Boyutlar Arası Korelasyon ile Madde Ayırt Ediciliği Arasındaki Etkileşimin Parametre Kestirimi Üzerine Etkisi
Öz
Alan yazında karışık yapılı çok boyutlu testlerin
tek boyutlu olarak kestirilmesi ile ilgili bazı çalışmalar bulunmaktadır. Bu
çalışmalarda boyutlar arası korelasyon arttıkça ayırt edicilik indeksine ait
hataların da arttığı belirtilmiştir. Bu çalışmada çok boyutlu yapıların tek
boyutlu olarak kestirildiği durumda maddelerin x ekseniyle arasındaki açı ile boyutlar
arası korelasyonun etkileşiminin madde ve birey parametrelerinin kestirimi üzerine etkisi
araştırılmıştır. Çalışmada SAS\IML aracılığıyla üretilen iki boyutlu 2PLM telafisel
modeldeki veri setleri kullanılmıştır. Araştırmada a parametrelerinin x ekseniyle yaptığı açılar sırasıyla 0.15o;
0.30o; 0.45o; 0.60o ve 0.75o olacak
şekilde değişimlenmiştir. Boyutlar arası korelasyonlar da maddelerin açıları
ile aynı olacak şekilde 0.15; 0.30; 0.45; 0.60 ve 0.75 alınmıştır. Yetenek
dağılımları ise standart normal, sağa ve sola çarpık dağılım şeklinde
belirlenmiştir. Böylece, 5 farklı madde açısı * 5 farklı boyutlar arası
korelasyon *3 farklı yetenek dağılımı olmak üzere 75 (5x5x3) koşullu bir
araştırma deseni tasarlanmıştır. Veri setlerinde madde sayısı 25 ve birey
sayısı 2000 olarak sabit tutulmuştur. Ele alınan her bir koşula ilişkin 100
tekrar yapılmıştır. Elde edilen her bir veri seti tek boyutlu olarak kestirilmiştir.
Parametrelerin kestirilmesinde BILOG programından yararlanılmıştır. Sonuçların
değerlendirilmesinde RMSE istatistiği kullanılmıştır. Genel olarak özellikle
ayırt edicilik indeksi için elde edilen sonuçların çok boyutlu verilerin tek
boyutlu olarak kestirildiği çalışmalarla ilgili alan yazından farklı bir örüntü
sergilediği söylenebilir.
Anahtar Kelimeler
Çok boyutlu veri tek boyutlu kestirim korelasyon ayırt edicilik indeksi
Kaynakça
- Ansley, T. N., & Forsyth, R. A. (1985). An examination of the characteristics of unidimensional IRT parameter estimates derived from two-dimensional data. Applied Psychological Measurement, 9(1), 37-48.
- Ackerman, T.A. (1989). Unidimensional IRT calibration of compensatory and noncompensatory multidimensional items. Applied Psychological Measurement, 13(2), 113-27.
- Ackerman, T.A., Gierl, M.J., & Walker, C.M. (2003). Using multidimensional item response theory to evaluate educational and psychological tests. Educational Measurement: Issues and Practice: MIRT Instructional Module.
- Bulut, O. (2013). Between-person and within-person subscore reliability: Comparison of unidimensional and multidimensional IRT models (Doctoral Dissertation). Available from ProQuest Dissertations and Theses database (No. 3589000).
- Doody, E. N. (1985, April). Examining the effects of multidimensional data on ability and item parameter estimation using the three-parameter logistic model. Paper presented at the annual meeting of the American Educational Research Association, Chicago.
- Drasgow, F., & Parsons, C. K. (1983). Application of unidimensional item response theory models to multidimensional data. Applied Psychological Measurement, 7, 189-199.
- Gocer Sahin (2015). Yarı karışık yapılı çok boyutlu yapıların tek boyutlu olarak ele alınması durumunda kestirilen parametrelerin incelenmesi (Doctoral Dissertation). Available from YOK Dissertations and Theses database (No. 454926).
- Gocer Sahin S., Walker, C. M., & Gelbal, S. (2015). The Impact of Model Misspecification with Multidimensional Test Data (pp.133-44). In van der Ark, L. A., Bolt, D. M., Chow, S. M., Douglas, J. A., and Wang, W. C. (Eds.), Quantitative Psychology Research: The 79th Annual Meeting of the Psychometric Society, New York, NY: Springer.
- Harrison, D. A. (1986). Robustness of IRT parameter estimation to violations of the unidimensionality assumption. Journal of Educational Statistics, 11(2), 91-115.
- Kahraman, N. (2013) Unidimensional interpretations for multidimensional test items. Journal of Educational Measurement, 50(2), 227-246.
- Kirisci, L., Hsu, T., & Yu, L. (2001). Robustness of item parameter estimation programs to assumptions of unidimensionality and normality. Applied Psychological Measurement, 25(2), 146-162.
- Leucht, R. M & Miller, T. R. (1992). Unidimensional calibrations and interpretations of composite traits for multidimensional tests. Applied Psychological Measurement, 16, 279-293.
- Reckase, M. D. (2009). Multidimensional item response theory (statistics for social and behavioral sciences). New York: Springer.
- Reckase, M.D., Ackerman, T.A., & Carlson, J.E. (1988). Building a unidimensional test using multidimensional items. Journal of Educational Measurement, 25, 193-203.
- Reckase, M.D., & McKinley, R. L. (1991). The discriminating power of items that measure more than one dimension. Applied Psychological Measurement, 15(4), 361-373.
- Sheng Y. & Wikle C. K. (2007). Comparing multidimensional and unidimensional item response theory models. Educational and Psychological Measurement, 68(3), 413-430.
- Zhang, J. (2005). Estimating multidimensional item response models with mixed structure (ETS Research Report 05-04). Princeton, NJ: Educational Testing Service.
