Decreasing Respondent Heterogeneity by Likert Scales Adjustment via Multipoles
Abstract
:1. Introduction
2. Reducing Respondents’ Heterogeneity
3. Summary
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Appendix A. Likert Scale in Multipole Description
References
- Likert, R. A technique for the measurement of attitudes. Arch. Psychol. 1932, 140, 1–55. [Google Scholar]
- Likert, R.; Roslow, S.; Murphy, G. A simple and reliable method of scoring the Thurstone attitude scales. J. Soc. Psychol. 1934, 5, 228–238. [Google Scholar] [CrossRef]
- Edmondson, D.R. Likert scales: A history. In Proceedings of the 12th Conference on Historical Analysis and Research in Marketing (CHARM), Long Beach, CA, USA, 28 April–1 May 2005; Neilson, L.C., Ed.; Sage: Thousand Oaks, CA, USA, 2005; pp. 127–133. [Google Scholar]
- Allen, E.; Seaman, C. Likert scales and data analysis. Qual. Prog. 2007, 40, 64–65. [Google Scholar]
- Carifio, J.; Perla, R.J. Ten common misunderstandings, misconceptions, persistent myths and urban legends about Likert scales and Likert response formats and their antidotes. J. Soc. Sci. 2007, 3, 106–116. [Google Scholar] [CrossRef]
- Burns, A.; Burns, R. Basic Marketing Research, 2nd ed.; Pearson Education: Hoboken, NJ, USA, 2008. [Google Scholar]
- Dawes, J. Do data characteristics change according to the number of scale points used? An experiment using 5-point, 7-point and 10-point scales. Int. J. Mark. Res. 2008, 50, 61–77. [Google Scholar] [CrossRef]
- Norman, G. Likert scales, levels of measurement and the “laws” of statistics”. Adv. Health Sci. Educ. 2010, 15, 625–632. [Google Scholar] [CrossRef] [PubMed]
- Lipovetsky, S. Factor analysis by limited scales—Which factors to analyze? J. Mod. Appl. Stat. Methods 2017, 16, 233–245. [Google Scholar] [CrossRef]
- Malhotra, N.K.; Agarwal, J.; Peterson, M. Methodological issues in cross-cultural marketing research: A state-of-the-art review. Int. Mark. Rev. 1996, 13, 7–43. [Google Scholar] [CrossRef]
- Rossi, P.E.; Gilula, Z.; Allenby, G.M. Overcoming scale usage heterogeneity: A Bayesian hierarchical approach. JASA 2001, 96, 20–31. [Google Scholar] [CrossRef]
- Van Rosmalen, J.; Van Herk, H.; Groenen, P.J.F. Identifying response styles: A latent-class bilinear multinomial logit model. J. Mark. Res. 2010, XLVII, 157–172. [Google Scholar] [CrossRef]
- Lipovetsky, S. Dual PLS analysis. Int. J. Inf. Technol. Decis. Mak. 2012, 11, 879–891. [Google Scholar] [CrossRef]
- Lipovetsky, S. Data fusion in several algorithms. Adv. Adapt. Data Anal. 2013, 5, 3. [Google Scholar] [CrossRef]
- Hoffmeyer-Zlotnik, J.H.P.; Warner, U. Harmonizing Demographic and Socio-Economic Variables for Cross-National Comparative Survey Research; Springer: Dordrecht, The Netherlands; New York, NY, USA, 2014. [Google Scholar]
- Arboretti, R.; Bathke, A.; Bonnini, S.; Bordignon, P.; Carrozzo, E.; Corain, L.; Salmaso, L. Parametric and Nonparametric Statistics for Sample Surveys and Customer Satisfaction Data; Springer: Cham, Switzerland, 2018. [Google Scholar]
- Malito, D.V.; Umbach, G.; Bhuta, N. (Eds.) The Palgrave Handbook of Indicators in Global Governance; Palgrave Macmillan: Basingstoke, UK; Springer: Cham, Switzerland, 2018. [Google Scholar]
- Camparo, J. A geometrical approach to the ordinal data of Likert scaling and attitude measurements: The density matrix in psychology. J. Math. Psychol. 2013, 57, 29–42. [Google Scholar] [CrossRef]
- Camparo, J.; Camparo, L.B. The analysis of Likert scales using state multipoles: An application of quantum methods to behavioral sciences data. J. Educ. Behav. Stat. 2013, 38, 81–101. [Google Scholar] [CrossRef]
- Busemeyer, J.R.; Bruza, P.D. Quantum Models of Cognition and Decision; Cambridge University Press: Cambridge, UK, 2012. [Google Scholar]
- Pothos, E.M.; Busemeyer, J.R. Can quantum probability provide a new direction for cognitive modeling? Behav. Brain Sci. 2013, 36, 255–327. [Google Scholar] [CrossRef] [PubMed]
