INVESTIGATION OF MEASUREMENT PRECISION OF LATENT VARIABLE DEPENDING ON THE RANGE OF VARIATION OF INDICATORS SET

A. A. Maslak, S. I. Moiseev, S. A. Osipov, S. A. Pozdnyakov

Abstract


Context. An important practical aspect of measurement of a latent variable is precision because the efficacy of accepted decisions depends
on it. One of possible ways of increasing precision of measurement of latent variables is the choice of best location of a set of indicators.
Objective. The objective is the investigation of precision of measurement of a latent variable depending on location of a set of indicators. In order to achieve this goal it is necessary to generate matrices of data based on Rasch model, to obtain estimations of latent variable, and to compare the obtained estimations of a latent variable to those values which were used for modelling.
Method. Taking into account that the model of measurement of latent variable is nonlinear, the analytical decision is complicated.
Therefore, research was conducted through the simulation experiment within the framework of the theory of measurement of latent variables.
Data from the simulation experiment was described by Rasch model for dichotomic indicators and processed using the dialogue system
«Measurement of latent variables».
Results. Investigation of precision of measurement of latent variable depending on location of a set of indicators was carried out within
the framework of the theory of latent variables based on simulation experiment. The analysis of variance has shown that narrowing the range of indicators compared to variation of latent variable raises precision of its measurement with other things being equal. Precision of
measurement of latent variable is higher at its center of variation than on the edges irrespective of range of variation of indicators.
Conclusions. The technique of the analysis of precision of measurement of latent variable depending on location of indicators is presented. Unlike the existing point of view, that the range of variation of indicators should cover range of variation of latent variable, it is shown that the greatest precision of measurement of latent variable is reached at location of indicators in the middle of range of latent variable
with other things being equal. The obtained results are used for the choice of optimum algorithm of adaptive testing. It is of interest to expand research and to estimate influence of other ranges of variation of latent variable and location of set of indicators on precision of measurement.

Keywords


latent variable, Rasch dichotomic model, precision of measurement, simulation experiment.

References


Bond Trevor G. Applying the Rasch Model : Fundamental Measurement in the Human Sciences / Trevor G. Bond & Christine M. Fox. – Mahwax, New Jersey, 2001. – 255 p. 2. Wright B. D. Making measures / B. D. Wright, M. Y. Stone. – The Phaneron Press, Chicago, 2004. – 127 p. 3. Rasch Measurement in Health Sciences. Ed. Bezruczko N. JAM Press, Maple Grove, Minnesota. 2005. – 483 p. 4. Маслак А. А. Теория и практика измерения латентных переменных в образовании : монография / А. А. Маслак. – М. : Издательство Юрайт, 2016. – 255 с. 5. Дроздов В. И. Использование современной теории тестологии при оценке качества АПИМ / В. И. Дроздов, А. А. Маслак, Ю. М. Новиков // Известия Юго-Западного государственного университета. – 2008. – № 4 (25). – С. 87–95. 6. Rasch G. Probabilistic models for some intelligence and attainment tests / G. Rasch. – Copenhagen, Denmark: Danish Institute for Educational Research. (Expanded edition, 1980. Chicago: University of Chicago Press), 1960. – 199 p. 7. Feinberg G. The Rationale for Precision Measurements / G. Feinberg // Rasch Measurement Transactions. – 2000. – 14:3. – P. 7645. 8. Linacre J. M. Estimation Methods for Rasch Measures / Ed. Smith E. V., Smith R. M. // In Introduction to Rasch Measurement. Theory, Models and Applications. – JAM Press, Maple Grove, Minnesota, 2004. – 25. – 47 p. 9. Исследование точности измерения латентной переменной в зависимости от числа дихотомических индикаторных переменных / [Т. С. Анисимова, А. А. Маслак, С. А. Осипов и др.] // Вестник СГПИ. – 2005. – № 1. – С. 136–144. 10. Данилов А. А. Исследование точности измерения латентной переменной в зависимости от числа градаций индикаторных переменных / А. А. Данилов, А. А. Маслак // Вестн. Воронеж. гос. техн. ун-та. – 2009. – Т. 5, № 11. – С. 106–114. 11. Анисимова Т. С. Исследование точности измерения латентной переменной в зависимости от коррелированности индикатор- ных переменных / Т. С. Анисимова, А. А. Маслак, С. А. Поздняков // Вестник СГПИ. – 2005. – № 1 (1). – С. 126–136. 12. Алейникова А. А. Анализ точности измерения латентной переменной в зависимости от сдвига набора тестовых заданий / А. А. Алейникова, А. А. Маслак // Теория и практика измерения латентных переменных в образовании : материалы XXIV Всерос. науч.-практ. конф., (г. Славянск-на-Кубани, 28–29 апр. 2016 г.) / под ред.: А. А. Маслака, С. А. Позднякова, С. А. Осипова. – Славянск-на-Кубани : Филиал Кубанского гос. ун-та в г. Славянске-на-Кубани, 2016. – С. 7–12. 13. Поздняков С. А. Исследование точности измерения латентных переменных в образовании : монография / С. А. Поздняков. – Славянск-на-Кубани : Издательский центр СГПИ, 2007. – 118 с. 14. Leroux A. J. A Comparison of Stopping Rules for Computerized Adaptive Screening Measures Using the Rating Scale Model / A. J. Leroux, B. G. Dodd // Journal of Applied Measurement. – 2014. – Vol. 15, No. 3. – P. 213–226.


GOST Style Citations






DOI: http://dx.doi.org/10.15588/1607-3274-2017-1-5



Copyright (c) 2017 A. A. Maslak, S. I. Moiseev, S. A. Osipov, S. A. Pozdnyakov

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Address of the journal editorial office:
Editorial office of the journal «Radio Electronics, Computer Science, Control»,
Zaporizhzhya National Technical University, 
Zhukovskiy street, 64, Zaporizhzhya, 69063, Ukraine. 
Telephone: +38-061-769-82-96 – the Editing and Publishing Department.
E-mail: rvv@zntu.edu.ua

The reference to the journal is obligatory in the cases of complete or partial use of its materials.