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

Authors

  • A. A. Maslak Chapter of Kuban State University at Slavyansk-on- Kuban, Russia, Russian Federation
  • S. I. Moiseev Voronezh Branch of «Plekhanov Russian University of Economics», Russia, Russian Federation
  • S. A. Osipov Chapter of Kuban State University at Slavyansk-on- Kuban, Russia, Russian Federation
  • S. A. Pozdnyakov Chapter of Kuban State University at Slavyansk-on- Kuban, Russia, Russian Federation

DOI:

https://doi.org/10.15588/1607-3274-2017-1-5

Keywords:

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

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.

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.

Downloads

How to Cite

Maslak, A. A., Moiseev, S. I., Osipov, S. A., & Pozdnyakov, S. A. (2017). INVESTIGATION OF MEASUREMENT PRECISION OF LATENT VARIABLE DEPENDING ON THE RANGE OF VARIATION OF INDICATORS SET. Radio Electronics, Computer Science, Control, (1). https://doi.org/10.15588/1607-3274-2017-1-5

Issue

No. 1 (2017): Radio Electronics, Computer Science, Control

Section

Mathematical and computer modelling

License

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.

Creative Commons Licensing Notifications in the Copyright Notices

The journal allows the authors to hold the copyright without restrictions and to retain publishing rights without restrictions.

The journal allows readers to read, download, copy, distribute, print, search, or link to the full texts of its articles.

The journal allows to reuse and remixing of its content, in accordance with a Creative Commons license СС BY -SA.

Authors who publish with this journal agree to the following terms:

  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License CC BY-SA that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.

  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.

  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.