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Year-Number: 2018-Volume 10, Issue 3
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Abstract
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Abstract
The aim of this study is to investigate the effect of measurement errors on the estimation of simple linear regression and compare the performance of the classical least squares (CLS) regression method and orthogonal regression according to the standard deviation of the residuals. For this aim, analyses were performed on three data sets of different size. The first set of data was consisting 10 data for hardness and durability of substances. The second set of data was collected from 157 eighth-grade students’ non-routine problem-solving test scores and mathematics scores on Examination for Transition to Basic Secondary Education. The third set of data was collected from 956 eighth-grade students’ PISA Mathematics Literacy Test scores and Level Determination Examination scores. As a result of comparisons on three data sets, ıt was seen that orthogonal regression gave the smaller standard deviation of residuals than CLS regression method. Depending on these findings, it was determined that orthogonal regression has better performance than CLS regression method in the estimating the linear relationship between two variables. The results of this study can be guiding for making important contributions about measurement error modeling to researchers working in social sciences.
Keywords
- Akdeniz, F. (2013). Olasılık ve istatistik (18. Baskı). Ankara, Nobel Kitabevi.
- Armağan, İ. (1983). Yöntembilim-2 bilimsel araştırma yöntemleri (No: 16/b). İzmir, Dokuz Eylül Üniversitesi Güzel Sanatlar Fakültesi Yayınları.
- Besalú, E., Ortiz, J.V., & Pogliani, L. (2006). Some plots are not that equivalent. MATCH Communications in Mathematical and in Computer Chemistry, 55, 281-286.
- Büyüköztürk, Ş., Çokluk, Ö., & Köklü, N. (2012). Sosyal bilimler için istatistik (11. Baskı). Ankara, Pegem Akademi.
- Büyüköztürk, Ş. (2012). Sosyal bilimler için veri analizi el kitabı: istatistik, araştırma deseni, spss uygulamaları ve yorum (17. Baskı). Ankara, Pegem Akademi.
- Calzada, M.E., & Scariano, S.M. (2003). Contrasting total least squares with ordinary least squares part II: Examples and comparisons. Mathematics and Computer Education, 37(2), 159-174.
- Can, A. (2013). SPSS ile bilimsel araştırma sürecinde nicel veri analizi (1. Baskı). Ankara, Pegem Akademi.
- Carr, J.R. (2012). Orthogonal regression: A Teaching perspective. International Journal of Mathematical Education in Science and Technology, 43(1), 134-143. http://dx.doi.org/10.1080/0020739X.2011.573876
- Carroll, R.J., & Ruppert D. (1996). The use and misuse of orthogonal regression in linear errors-in-variables models. The American Statistician, 50 (1), 1-6.
- Cheng, C.L., & van Ness, J.W. (1992). Generalized M-estimators for errors in variables regression. The Annals of Statistics, 20(1), 385–397.
- Coşkuntuncel, O. (2013). The Use of alternative Regression Methods in Social Sciences and the Comparison of Least Squares and M Estimation Methods in Terms of the Determination of Coefficient. Educational Sciences. Theory & Practice, 13(4), 2139-2158. http://dx.doi.org/10.12738/estp.2013.4.1867
- Deming, E.W. (1948). Statistical Adjustment of Data (Fourth printing). New York, John Wiley and Sons Interscience.
- Ding, G., Chu, B., Jin, Y., & Zhu, C. (2013). Comparison of orthogonal regression and least squares in measurement error modeling for prediction of material property. Nanotechnology and Material Engineering Research, Advanced Materials Research, 661, 166-170. http://dx.doi.org/10.4028/ www.scientific.net/AMR.661.166
- Draper, N. R., & Smith, H. (1981). Applied regression analysis (2nd Ed.). New York, John Wiley and Sons Interscience Publication.
- Elfessi, A., & Hoar, R.H. (2001). Simulation study of a linear relationship between two variables affected by errors. Journal of Statistical Computation and Simulation, 71(1), 29-40. http://dx.doi.org/10.1080 /00949650108812132
- Ercan, İ., & Kan, İ. (2006). Ölçme ve ölçmede hata. Anadolu Üniversitesi Bilim ve Teknoloji Dergisi, 7 (1) 51-56.
- Fišerová, E., & Hron, K. (2010). Total least squares solution for compositional data using linear models. Journal of Applied Statistics, 37(7), 1137-1152. http://dx.doi.org/10.1080/02664760902914532
- Freund, R. J., & Wilson, W. J. (1998). Regression analysis: statistical modeling of a response variable. San Diego, Academic press.
- Fuller, W.A. (1987). Measurement Error Models. New York, John Wiley and Sons.
- Gazeloğlu, C., & Saraçlı, S. (2013). Doğrusal olmayan tip II regresyon analizi üzerine bir simülasyon çalışması. IAAOJ, Scientific Science, 1(1), 13-18.
- Glaister, P. (2005). The use of orthogonal distances in generating the total least squares estimate. Mathematics and Computer Education, 39(1), 21-30.
- Golub, G.H., & Van Loan, C.F. (1980). An Analysis of the total least squares problem. SIAM Journal on Numerical Analysis, 17(6), 883-893.
- Isobe, T., Feigelson, E.D, Akritas, M.G., & Babu, G.J. (1990). Linear regression in astronomy I. The Astrophysical Journal, 364, 104-113.