- Haven, E.; Khrennikov, A. (Eds.) The Palgrave Handbook of Quantum Models in Social Science: Applications and Grand Challenges; Palgrave Macmillan: London, UK, 2017. [Google Scholar]
- Camparo, J.; Camparo, L.B. Being of “two minds”: Assessing vacillating and simultaneous ambivalence with the density matrix. Behav. Res. Methods 2018, 50, 1141–1153. [Google Scholar] [CrossRef] [PubMed]
- Kovalenko, T.; Sornette, D. The Conjunction Fallacy in Quantum Decision Theory; Research Paper Series N°18-15; Swiss Finance Institute: Geneva, Switzerland, 2018. [Google Scholar]
- Yukalov, V.I.; Yukalova, E.P.; Sornette, D. Information processing by networks of quantum decision makers. Phys. A Stat. Mech. Appl. 2018, 492, 747–766. [Google Scholar] [CrossRef] [Green Version]
- Lipovetsky, S. Quantum paradigm of probability amplitude and complex utility in entangled discrete choice modeling. J. Choice Model. 2018, 27, 62–73. [Google Scholar] [CrossRef]
- Lipovetsky, S.; Conklin, M. Predictor relative importance and matching regression parameters. J. Appl. Stat. 2015, 42, 1017–1031. [Google Scholar] [CrossRef]
- Lipovetsky, S.; Conklin, M. Singular value decomposition in additive, multiplicative, and logistic forms. Pattern Recognit. 2005, 38, 1099–1110. [Google Scholar] [CrossRef]
- Lipovetsky, S. Trinomial response modeling in one logit regression. Ann. Data Sci. 2015, 2, 157–163. [Google Scholar] [CrossRef]
- Landau, L.D.; Lifshitz, E.M. Quantum Mechanics: Non-Relativistic Theory, 3rd ed.; Butterworth-Heinemann: Burlington, MA, USA, 2003. [Google Scholar]
Segment Prediction with the Row-Centered Data | Segment Prediction with the Dipole-Adjusted Data | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
LDA | 1 | 2 | 3 | 4 | 5 | 6 | LDA | 1 | 2 | 3 | 4 | 5 | 6 |
1 | 5337 | 39 | 26 | 0 | 0 | 378 | 1 | 10121 | 2 | 11 | 0 | 41 | 0 |
2 | 117 | 4371 | 115 | 63 | 7 | 352 | 2 | 99 | 2906 | 216 | 11 | 167 | 17 |
3 | 107 | 199 | 4783 | 10 | 109 | 78 | 3 | 845 | 11 | 4335 | 2 | 67 | 0 |
4 | 0 | 452 | 78 | 3267 | 70 | 0 | 4 | 0 | 32 | 230 | 1823 | 18 | 37 |
5 | 0 | 105 | 140 | 91 | 3562 | 0 | 5 | 325 | 20 | 312 | 0 | 3082 | 7 |
6 | 1418 | 1004 | 101 | 2 | 0 | 683 | 6 | 3 | 51 | 160 | 26 | 150 | 1937 |
Hit-rate, % | 81.3 | Hit-rate, % | 89.4 | ||||||||||
Logit-ROC | 1 | 2 | 3 | 4 | 5 | 6 | Logit-ROC | 1 | 2 | 3 | 4 | 5 | 6 |
1 | 5056 | 134 | 238 | 0 | 0 | 352 | 1 | 9812 | 76 | 126 | 0 | 160 | 1 |
2 | 96 | 3487 | 104 | 586 | 70 | 682 | 2 | 4 | 3240 | 62 | 16 | 65 | 29 |
3 | 45 | 184 | 4748 | 4 | 230 | 75 | 3 | 232 | 178 | 4262 | 252 | 278 | 58 |
4 | 0 | 288 | 79 | 3366 | 100 | 34 | 4 | 0 | 64 | 132 | 1895 | 15 | 34 |
5 | 0 | 73 | 178 | 82 | 3565 | 0 | 5 | 99 | 102 | 133 | 7 | 3140 | 265 |
6 | 1177 | 854 | 281 | 42 | 5 | 849 | 6 | 0 | 66 | 57 | 29 | 181 | 1994 |
Hit-rate, % | 77.9 | Hit-rate, % | 89.9 | ||||||||||
MNL | 1 | 2 | 3 | 4 | 5 | 6 | MNL | 1 | 2 | 3 | 4 | 5 | 6 |
1 | 4814 | 143 | 169 | 1 | 0 | 653 | 1 | 10124 | 2 | 21 | 0 | 28 | 0 |
2 | 162 | 3738 | 164 | 477 | 90 | 394 | 2 | 14 | 3203 | 82 | 35 | 54 | 28 |
3 | 112 | 131 | 4716 | 61 | 239 | 27 | 3 | 158 | 33 | 4888 | 61 | 103 | 17 |
4 | 0 | 561 | 107 | 3063 | 132 | 4 | 4 | 0 | 40 | 52 | 2009 | 1 | 38 |
5 | 0 | 53 | 211 | 81 | 3553 | 0 | 5 | 50 | 38 | 85 | 12 | 3442 | 119 |
6 | 1173 | 963 | 242 | 38 | 8 | 784 | 6 | 0 | 33 | 50 | 55 | 43 | 2146 |
Hit-rate, % | 76.4 | Hit-rate, % | 95.4 |
© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Lipovetsky, S.; Conklin, M. Decreasing Respondent Heterogeneity by Likert Scales Adjustment via Multipoles. Stats 2018, 1, 169-175. https://doi.org/10.3390/stats1010012
Lipovetsky S, Conklin M. Decreasing Respondent Heterogeneity by Likert Scales Adjustment via Multipoles. Stats. 2018; 1(1):169-175. https://doi.org/10.3390/stats1010012
Chicago/Turabian StyleLipovetsky, Stan, and Michael Conklin. 2018. "Decreasing Respondent Heterogeneity by Likert Scales Adjustment via Multipoles" Stats 1, no. 1: 169-175. https://doi.org/10.3390/stats1010012