Abstract
Multi-objective decision making often requires the comparison of qualitatively different entities. For example, a forest owner has to assess the aesthetic and recreation values of the forest in addition to the income from selling wood. Pairwise comparisons can be used to elicit relative preferences concerning such entities. Eigenvalue techniques introduced by Saaty (1977) are one way to analyse pairwise comparisons data. A weak point of the original methodology has been that it does not allow a statistical analysis of uncertainties in judgements. The eigenvalue technique also requires that all entities have been compared with each other. In many applications, this is impracticable because of the large number of pairs. The number of judges can also be large, and there can be missing observations. Moreover, it is frequently of interest to analyse how different attributes of the entities, or different attributes of the judges, influence the relative preference. In this paper, we first review our previous work with an alternative methodology based on regression analysis. Then, we show how explanatory variables can be incorporated. The construction of the design matrix is detailed and the interpretation of the results is discussed.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alho, IM. and Kangas, J. 1997. Analysing uncertainties in experts’ opinions of forest plan performance. Forest Science 43: 521–528.
Alho, J.M., Kangas, J. and Kolehmainen, O. 1996. Uncertainty in the expert predictions of the ecological consequences of forest plans. Applied Statistics 45: 1–14.
Basak, I. 1989. Estimation of the multi-criteria worths of the alternatives in a hierarchical structure of comparisons. Communications in Statistics, Theory and Methods 18: 3719–3738.
Basak, I. 1990. Testing for the rank ordering of the priorities of the alternatives in Saaty’s ratio-scale method. European Journal of Operations Research 48: 148–152.
Basak, I. 1991. Inference in pairwise comparison experiments based on ratio scales. Journal of Mathematical Psychology 35: 80–91.
Box, G.E.P. and Tiao G. C. 1973. Bayesian Inference in Statistical Analysis. Wiley, New York, NY.
Budescu, D.V., Zwick, R. and Rapoport A. 1986. A comparison of the eigenvalue method and the geometric mean procedure for ratio scaling. Applied Psychological Measurement 10: 69–78.
Carriere, J. and Finster, M. 1992. Statistical theory for the ratio model of paired comparisons. Journal of Mathematical Psychology 36: 450–460.
Crawford, G. and Williams, C. 1985. A note on the analysis of subjective judgement matrices. Journal of Mathematical Psychology 29: 387–405.
De Jong, P. 1984. A statistical approach to Saaty’s scaling method for priorities. Journal of Mathematical Psychology 28: 467–478.
Dittrich, R., Hatzinger, R. and Katzenbeisser W. 1998. Modelling the effect of subject-specific covariates in paired comparison studies with an application to university rankings. Applied Statistics 47: 511–525.
Genest, C. and Rivest, L.-P. 1994. A statistical look at Saaty’s method of estimating pairwise preferences expressed on a ratio scale. Journal of Mathematical Psychology 38: 477–496.
Kangas, J., Alho, J., Kolehmainen, O. and Mononen, O. 1998. Analysing consistency of experts’ judgements — case of assessing forest biodiversity. Forest Science 44: 610–617.
Kangas, J., Karsikko, J., Laasonen, L. and Pukkala, T. 1993. A method for estimating habitat suitability on the basis of expertise. Silva Fennica 27: 259–268.
Leskinen, P. and Kangas, J. 1998. Analysing uncertainties of interval judgement data in multiple criteria evaluation of forest plans. Silva Fennica 32: 363–372.
Linstone, H.A. and TUROFF M. (eds.) 1975. The Delphi Method: Techniques and Applications. Addison-Wesley, Reading, MA.
Lootsma, F.A. 1993. Scale sensitivity in the multiplicative AHP and SMART. Journal of Multi-Criteria Decision Analysis 2: 87–110.
Mcfadden, D. 1974. Conditional logit analysis of qualitative choice behaviour. Pages 105–142 in Zarembka, P. (ed.) Frontiers in Econometrics. Academic Press, New York, NY.
Mcfadden, D. 1981. Econometric models of probabilistic choice. Pages 198–272 in Manski, C.F. and McFadden, D. (eds.) Structural Analysis of Discrete Data with Econometric Applications. MIT Press, Cambridge MA.
Pukelsheim, F. 1993. Optimal Design of Experiments. Wiley, New York, NY.
Saaty, T.L. 1977. A scaling method for priorities in hierarchical structures. Journal of Mathematical Psychology 15: 234–281.
Saaty, T.L. and Vargas, F. 1984. Comparison of Eigenvalue, logarithmic least squares and least squares methods in estimating ratios. Mathematical Modelling 5: 309–324.
Salo, A.A. and Hämäläinen, R.P. 1997. On the measurement of preferences in the analytic hierarchy process. Journal of Multi-Criteria Decision Analysis 6: 309–319.
Tahvanainen L., Tyrväinen L., Ihalainen M., Vuorela N. and Kolehmainen O. 2001. Forest management and public perceptions — visual versus verbal information. Landscape and Urban Planning 53: 53–70.
Wolfram, S. 1996. Mathematica Book 3rd ed. Addison-Wesley, New York.
Zahedi, F. 1986. A simulation study of estimation methods in the analytic hierarchy process. Socio-Economic Planning Sciences 20: 347–354.
Zhang, S.-S. and Genest, C. 1996. Etude d’un test de confirmation des priorités dans le cadre du procédé d’analyse hiérarchique. Revue de Statistique Appliquée 44: 81–103.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Alho, J.M., Kolehmainen, O., Leskinen, P. (2001). Regression Methods for Pairwise Comparison Data. In: Schmoldt, D.L., Kangas, J., Mendoza, G.A., Pesonen, M. (eds) The Analytic Hierarchy Process in Natural Resource and Environmental Decision Making. Managing Forest Ecosystems, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9799-9_15
Download citation
DOI: https://doi.org/10.1007/978-94-015-9799-9_15
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5735-8
Online ISBN: 978-94-015-9799-9
eBook Packages: Springer Book Archive