Using a Bayesian approach to quantify scale compatibility bias

This paper proposes a new analytical framework to quantify and correct for scale compatibility bias in the assessment of trade-off weights in multiattribute value analysis. The procedure is demonstrated with an application to a fisheries management problem. Trade-off judgments are elicited from a group of fisheries experts with management responsibility in the Lake Erie basin. Then we use a Bayesian method to compute posterior probability distributions of attribute weights. In computing the Bayesian weights, our measurement model assumes that the weight ratios produced by each respondent's judgments are subject to random error and an unknown scale compatibility bias. Ratios are log-transformed and analyzed by a Bayesian linear model with a noninformative prior distribution. Posterior distributions are then developed for the weights and the bias. We estimate the compatibility bias for each person and, in most cases, it is found to be large and in the predicted direction, suggesting the importance of its consideration in deriving trade-off weights. In addition, the Bayesian framework is shown to be useful for quantifying the value of additional information about multiattribute weights. Finally, a simple heuristic procedure for assessing the weights appears to be effective in eliminating the bias.