**Title:**Analyzing AHP-matrices by Regression

**Authors: **Pertti Laininen and Raimo P. Hämäläinen

**Status: **European Journal of Operational Research, 148, 2003, pp. 514-524.

**Keywords:** Analytical Hierarchy Process, eigenvector method, regression, robust regression, multiple comparisons, simultaneous comparisons.

In the analytical hierarchy process (AHP) the decision maker makes comparisons between pairs of attributes and alternatives. In real applications the comparisons are subject to judgemental errors. Many AHP-matrices reported in the literature are found to be such that the logarithm of the comparison ratio can be sufficiently modelled by a normal distribution with 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 given by the 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. A dissimilarity matrix approach is presented for the statistical simultaneous comparisons of the AHP-weights. The results are illustrated by simulation experiments.