement in Education. Chicago, Illinois.

Liu, H., You, X., Wang, W., Ding, S., \& Chang, H. (2013). The development of computerized adaptive testing with cognitive diagnosis for an English achievement test in China. Journal of Classification, 30, 152-172.

Rupp, A. A., \& Templin, J. L., \& Henson, R. A. (2010). Diagnostic Measurement. Theory, Methods, and Applications. New York: Guilford.

Tatsuoka, K.K., \& Tatsuoka, M.M. (1997), Computerized cognitive diagnostic adaptive testing: Effect on remedial instruction as empirical validation. Journal of Educational Measurement, 34, 3\–20.

Session Video

}, keywords = {CD-CAT, non-parametric approach}, author = {Yuan-Pei Chang and Chia-Yi Chiu and Rung-Ching Tsai} } @conference {2656, title = {Efficiency of Item Selection in CD-CAT Based on Conjunctive Bayesian Network Modeling Hierarchical attributes}, booktitle = {IACAT 2017 Conference}, year = {2017}, month = {08/2017}, publisher = {Niigata Seiryo University}, organization = {Niigata Seiryo University}, address = {Niigata, Japan}, abstract = {

Cognitive diagnosis models (CDM) aim to diagnosis examinee\’s mastery status of multiple fine-grained skills. As new development for cognitive diagnosis methods emerges, much attention is given to cognitive diagnostic computerized adaptive testing (CD-CAT) as well. The topics such as item selection methods, item exposure control strategies, and online calibration methods, which have been wellstudied for traditional item response theory (IRT) based CAT, are also investigated in the context of CD-CAT (e.g., Xu, Chang, \& Douglas, 2003; Wang, Chang, \& Huebner, 2011; Chen et al., 2012).

In CDM framework, some researchers suggest to model structural relationship between cognitive skills, or namely, attributes. Especially, attributes can be hierarchical, such that some attributes must be acquired before the subsequent ones are mastered. For example, in mathematics, addition must be mastered before multiplication, which gives a hierarchy model for addition skill and multiplication skill. Recently, new CDMs considering attribute hierarchies have been suggested including the Attribute Hierarchy Method (AHM; Leighton, Gierl, \& Hunka, 2004) and the Hierarchical Diagnostic Classification Models (HDCM; Templin \& Bradshaw, 2014).

Bayesian Networks (BN), the probabilistic graphical models representing the relationship of a set of random variables using a directed acyclic graph with conditional probability distributions, also provide an efficient framework for modeling the relationship between attributes (Culbertson, 2016). Among various BNs, conjunctive Bayesian network (CBN; Beerenwinkel, Eriksson, \& Sturmfels, 2007) is a special kind of BN, which assumes partial ordering between occurrences of events and conjunctive constraints between them.

In this study, we propose using CBN for modeling attribute hierarchies and discuss the advantage of CBN for CDM. We then explore the impact of the CBN modeling on the efficiency of item selection methods for CD-CAT when the attributes are truly hierarchical. To this end, two simulation studies, one for fixed-length CAT and another for variable-length CAT, are conducted. For each studies, two attribute hierarchy structures with 5 and 8 attributes are assumed. Among the various item selection methods developed for CD-CAT, six algorithms are considered: posterior-weighted Kullback-Leibler index (PWKL; Cheng, 2009), the modified PWKL index (MPWKL; Kaplan, de la Torre, Barrada, 2015), Shannon entropy (SHE; Tatsuoka, 2002), mutual information (MI; Wang, 2013), posterior-weighted CDM discrimination index (PWCDI; Zheng \& Chang, 2016) and posterior-weighted attribute-level CDM discrimination index (PWACDI; Zheng \& Chang, 2016). The impact of Q-matrix structure, item quality, and test termination rules on the efficiency of item selection algorithms is also investigated. Evaluation measures include the attribute classification accuracy (fixed-length experiment) and test length of CDCAT until stopping (variable-length experiment).

The results of the study indicate that the efficiency of item selection is improved by directly modeling the attribute hierarchies using CBN. The test length until achieving diagnosis probability threshold was reduced to 50-70\% for CBN based CAT compared to the CD-CAT assuming independence of attributes. The magnitude of improvement is greater when the cognitive model of the test includes more attributes and when the test length is shorter. We conclude by discussing how Q-matrix structure, item quality, and test termination rules affect the efficiency.

References

Beerenwinkel, N., Eriksson, N., \& Sturmfels, B. (2007). Conjunctive bayesian networks. Bernoulli, 893- 909.

Chen, P., Xin, T., Wang, C., \& Chang, H. H. (2012). Online calibration methods for the DINA model with independent attributes in CD-CAT. Psychometrika, 77(2), 201-222.

Cheng, Y. (2009). When cognitive diagnosis meets computerized adaptive testing: CD-CAT. Psychometrika, 74(4), 619-632.

Culbertson, M. J. (2016). Bayesian networks in educational assessment: the state of the field. Applied Psychological Measurement, 40(1), 3-21.

Kaplan, M., de la Torre, J., \& Barrada, J. R. (2015). New item selection methods for cognitive diagnosis computerized adaptive testing. Applied Psychological Measurement, 39(3), 167-188.

Leighton, J. P., Gierl, M. J., \& Hunka, S. M. (2004). The attribute hierarchy method for cognitive assessment: a variation on Tatsuoka\&$\#$39;s rule-space approach. Journal of Educational Measurement, 41(3), 205-237.

