1. It alleviates the trade-off between computational costs and differences in fitting errors.
2. It approximately maximizes the number of test forms with overlapping constraints.
1. In order to construct equivalent test forms, the traditional methods enable test forms to be constructed that minimize the differences in fitting errors between all forms. However, the differences in fitting errors decrease as the computational costs increase. That is, there is a trade-off between the differences in fitting errors between the test forms and the computational costs.
2. A maximum number of test forms from an item bank that cannot be guaranteed and overlapping constraints are difficult to be implemented. That is, the item bank cannot effectively be used in practice.
1. The item-selection probability of each remaining item is inversely proportional to the fitting error of the constructed test form if this form includes the remaining item.
2. The item-selection probability of each remaining item becomes zero if no test constraints are satisfied.
1. The rules in Step A-1.
2. If each remaining item is included in the selected test form, the selection probability of this item is higher than the selection probabilities of the other items.
1. The fitting errors of the test forms are smaller than the smallest fitting error in the system memory.
2. The test forms are not the same as the stored test forms in the system memory.
1. The rule in Step B-1.
2. If each remaining test form is included in the selected set of test forms, the form-selection probability of this form is higher than the form-selection probabilities of the other forms.
1. The differences in fitting errors of extracted sets of test forms are not lower than the smallest difference of fitting errors of stored set of test forms in the system memory.
2. The fitting errors of extracted sets of test forms are not lower than the smallest fitting error of stored set of test forms in the system memory.
P. Songmuang is with the Faculty of Human Sciences, Waseda University, 2-579-15, Mikashima, Tokorozawa-shi, Saitama-ken, 359-1192, Japan. E-mail: firstname.lastname@example.org.
M. Ueno is with the Department of Social Intelligence and Informatics, Graduate School of Information Systems, The University of Electro-Communications, 1-5-1, Chofugaoka, Chofu-shi, Tokyo 182-8585, Japan. E-mail: email@example.com.
Manuscript received 23 Dec. 2009; revised 22 Mar. 2010; accepted 3 Aug. 2010; published online 27 Aug. 2010.
For information on obtaining reprints of this article, please send e-mail to: firstname.lastname@example.org, and reference IEEECS Log Number TLT-2009-12-0205.
Digital Object Identifier no. 10.1109/TLT.2010.29.
Pokpong Songmuang received the BEng degree from Thammasat University in 2003, the MEng degree from Nagaoka University of Technology in 2006, and the PhD degree in computer science from the University of Electro-Communications in 2010. He is currently an assistant professor at Waseda University. His research interests include e-testing, data mining, and web technologies.
Maomi Ueno received the PhD degree in computer science from the Tokyo Institute of Technology in 1994. He has been an associate professor in the Graduate School of Information Systems at the University of Electro-Communications since 2007. He has also worked at the Tokyo Institute of Technology (1994-1996), Chiba University (1996-2000), and the Nagaoka University of Technology (2000-2007). He received best paper awards from the 20th IEEE International Conference on Tools with Artificial Intelligence (ICTAI 2008), ED-MEDIA 2008, e-Learn2004, e-Learn2005, and e-Learn2007. His interests are in e-learning, e-testing, e-portfolio, machine learning, data mining, Bayesian statistics, Bayesian networks, and so on. He is a member of the IEEE.