Hari Purnomo Susanto (1), Heri Retnawati (2), Farida Agus Setiawati (3)
Teori respon butir memiliki banyak kelebihan Ketika digunakan untuk menentukan karateristik butir instrumen jika ukuran sampel yang digunakan besar. Sebaliknya, jika ukuran sampel kecil IRT memiliki kecenderunga kurang akurat dalam menentukan karakteristik suatu instrumen. Penelitian ini bertujuan untuk menentukan efek ukuran sampel pada GRM yang didasarkan pada data awal yang memiliki korelasi inter item yang sama secara statistik. Penelitian ini merupakan penelitian simulasi yang didasarkan pada data empiris. Data skunder dari 43 responden digunakan sebagai data awal. Akurasi efek dari ukuran sampel baru dihitung dengan menggunakn RMSE dan koelasi. Teknik membangkitkan data yang digunakan yaitu metode multivariat variabel random diskrit. perangkat lunak R. Hasil penelitian menunjukkan nilai RMSE berkisar 0,6 > 0,33 dan korelasi sekitar 0,5 < 0,7 tidak memenuhi standar akurasi.. Dapat disimpulkan bahwa ukuran sampel dengan matriks korelsi yang sama, tidak memiliki efek pada parameter GRM dan data baru yang dihasilkan tidak dapat digunakan untuk pemulihan parameter GRM
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The effect of sample size on GRM parameters based on the correlation between items
Abstract: Item response theory has many advantages in determining the instrument's item characteristics when the sample size used is large. On the other hand, if the sample size is small, the IRT tends to be less accurate in determining an instrument. This study aims to determine the effect of sample size on GRM based on the inter-item correlation matrix of initial data. This research was conducted on simulation research based on empirical data. Secondary data from 43 respondents was used as initial data. The effect accuracy of the new sample size was calculated using RMSE and correlation. The data generation method used was the multivariate method of discrete random variables. The results show that the RMSE value is around 0.6 > 0.33, and the correlation of about 0.5 < 0.7 did not meet the standard of accuracy. It could be concluded that the sample size with the same inter-item correlation matrix has no effect on the GRM parameters, and the new data generated couldn’t be used for GRM parameter recovery.
Bahry, M. L. (2012). Polytomous item response theory parameter recovery: An investigation of non-normal distributions and small sample size [University of Alberta]. https://doi.org/10.7939/R36H8X
Barbiero, A., & Ferrari, P. A. (2015). GenOrd: Simulation of discrete random variables with given correlation matrix and marginal distributions. https://rdrr.io/cran/GenOrd/
Barnes, L. L. B., & Wise, S. L. (1991). The utility of a modified one-parameter IRT model with small samples. Applied Measurement in Education, 4(2), 143–157. https://doi.org/10.1207/s15324818ame0402_4
Cho, Y. (2014). The mixture distribution polytomous rasch model used to account for response styles on rating scales: A simulation study of parameter recovery and classification accuracy. [University of Maryland]. http://hdl.handle.net/1903/14511
de la Torre, J., & Hong, Y. (2010). Parameter estimation with small sample size a higher-order IRT model approach. Applied Psychological Measurement, 34(4), 267–285. https://doi.org/10.1177/0146621608329501
Ferrari, P. A., & Barbiero, A. (2012). Simulating ordinal data. Multivariate Behavioral Research, 47(4), 566–589. https://doi.org/10.1080/00273171.2012.692630
Finch, H., & French, B. F. (2019). A comparison of estimation techniques for IRT models with small samples. Applied Measurement in Education, 32(2), 77–96. https://doi.org/10.1080/08957347.2019.1577243
Hair, J. F., Black, W. C., & Babin, B. J. (2010). Multivariate data analysis: A Global Perspective (7th ed.). Prentice Hall.
Hambleton, R. K. (1989). Principles and selected applications of item response theory (R. L. Linn (ed.); 3rd ed.). Macmillan.
Huang, H.-Y. (2016). Mixture random-effect IRT models for controlling extreme response style on rating scales. Frontiers in Psychology, 7. https://doi.org/10.3389/fpsyg.2016.01706
Jiang, S., Wang, C., & Weiss, D. J. (2016). Sample size requirements for estimation of item parameters in the multidimensional graded response model. Frontiers in Psychology, 7. https://doi.org/10.3389/fpsyg.2016.00109
Kieftenbeld, V., & Natesan, P. (2012). Recovery of graded response model parameters. Applied Psychological Measurement, 36(5), 399–419. https://doi.org/10.1177/0146621612446170
Kutscher, T., Eid, M., & Crayen, C. (2019). Sample size requirements for applying mixed polytomous item response models: Results of a Monte Carlo simulation study. Frontiers in Psychology, 10. https://doi.org/10.3389/fpsyg.2019.02494
Reise, S. P., & Yu, J. (1990). Parameter recovery in the graded response model using MULTILOG. Journal of Educational Measurement, 27(2). https://doi.org/10.1111/j.1745-3984.1990.tb00738.x
Şahin, A., & Anıl, D. (2017). The effects of test length and sample size on item parameters in item response theory. Educational Sciences: Theory & Practice. https://doi.org/10.12738/estp.2017.1.0270
Sarstedt, M., & Mooi, E. (2014). A concise guide to market research. In A Concise Guide to Market Research. Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-53965-7
Suwarto, S., Widoyoko, E. P., & Setiawan, B. (2019). The effects of sample size and logistic models on item parameter estimation. Proceedings of the 2nd International Conference on Education, 323–330. https://doi.org/10.4108/eai.28-9-2019.2291082
Swaminathan, H., Hambleton, R. K., Sireci, S. G., Xing, D., & Rizavi, S. M. (2003). Small sample estimation in dichotomous item response models: Effect of priors based on judgmental information on the accuracy of item parameter estimates. Applied Psychological Measurement, 27(1), 27–51. https://doi.org/10.1177/0146621602239475
Yen, W. M. (1987). A comparison of the efficiency and accuracy of BILOG and LOGIST. Psychometrika, 52(2), 275–291. https://doi.org/10.1007/BF02294241