The adaptive measurement of change (AMC) refers to the use of computerized adaptive testing (CAT) at multiple occasions to efficiently assess a respondent’s improvement, decline, or sameness from occasion to occasion. Whereas previous AMC research focused on administering the most informative item to a respondent at each stage of testing, the current research proposes the use of Fisher information per time unit as an item selection procedure for AMC. The latter procedure incorporates not only the amount of information provided by a given item but also the expected amount of time required to complete it. In a simulation study, the use of Fisher information per time unit item selection resulted in a lower false positive rate in the majority of conditions studied, and a higher true positive rate in all conditions studied, compared to item selection via Fisher information without accounting for the expected time taken. Future directions of research are suggested.

%B Journal of Computerized Adaptive Testing %V 7 %P 15-34 %G English %U http://iacat.org/jcat/index.php/jcat/article/view/73/35 %N 2 %R 10.7333/1909-0702015 %0 Conference Paper %B IACAT 2017 Conference %D 2017 %T Adaptive Item and Feedback Selection in Personalized Learning with a Network Approach %A Nikky van Buuren %A Hendrik Straat %A Theo Eggen %A Jean-Paul Fox %K feedback selection %K item selection %K network approach %K personalized learning %XPersonalized learning is a term used to describe educational systems that adapt student-specific curriculum sequencing, pacing, and presentation based on their unique backgrounds, knowledge, preferences, interests, and learning goals. (Chen, 2008; Netcoh, 2016). The technological approach to personalized learning provides data-driven models to incorporate these adaptations automatically. Examples of applications include online learning systems, educational games, and revision-aid systems. In this study we introduce Bayesian networks as a methodology to implement an adaptive framework within a personalized learning environment. Existing ideas from Computerized Adaptive Testing (CAT) with Item Response Theory (IRT), where choices about content provision are based on maximizing information, are related to the goals of personalized learning environments. Personalized learning entails other goals besides efficient ability estimation by maximizing information, such as an adaptive configuration of preferences and feedback to the student. These considerations will be discussed and their application in networks will be illustrated.

Adaptivity in Personalized Learning.In standard CAT’s there is a focus on selecting items that provide maximum information about the ability of an individual at a certain point in time (Van der Linden & Glas, 2000). When learning is the main goal of testing, alternative adaptive item selection methods were explored by Eggen (2012). The adaptive choices made in personalized learning applications require additional adaptivity with respect to the following aspects; the moment of feedback, the kind of feedback, and the possibility for students to actively influence the learning process.

Bayesian Networks and Personalized Learning.Personalized learning aims at constructing a framework to incorporate all the aspects mentioned above. Therefore, the goal of this framework is not only to focus on retrieving ability estimates by choosing items on maximum information, but also to construct a framework that allows for these other factors to play a role. Plajner and Vomlel (2016) have already applied Bayesian Networks to adaptive testing, selecting items with help of entropy reduction. Almond et al. (2015) provide a reference work on Bayesian Networks in Educational Assessment. Both acknowledge the potential of the method in terms of features such as modularity options to build finer-grained models. IRT does not allow to model sub-skills very easily and to gather information on fine-grained level, due to its dependency on the assumption of generally one underlying trait. The local independence assumption in IRT implies being interested in mainly the student’s overall ability on the subject of interest. When the goal is to improve student’s learning, we are not just interested in efficiently coming to their test score on a global subject. One wants a model that is able to map educational problems and talents in detail over the whole educational program, while allowing for dependency between items. The moment in time can influence topics to be better mastered than others, and this is exactly what we can to get out of a model. The possibility to model flexible structures, estimate abilities on a very detailed level for sub-skills and to easily incorporate other variables such as feedback in Bayesian Networks makes it a very promising method for making adaptive choices in personalized learning. It is shown in this research how item and feedback selection can be performed with help of the promising Bayesian Networks. A student involvement possibility is also introduced and evaluated.

References

Almond, R. G., Mislevy, R. J., Steinberg, L. S., Yan, D., & Williamson, D. M. (2015). Bayesian Networks in Educational Assessment. Test. New York: Springer Science+Business Media. http://doi.org/10.1007/978-0-387-98138-3

Eggen, T.J.H.M. (2012) Computerized Adaptive Testing Item Selection in Computerized Adaptive Learning Systems. In: Eggen. TJHM & Veldkamp, BP.. (Eds). Psychometrics in Practice at RCEC. Enschede: RCEC

Netcoh, S. (2016, March). “What Do You Mean by ‘Personalized Learning?’. Croscutting Conversations in Education – Research, Reflections & Practice. Blogpost.

Plajner, M., & Vomlel, J. (2016). Student Skill Models in Adaptive Testing. In Proceedings of the Eighth International Conference on Probabilistic Graphical Models (pp. 403-414).

Van der Linden, W. J., & Glas, C. A. (2000). Computerized adaptive testing: Theory and practice. Dordrecht: Kluwer Academic Publishers.

%B IACAT 2017 Conference %I Niigata Seiryo University %C Niigata, Japan %8 08/2017 %G eng %0 Conference Paper %B IACAT 2017 Conference %D 2017 %T Efficiency of Item Selection in CD-CAT Based on Conjunctive Bayesian Network Modeling Hierarchical attributes %A Soo-Yun Han %A Yun Joo Yoo %K CD-CAT %K Conjuctive Bayesian Network Modeling %K item selection %XCognitive 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'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.

%B IACAT 2017 Conference %I Niigata Seiryo University %C Niigata, Japan %8 08/2017 %G eng %U https://drive.google.com/open?id=1RbO2gd4aULqsSgRi_VZudNN_edX82NeD %0 Conference Paper %B Annual Conference of the International Association for Computerized Adaptive Testing %D 2011 %T Item Selection Methods based on Multiple Objective Approaches for Classification of Respondents into Multiple Levels %A Maaike van Groen %A Theo Eggen %A Bernard Veldkamp %K adaptive classification test %K CAT %K item selection %K sequential classification test %XIs it possible to develop new item selection methods which take advantage of the fact that we want to classify into multiple categories? New methods: Taking multiple points on the ability scale into account; Based on multiple objective approaches.

Conclusions

- Sequential Classification Tests higher ATL than Adaptive Classification Tests
- Sequential Classification Tests slightly lower PCD than Adaptive Classification Tests
- Results also hold with three and four cutting points