The Rusch model-based knowledge assessment algorithm


  • Alexander A. Kostikov,Donbass State Engineering Academy image/svg+xml
  • Kateryna V. Vlasenko,National University of Kyiv Mohyla Academy image/svg+xml
  • Iryna V. Lovianova,Kryvyi Rih State Pedagogical University
  • Sergii V. Volkov,Volodymyr Dahl East Ukrainian National University image/svg+xml
  • Evgeny O. Avramov,Donbass State Engineering Academy image/svg+xml



adaptive algorithm, Rasch model, Item Response Theory (IRT), information function of test item, latent variables


In this paper, an algorithm for adaptive testing of students' knowledge in distance learning is proposed, along with an assessment of its effectiveness in the educational process. The paper provides an overview of the results of modern test theory application, a description and block diagram of the proposed algorithm, and the results of its application in the real educational process. The effectiveness of using this algorithm for objectively assessing students' knowledge has been demonstrated experimentally.


Download data is not yet available.


Metrics Loading ...


Al-A’ali, M.: IRT-Item Response Theory Assessment for an Adaptive Teaching Assessment System. In: Proceedings of the 10th WSEAS International Conference on Applied Mathematics. p. 518–522. MATH’06, World Scientific and Engineering Academy and Society (WSEAS), Stevens Point, Wisconsin, USA (2006)

Andersen, E.B.: The asymptotic distribution of conditional likelihood ratio tests. Journal of the American Statistical Association 66(335), 630–633 (1971). DOI:

Andersen, E.B.: A goodness of fit test for the Rasch model. Psychometrika 38(1), 123–140 (1973). DOI:

Andrich, D.: The Rasch model explained. In: Applied Rasch measurement: A book of exemplars, pp. 27–59. Springer (2005) DOI:

Andrich, D.: Rasch Models for Measurement. Thousand Oaks (2021).,

Andrich, D., Sheridan, B., Luo, G.: Rumm2010: Rasch unidimensional measurement models (2001),

Avanesov, V.S.: The problem of psychological tests. Soviet Education 22(6), 6–23 (1980). DOI:

Bezruczko, N. (ed.): Rasch measurement in health sciences. Jam Press Maple Grove, MN (2005)

Birnbaum, A.: Combining independent tests of significance*. Journal of the American Statistical Association 49(267), 559–574 (1954). DOI:

Bond, T., Fox, C.: Applying the Rasch model: Fundamental measurement in the human sciences. Second edn. (2007). DOI:

Bond, T., Yan, Z., Heene, M.: Applying the Rasch model: Fundamental measurement in the human sciences. Routledge, fourth edn. (2020) DOI:

Brown, W.: Some experimental results in the correlation of mental abilities. British Journal of Psychology, 1904-1920 3(3), 296–322 (1910). DOI:

Cronbach, L.J.: Coefficient alpha and the internal structure of tests. Psychometrika 16(3), 297–334 (1951). DOI:

Eckes, T.: Introduction to Many-Facet Rasch Measurement. Peter Lang, Bern, Switzerland (2011), DOI:

Fischer, G.H., Molenaar, I.W. (eds.): Rasch models: Foundations, recent developments, and applications. Springer Science & Business Media (1995). DOI:

Guilford, J.P.: Fundamental statistics in psychology and education. McGraw-Hill, New York (1942)

Gulliksen, H.: Perspective on Educational Measurement. Applied Psychological Measurement 10(2), 109–132 (1986). DOI:

Guttman, L.: A basis for scaling qualitative data. American Sociological Review 9, 139–150 (1944). DOI:

Ingebo, G.S.: Probability in the Measure of Achievement. Mesa Press (1997)

Kim, S.H., Baker, F.B.: birtr: A Package for “The Basics of Item Response Theory Using R”. Applied Psychological Measurement 42(5), 403–404 (2018). DOI:

Kuder, G.F., Richardson, M.W.: The theory of the estimation of test reliability. Psychometrika 2(3), 151–160 (1937). DOI:

Lazarsfeld, P.F.: Regression analysis with dichotomous attributes. Social Science Research 1(1), 25–34 (1972). DOI:

Linacre, J.M.: Predicting responses from Rasch measures. Journal of Applied Measurement 11(1), 1–10 (2010)

van der Linden, W.J., Hambleton, R.K. (eds.): Handbook of Modern Item Response Theory. Springer Science & Business Media (1997). DOI:

Lord, F.M., Novick, M.R., Birnbaum, A.: Statistical theories of mental test scores. Addison-Wesley, Oxford (1968)

Lord, F.M.: Applications of Item Response Theory To Practical Testing Problems. Routledge (1980). DOI:

Luce, R.D., Tukey, J.W.: Simultaneous conjoint measurement: A new type of fundamental measurement. Journal of Mathematical Psychology 1(1), 1–27 (1964). DOI:

Maslak, A.A., Karabatsos, G., Anisimova, T.S., Osipov, S.A.: Measuring and comparing higher education quality between countries worldwide. Journal of Applied Measurement 6(4), 432–442 (2005)

Masters, G.N.: Educational measurement: Prospects for research and innovation. The Australian Educational Researcher 15(4), 23–34 (1988). DOI:

Perline, R., Wright, B.D., Wainer, H.: The Rasch model as additive conjoint measurement. Applied Psychological Measurement 3(2), 237–255 (1979). DOI:

Rasch, G.: Studies in mathematical psychology: I. Probabilistic models for some intelligence and attainment tests. Nielsen & Lydiche (1960)

Sax, G.: Principles of educational and psychological measurement and evaluation. Wadsworth Pub. Co., Belmont, 3rd edn. (1989)

Smith, E.V., Smith, R.M. (eds.): Introduction to Rasch measurement: Theory, models and applications. JAM Press (2004)

Spearman, C.: Correlation calculated from faulty data. British Journal of Psychology, 1904-1920 3(3), 271–295 (1910). DOI:

Weiss, D.J.: Improving measurement quality and efficiency with adaptive testing. Applied Psychological Measurement 6(4), 473–492 (1982). DOI:

Weiss, D.J.: Computerized adaptive testing for effective and efficient measurement in counseling and education. Measurement and Evaluation in Counseling and Development 37(2), 70–84 (2004). DOI:

Wilson, M.: Constructing Measures: An Item Response Modeling Approach. Routledge (2005)

Wright, B.D., Linacre, J.M.: Dichotomous rasch model derived from specific objectivity. Rasch measurement transactions 1(1), 5–6 (1987),

Wright, B.D.: Solving Measurement Problems with the Rasch Model. Journal of Educational Measurement 14(2), 97–116 (1977), DOI:

Wright, B.D., Masters, G.N.: Rating scale analysis. Mesa Press, Chicago (1982)

Wright, B.D., Stone, M.H.: Best test design. Mesa Press, Chicago (1979),[reduced%20size]/Best%20Test%20Design.pdf




How to Cite

Kostikov, A., Vlasenko, K., Lovianova, I., Volkov, S., & Avramov, E. (2022). The Rusch model-based knowledge assessment algorithm. Educational Dimension, 58, 40–54.



Theories of Learning, Education and Training