L.S. Kuravsky − Dr.Sc. (Eng.), Professor, Dean of Computer Science Faculty, Moscow State University of Psychology and Education

E-mail: l.s.kuravsky@gmail.com

S.L. Artemenkov − Ph.D. (Eng.), Professor, Computer Science Faculty,  Moscow State University of Psychology and Education

E-mail: slart@inbox.ru

G.A. Yuryev − Ph.D. (Phys.-Math.), Associate Professor, Deputy Dean, Computer Science Faculty, Moscow State University of Psychology and Education

E-mail: g.a.yuryev@gmail.com

The features of the organization of the adaptive diagnostic procedure areconsidered, for which the model of presenting tasks is described with the help of Markov random processes with discrete states and discrete time. Its effectiveness in testing cognitive abilities is estimated. Acceptable reliability of recognition of the levels of abilities is revealed using the means of simulation while significantly saving the time and effort of the subjects.

1. Valueva E.A., Ushakov D.V. Jempiricheskaja verifikacija modeli sootnoshenija predmetnyh i jemocional'nyh sposobnostej // Psihologija. Zhurnal Vysshej shkoly jekonomiki, 2010. T. 7. № 2. S. 103–114. 
2. Kuravskij L.S., Artemenkov S.L., Jur'ev G.A., Grigorenko E.L. Novyj podhod k komp'juterizirovannomu adaptivnomu testirovaniju // Jeksperimental'naja psihologija. 2017. T. 10. № 3. S. 33–45. doi:10.17759/exppsy.2017100303. 
3. Kuravskij L.S., Margolis A.A., Marmaljuk P.A., Jur'ev G.A., Dumin P.N. Obuchaemye markovskie modeli v zadachah optimizacii porjadka pred#javlenija psihologicheskih testov // Nejrokomp'jutery: razrabotka i primenenie. 2013. № 4. S. 28–38.
4. Kuravskij L.S., Margolis A.A., Marmaljuk P.A., Panfilova A.S., Jur'ev G.A. Matematicheskie aspekty koncepcii adaptivnogo trenazhera // Psihologicheskaja nauka i obrazovanie. 2016. T. 21. № 2. C. 84–95. doi: 10.17759/pse.2016210210.
5. Kuravskij L.S., Margolis A.A., Jur'ev G.A., Marmaljuk P.A. Koncepcija sistemy podderzhki prinjatija reshenij dlja psihologicheskogo testirovanija // Psihologicheskaja nauka i obrazovanie. 2012. № 1. S. 56−65.
6. Kuravskij L.S., Jur'ev G.A. Adaptivnoe testirovanie kak markovskij process: modeli i ih identifikacija // Nejrokomp'jutery: razrabotka i primenenie. 2011. № 2. S. 21−29. 
7. Kuravskij L.S., Jur'ev G.A. Verojatnostnyj metod fil'tracii artefaktov pri adaptivnom testirovanii // Jeksperimental'naja psihologija. 2012. T. 5. № S. 119−131.
8. Kuravskij L.S., Jur'ev G.A. Ispol'zovanie markovskih modelej pri obrabotke rezul'tatov testirovanija // Voprosy psihologii. 2011. № 2. S. 98−107. 
9. Kuravskij L.S., Jur'ev G.A. Ob odnom podhode k adaptivnomu testirovaniju i ustraneniju ego artefaktov // Nejrokomp'jutery: razrabotka i primenenie. 2012. № 1.
10. Markovskie modeli v zadachah diagnostiki i prognozirovanija: Ucheb. posobie / Pod red. L.S. Kuravskogo. 2-e izd., dop. M.: Izd-vo MGPPU. 2017. 203 s.
11. Baker F.B. The Basics of Item Response Theory. ERIC Clearinghouse on Assessment and Evaluation, University of Maryland. College Park. MD. 2001.
12. Burden R.L., Faires J.D. Numerical Analysis, Brooks/Cole, Cengage Learning. 9-th Ed. 2011. 895 p. 
13. Gregory R.J. Psychological testing: History, principles, and applications (5th edition). New York: Pearson. 2007.
14. Gulliksen H. Theory of Mental Tests. John Wiley & Sons Inc. 1950.
15. Kohonen T. Self-Organizing Maps, Springer. 3th Ed., 2001. 501 p. 
16. Kuravsky L.S., Marmalyuk P.A., Yuryev G.A., Dumin P.N. A Numerical Technique for the Identification of Discrete-State Continuous-Time Markov Models// Applied Mathematical Sciences. 2015. V. 9. № 8. Р. 379–391. URL: http://dx.doi.org/10.12988/ams. 2015.410882. 
17. Kuravsky L.S., Marmalyuk P.A., Baranov S.N., Alkhimov V.I., Yuryev G.A., Artyukhina S.V. A New Technique for Testing Professional Skills and Competencies and Examples of its Practical Applications // Applied Mathematical Sciences. 2015. V. 9. № 21. Р. 1003–1026. http://dx.doi.org/10.12988/ams.2015.411899.
18. Kuravsky L.S., Marmalyuk P.A., Yuryev G.A., Dumin P.N. A Numerical Technique for the Identification of Discrete-State Continuous-Time Markov Models// Applied Mathematical Sciences. 2015. V. 9. № 8. Р. 379–391. URL: http://dx.doi.org/10.12988/ams. 2015.410882. 
19. Rasch G. Probabilistic models for some intelligence and attainment tests. // Copenhagen, Danish Institute for Educational Research, expanded edition (1980) with foreword and afterword by B.D. Wright. Chicago: The University of Chicago Press. 1960/1980. 
20. Thompson N.A., Weiss D.J. A framework for the development of computerized adaptive tests // Practical Assessment, Research & Evaluation. 2011. № 16(1). Р. 1−9.
21. de la Torre J., Patz R.J. Making the Most of What We Have: A Practical Application of Multidimensional Item Response Theory in Test Scoring // Journal of Educational and Behavioral Statistics. 2005. № 30(3). Р. 295−311. doi:10.3102/10769986030003295.
22. Wilkinson J.H. The Algebraic Eigenvalue Problem. Oxford, Clarendon Press. 1988. 662 p. 
23. Wright B.D., Masters G.N. Rating scale analysis. Rasch measurements. Chicago: MESA Press. 1982.