- Zhang, B. (2008). Application of unidimensional item response models to tests with items sensitive to secondary dimension. The Journal of Experimental Education, 77(2), 147-166.
- Zhang, J. (2012). Calibration of response data using MIRT models with simple and mixed structures. Applied Psychological Measurement, 36(5), 375-398.
The Interaction Effect of the Correlation between Dimensions and Item Discrimination on Parameter Estimation
Öz
There are
some studies in the literature that have considered the impact of modeling
multidimensional mixed structured tests as unidimensional. These studies have demonstrated
that the error associated with the discrimination parameters increases as the
correlation between dimensions increases. In this study, the interaction between
items’ angles on coordinate system and the correlations between dimensions was
investigated when estimating multidimensional tests as unidimensional. Data were
simulated based on two dimensional, and two-parameter compensatory MIRT model.
Angles of items were determined as 0.15o; 0.30o; 0.45o; 0.60o and
0.75orespectively. The correlations between
ability parameters were set to 0.15, 0.30, 0.45, 0.60 and 0.75 respectively,
which are same with the angles of discrimination parameters. The ability
distributions were generated from standard normal, positively and negatively
skewed distributions. A total of 75 (5 x
5 x 3) conditions were studied: five different conditions for the correlation
between dimensions; five different angles of items and three different ability
distributions. For all conditions, the number of items was fixed at 25 and the
sample size was fixed at n = 2,000.
Item and ability parameter estimation were conducted using BILOG. For each
condition, 100 replications were performed. The RMSE statistic was used to
evaluate parameter estimation errors, when multidimensional response data were scaled
using a unidimensional IRT model. Based on the findings, it can be concluded
that the pattern of RMSE values especially for discrimination parameters are
different from the existing studies in the literature in which multidimensional
tests were estimated as unidimensional.
Anahtar Kelimeler
Multidimensional data unidimensional estimation correlation discriminaton index
Kaynakça
- Ansley, T. N., & Forsyth, R. A. (1985). An examination of the characteristics of unidimensional IRT parameter estimates derived from two-dimensional data. Applied Psychological Measurement, 9(1), 37-48.
- Ackerman, T.A. (1989). Unidimensional IRT calibration of compensatory and noncompensatory multidimensional items. Applied Psychological Measurement, 13(2), 113-27.
- Ackerman, T.A., Gierl, M.J., & Walker, C.M. (2003). Using multidimensional item response theory to evaluate educational and psychological tests. Educational Measurement: Issues and Practice: MIRT Instructional Module.
- Bulut, O. (2013). Between-person and within-person subscore reliability: Comparison of unidimensional and multidimensional IRT models (Doctoral Dissertation). Available from ProQuest Dissertations and Theses database (No. 3589000).
- Doody, E. N. (1985, April). Examining the effects of multidimensional data on ability and item parameter estimation using the three-parameter logistic model. Paper presented at the annual meeting of the American Educational Research Association, Chicago.
- Drasgow, F., & Parsons, C. K. (1983). Application of unidimensional item response theory models to multidimensional data. Applied Psychological Measurement, 7, 189-199.
- Gocer Sahin (2015). Yarı karışık yapılı çok boyutlu yapıların tek boyutlu olarak ele alınması durumunda kestirilen parametrelerin incelenmesi (Doctoral Dissertation). Available from YOK Dissertations and Theses database (No. 454926).
- Gocer Sahin S., Walker, C. M., & Gelbal, S. (2015). The Impact of Model Misspecification with Multidimensional Test Data (pp.133-44). In van der Ark, L. A., Bolt, D. M., Chow, S. M., Douglas, J. A., and Wang, W. C. (Eds.), Quantitative Psychology Research: The 79th Annual Meeting of the Psychometric Society, New York, NY: Springer.
- Harrison, D. A. (1986). Robustness of IRT parameter estimation to violations of the unidimensionality assumption. Journal of Educational Statistics, 11(2), 91-115.
- Kahraman, N. (2013) Unidimensional interpretations for multidimensional test items. Journal of Educational Measurement, 50(2), 227-246.
- Kirisci, L., Hsu, T., & Yu, L. (2001). Robustness of item parameter estimation programs to assumptions of unidimensionality and normality. Applied Psychological Measurement, 25(2), 146-162.
- Leucht, R. M & Miller, T. R. (1992). Unidimensional calibrations and interpretations of composite traits for multidimensional tests. Applied Psychological Measurement, 16, 279-293.
- Reckase, M. D. (2009). Multidimensional item response theory (statistics for social and behavioral sciences). New York: Springer.
- Reckase, M.D., Ackerman, T.A., & Carlson, J.E. (1988). Building a unidimensional test using multidimensional items. Journal of Educational Measurement, 25, 193-203.
- Reckase, M.D., & McKinley, R. L. (1991). The discriminating power of items that measure more than one dimension. Applied Psychological Measurement, 15(4), 361-373.
- Sheng Y. & Wikle C. K. (2007). Comparing multidimensional and unidimensional item response theory models. Educational and Psychological Measurement, 68(3), 413-430.
- Zhang, J. (2005). Estimating multidimensional item response models with mixed structure (ETS Research Report 05-04). Princeton, NJ: Educational Testing Service.
- Zhang, B. (2008). Application of unidimensional item response models to tests with items sensitive to secondary dimension. The Journal of Experimental Education, 77(2), 147-166.
- Zhang, J. (2012). Calibration of response data using MIRT models with simple and mixed structures. Applied Psychological Measurement, 36(5), 375-398.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 29 Eylül 2018 |
| Kabul Tarihi | 5 Temmuz 2018 |
| Yayımlandığı Sayı | Yıl 2018 Cilt: 9 Sayı: 3 |
