Analyzing AHP-matrices by regression

• Published in: European journal of operational research Vol. 148; no. 3; pp. 514 - 524
• Main Authors: Laininen, Pertti, Hämäläinen, Raimo P.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.08.2003; Elsevier; Elsevier Sequoia S.A
• Series: European Journal of Operational Research
• Subjects: Analytical hierarchy process; Comparative analysis; Decision making; Eigenvector method; Hierarchies; Mathematical models; Multiple comparisons; Regression; Regression analysis; Robust regression; Simultaneous comparisons; Studies; Regression; Analytical hierarchy process; Eigenvector method; Robust regression; Simultaneous comparisons; Multiple comparisons
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/S0377-2217(02)00430-7

In the analytic hierarchy process (AHP) the decision maker makes comparisons between pairs of attributes or alternatives. In real applications the comparisons are subject to judgmental errors. Many AHP-matrices reported in the literature are found to be such that the logarithm of the comparison ratio can be sufficiently well modeled by a normal distribution with a constant variance. On the basis of this model we present the formulae for the evaluation of the standard deviations of the estimates of the AHP-weights obtained by regression analysis. In order to eliminate the effect of an outlier in the comparison ratios a robust regression technique is elaborated, and compared with the eigenvector method and the logarithmic least squares regression. A dissimilarity matrix approach is presented for the statistical simultaneous comparisons of the AHP-weights. The results are illustrated by simulation experiments.