- Kane, M.T., & Mroch, A.A. (2010). Modeling group differences in OLS and Orthogonal Regression: Implications for differential validity studies. Applied Measurement in Education, 23, 215-241. http://dx.doi.org/10.1080/08957347.2010.485990
- Keleş, T., & Altun, M. (2016). Comparison of classical linear regression and orthogonal regression with respect to the sum of squared perpendicular distances. Journal of Measurement and Evaluation in Education and Psychology, 7(2);296-308. http://dx.doi.org/10.21031/epod.277885
- Kermack, K.A., & Haldane, J.B.S. (1950). Organic correlation and allometry. Biometrika Trust, 37(1), 30–41.
- Küçüksille, E. (2016). Basit doğrusal regresyon[Simple linear regression]. In Ş. Kalaycı (Ed.), SPSS uygulamalı çok değişkenli istatistik teknikleri (7th Ed.), (pp. 199-204). Ankara, Asil Yayın.
- Leng, L., Zhang, T. Kleinman, L., & Zhu, W. (2007). Ordinary least square regression, orthogonal regression, geometric mean regression and their applications in aerosol science. Journal of Physics, Conference Series 78(1), 1-5. Retrieved from http://iopscience.iop.org/1742-6596/78/1/012084
- Li, H.C. (1984). Generalized problem of least squares. The American Mathematical Monthly, 91(2), 135-137.
- Lolli, B., & Gasperini, P. (2012). A Comparison among general orthogonal regression methods applied to earthquake magnitude conversions. Geophysical Journal International, 190, 1135-1151. http://dx.doi.org/ 10.1111/j.1365-246X.2012.05530.x
- Ludbrook, J. (2010). Linear regression analysis for comparing two measurers or methods of measurement: But which regression?. Clinical and Experimental Pharmacology and Physiology, 37, 692-699. http://dx.doi.org/10.1111/j.1440-1681.2010.05376.x
- Markovsky, I., & Van Huffel, S. (2007). Overview of total least- squares methods. Signal Processing, 87, 2283- 2302. http://dx.doi.org/10.1016/j.sigpro.2007.04.004
- McCartin, B. J, (2003). A geometric characterization of linear regression. Statistics, 37(2), 101–117. http://dx.doi.org/10.1080=0223188031000112881
- Montgomery D. C., Peck E. A., & Vining G.G. (2001). Introduction to linear regression analysis (3rd Ed.). New York, John Wiley and Sons Interscience Publication.
- Nievergelt, Y. (1994). Total least squares: State-of-the-art regression in numerical analysis. SIAM Review (Society for Industrial and Applied Mathematics), 36(2), 258–264.
- Ortiz, J.V., Pogliani, L., & Besalú, E. (2010). Two-variable linear regression: Modeling with orthogonal least- squares analysis. Journal of Chemical Education, 87(9), 994-995.
- Öztürk, S. (2012). İstatistiksel regresyon yöntemlerinin farklı veri gruplarına uygulanması üzerine bir analiz. Gümüşhane Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2(2), 55-67.
- Saraçlı, S. (2011). Tip II regresyon tekniklerinin Monte-Carlo simülasyonu ile karşılaştırılması. e-Journal of New World Sciences Academy, 6(2), 26-35.
- Saraçlı, S., Doğan, İ., & Doğan, N. (2009a). Medikal metod karşılaştırma çalışmalarında Deming regresyon tekniği. Türkiye Klinikleri J Biostat, 1(1), 9-15.
- Saraçlı, S., Yılmaz, V., & Doğan, İ. (2009b). Simple linear regression techniques in measurement error models. Anadolu University Journal of Science and Technology, 10(2), 335-342.
- Scariano, S.M., & Barnet, II.W. (2003). Contrasting total least squares with ordinary least squares part I: Basic ideas and result. Mathematics and Computer Education, 37(2), 141-158.
- Schafer, D.W., & Purdy, K. (1996). Likelihood analysis for errors-in-variables regression with replicate measurement. Biometrika, 83(4), 813–824.
- Sen, A., & Srivastava, M. (1990). Regression analysis: theory, methods, and applications. New York, Springer.
- Shi, Y., Xu, P., Liu, J., & Shi, C. (2015). Alternative formulae for parameter estimation in partial errors-in- variables models. Journal of Geodesy, 89 (1), 13-16. http://dx.doi.org/10.1007/s00190-014-0756-2
- Stefanski, L.A. (2000). Measurement error models. Journal of the American Statistical Association, 95(452), 1353-
- Stöckl, D., Dewitte, K., & Thienpont, L.M., (1998). Validity of linear regression in method comparison studies: is it limited by the statistical model or the quality of the analytical input data?. Clinical Chemistry, 44(11), 2340–2346.
- Sykes, A.O. (1993). An Introduction to Regression Analysis. Coase-Sandor Institute for Law & Economics Working, 20, 1-34.
- von Eye, A., & Schuster, C. (1998). Regression analysis for social sciences. San Diago, California, Academic Press.
- Warton, D.I., Wright, I.J., Falster, D.S., & Westoby, M. (2006). Bivariate line-fitting methods for allometry. Biological Reviews, 81(2), 259-291. http://dx.doi.org/ 10.1017/S1464793106007007
- Weisberg, S. (2005). Applied linear regression (3rd Ed.). New York, John Wiley and Sons Interscience Publication.
- Yan, X., & Su, X. (2009). Linear regression analysis theory and computing. Singapore, World Scientific.
