© Joanna Dębicka, Edyta Mazurek, Katarzyna Anna Ostasiewicz Artykuł udostępniony na licencji CC BY-SA 4.0
The Thurstone method is a method of aggregation of preferences that leads to ordering objects at an interval scale, in contrast to other methods of aggregation, the application of which results in obtaining the ordinal scale only. However, we demonstrate that the interval scale obtained by means of the Thurstone method is not fully reliable, as it is strongly susceptible to the problem of irrelevant alternatives, i.e., the order of two objects might be dependent on whether there is or not a third, completely independent object in the studied collectivity.
The other issue examined in the paper is the formula that is to be minimised in the Thurstone method. Thurstone proposed a formula easy to be minimised with tabularised values of normal distribution. However, today’s calculation powers of computers make it possible to minimise another formula, which allows a better fit of observed frequencies to the predicted ones, and makes it possible to avoid the problem with empirical frequencies close to 1.
The aim of the paper is to propose two improvements to the Thurstone method. The first one involves the application of the rule of thumb to the minimal spacing (in terms of standard deviations), below which the ordering of objects cannot be regarded as reliable, and the use of the method of empirical examining of the stability of order. The second of the proposed improvements consists in minimising a formula other than the original one, especially in the cases where empirical frequencies reach very high values.
the Thurstone method, dependence on irrelevant alternatives, aggregation of preferences, ordering of objects
C18, C83, C46
Arrow, K. J. (1951). Social Choice and Individual Values. Wiley.
Dębicka, J., Mazurek, E., & Ostasiewicz, K. (2022). Methodological Aspects of Measuring Preferences Using the Rank and Thurstone Scale. Statistika, 102(3), 236–248. https://doi.org/10.54694/stat.2022.5.
Dębicka, J., Mazurek, E., & Ostasiewicz, K. (2023). Thurstone model – a model or a procedure? [manuscript submitted for publication].
Dragonetti, R., Ponticorvo, M., Dolce, P., Di Filippo, S., & Mercogliano, F. (2017). Pairwise comparison psychoacoustic test on the noise emitted by DC electrical motors. Applied Acoustics, 119, 108–118. https://doi.org/10.1016/j.apacoust.2016.12.016.
Handley, J. C. (2001). Comparative Analysis of Bradley-Terry and Thurstone-Mosteller Paired Comparison Models for Image Quality Assessment. PICS: Image Processing, Image Quality, Image Capture, Systems Conference, Montreal. https://www.imaging.org/common/uploaded%20files/pdfs/Papers/2001/PICS-0-251/4604.pdf.
Heldsinger, S., & Humphry, S. (2010). Using the Method of Pairwise Comparison to Obtain Reliable Teacher Assessments. The Australian Educational Researcher, 37(2), 1–19. https://doi.org/10.1007/BF03216919.
Kanda, T. (2002). Classification of menus on home dining tables based upon human meal Kansei. Kansei Engineering International, 3(4), 9–14. https://doi.org/10.5057/kei.3.4_9.
Krabbe, P. F. (2008). Thurstone Scaling as a Measurement Method to Quantify Subjective Health Outcomes. Medical Care, 46(4), 357–365. https://doi.org/10.1097/MLR.0b013e31815ceca9.
Lipovetsky, S. (2007). Thurstone scaling in order statistics. Mathematical and Computer Modelling, 45(7–8), 917–926. https://doi.org/10.1016/j.m cm.2006.09.009 .
Lipovetsky, S., & Conklin, W. M. (2004). Thurstone scaling via binary response regression. Statistical Methodology, 1(1–2), 93–104. https://doi.org/10.1016/j.statmet.2004.04.001.
Mosteller, F. (1951). Remarks on the method of paired comparisons: III. A test of significance for paired comparisons when equal standard deviations and equal correlations are assumed. Psychometrika, 16(2), 207–218. https://doi.org/10.1007/BF02289116.
Orbán-Mihálykó, É., Mihálykó, C., & Gyarmati, L. (2022). Application of the Generalized Thurstone Method for Evaluations of Sports Tournaments’ Results. Knowledge, 2(1), 157–166. https://doi.org/10.3390/knowledge2010009.
Temesi, J., Szádoczki, Z., & Bozóki, S. (2023). Incomplete pairwise comparison matrices: Ranking top women tennis players. Journal of the Operational Research Society, 75(1), 145–157. https://doi.org/10.1080/01605682.2023.2180447.
Thurstone, L. L. (1927). The method of paired comparisons for social values. The Journal of Abnormal and Social Psychology, 21(4), 384–400. https://psycnet.apa.org/doi/10.1037/h0065439.
Thurstone, L. L., & Chave, E. J. (1929). The measurement of attitude. The University of Chicago Press.
Thurstone, L. L., & Jones, L. V. (1957). The Rational Origin for Measuring Subjective Values. Journal of the American Statistical Association, 52(280), 458–471. https://psycnet.apa.org/doi /10.2307/2281694 .
Vojnovic, M., & Yun, S.-Y. (2016). Parameter Estimation for Generalized Thurstone Choice Models. In M. F. Balcan & K. Q. Weinberger (Eds.), Proceedings of the 33rd International Conference on Machine Learning (vol. 48, pp. 498–506). JMLR.org.
van Wijk, A., & Hoogstraten, J. (2004). Paired comparisons of sensory pain adjectives. European Journal of Pain, 8(4), 293–297. https://doi.org/10.1016/j.ejpain.2003.10.002.
Woods, R. L., Satgunam, P., Bronstad, M., & Peli, E. (2010). Statistical analysis of subjective preferences for video enhancement. In B. E. Rogowitz & T. N. Pappas (Eds.), Human Vision and Electronic Imaging XV (vol. 7527, pp. 98–107). SPIE.
Yellott, Jr., J. I. (1980). Generalized Thurstone models for ranking: equivalence and reversibility. Journal of Mathematical Psychology, 22(1), 48–69. https://doi.org/10.1016/0022-2496(80)90046-2.
