Limitations of Additive Conjoint Scaling Procedures: Detecting Nonadditivity When Additivity Is Known to Be Violated

Abstract

Two sets of three-outcome gambles were construc ted to vary factorially along the factors Amount to Lose, Amount to Win, Probability of Losing, and Probability of Winning. Single stimulus ratings of attractiveness and risk were obtained for each of the constructed gambles from 19 subjects. In addi tion, paired comparison strength of preference and difference in risk judgments were obtained for a subset of these gambles. Two additive conjoint scal ing procedures, Carroll's (1972) MDPREF and Johnson's (1975) NMRG, were used to generate pre dicted paired comparison preference and risk judg ments from the single stimulus ratings for each subject. These predictions were then compared with the observed paired comparison judgments. Results indicated that although the goodness-of-fit mea sures associated with each of the scaling models in dicated that the subject's data were being fit very well by the additive models, additivity among the payoff and probability factors was clearly violated. A procedure for detecting nonadditivity is outlined and illustrated with the data. The limitations of using these additive conjoint scaling procedures as predictive techniques when additivity is violated are shown and their implications are discussed.