Tatsuoka, C. (2002). Data analytic methods for latent partially ordered classification models. Journal of the Royal Statistical Society: Series C (Applied Statistics), 51(3), 337-350.

Templin, J., \& Bradshaw, L. (2014). Hierarchical diagnostic classification models: A family of models for estimating and testing attribute hierarchies. Psychometrika, 79(2), 317-339. Wang, C. (2013). Mutual information item selection method in cognitive diagnostic computerized adaptive testing with short test length. Educational and Psychological Measurement, 73(6), 1017-1035.

Wang, C., Chang, H. H., \& Huebner, A. (2011). Restrictive stochastic item selection methods in cognitive diagnostic computerized adaptive testing. Journal of Educational Measurement, 48(3), 255-273.

Xu, X., Chang, H., \& Douglas, J. (2003, April). A simulation study to compare CAT strategies for cognitive diagnosis. Paper presented at the annual meeting of National Council on Measurement in Education, Chicago.

Zheng, C., \& Chang, H. H. (2016). High-efficiency response distribution\–based item selection algorithms for short-length cognitive diagnostic computerized adaptive testing. Applied Psychological Measurement, 40(8), 608-624.

Session Video

}, keywords = {CD-CAT, Conjuctive Bayesian Network Modeling, item selection}, url = {https://drive.google.com/open?id=1RbO2gd4aULqsSgRi_VZudNN_edX82NeD}, author = {Soo-Yun Han and Yun Joo Yoo} } @conference {2638, title = {A New Cognitive Diagnostic Computerized Adaptive Testing for Simultaneously Diagnosing Skills and Misconceptions}, booktitle = {IACAT 2017 Conference}, year = {2017}, month = {08/2017}, publisher = {Niigata Seiryo University}, organization = {Niigata Seiryo University}, address = {Niigata, Japan}, abstract = {

In education diagnoses, diagnosing misconceptions is important as well as diagnosing skills. However, traditional cognitive diagnostic computerized adaptive testing (CD-CAT) is usually developed to diagnose skills. This study aims to propose a new CD-CAT that can simultaneously diagnose skills and misconceptions. The proposed CD-CAT is based on a recently published new CDM, called the simultaneously identifying skills and misconceptions (SISM) model (Kuo, Chen, \& de la Torre, in press). A new item selection algorithm is also proposed in the proposed CD-CAT for achieving high adaptive testing performance. In simulation studies, we compare our new item selection algorithm with three existing item selection methods, including the Kullback\–Leibler (KL) and posterior-weighted KL (PWKL) proposed by Cheng (2009) and the modified PWKL (MPWKL) proposed by Kaplan, de la Torre, and Barrada (2015). The results show that our proposed CD-CAT can efficiently diagnose skills and misconceptions; the accuracy of our new item selection algorithm is close to the MPWKL but less computational burden; and our new item selection algorithm outperforms the KL and PWKL methods on diagnosing skills and misconceptions.

References

Cheng, Y. (2009). When cognitive diagnosis meets computerized adaptive testing: CD-CAT. Psychometrika, 74(4), 619\–632. doi: 10.1007/s11336-009-9123-2

Kaplan, M., de la Torre, J., \& Barrada, J. R. (2015). New item selection methods for cognitive diagnosis computerized adaptive testing. Applied Psychological Measurement, 39(3), 167\–188. doi:10.1177/0146621614554650

Kuo, B.-C., Chen, C.-H., \& de la Torre, J. (in press). A cognitive diagnosis model for identifying coexisting skills and misconceptions. Applied Psychological Measurement.

Session Video

}, keywords = {CD-CAT, Misconceptions, Simultaneous diagnosis}, author = {Bor-Chen Kuo and Chun-Hua Chen} } @conference {2633, title = {Using Bayesian Decision Theory in Cognitive Diagnosis Computerized Adaptive Testing}, booktitle = {IACAT 2017 Conference}, year = {2017}, month = {08/2017}, publisher = {Niigata Seiryo University}, organization = {Niigata Seiryo University}, address = {Niigata Japan}, abstract = {

Cognitive diagnosis computerized adaptive testing (CD-CAT) purports to provide each individual a profile about the strengths and weaknesses of attributes or skills with computerized adaptive testing. In the CD-CAT literature, researchers dedicated to evolving item selection algorithms to improve measurement efficiency, and most algorithms were developed based on information theory. By the discontinuous nature of the latent variables in CD-CAT, this study introduced an alternative for item selection, called the minimum expected cost (MEC) method, which was derived based on Bayesian decision theory. Using simulations, the MEC method was evaluated against the posterior weighted Kullback-Leibler (PWKL) information, the modified PWKL (MPWKL), and the mutual information (MI) methods by manipulating item bank quality, item selection algorithm, and termination rule. Results indicated that, regardless of item quality and termination criterion, the MEC, MPWKL, and MI methods performed very similarly and they all outperformed the PWKL method in classification accuracy and test efficiency, especially in short tests; the MEC method had more efficient item bank usage than the MPWKL and MI methods. Moreover, the MEC method could consider the costs of incorrect decisions and improve classification accuracy and test efficiency when a particular profile was of concern. All the results suggest the practicability of the MEC method in CD-CAT.

Session Video

}, keywords = {Bayesian Decision Theory, CD-CAT}, author = {Chia-Ling Hsu and Wen-Chung Wang and ShuYing Chen} }