Conjoint Analysis: A Comparative Analysis of Specification Tests for the Utility Function

The focus of this paper is on determining appropriate combination rules for idiosyncratic ordinal utility functions in conjoint measurement. An axiomatic diagnosis is used which is based on explanatory criteria rather than goodness-of-fit or predictive criteria. Experimental results are presented comparing the selection of combination rules based on axiomatic tests and empirical fitting procedures for additive (x + y + z) and distributive (x(y + z)) combinations of three factors. A number of conflicting diagnoses result from the simultaneous applications of axiomatic tests and goodness-of-fit criteria, suggesting the importance of testing certain necessary conditions for simple polynomial combination rules, such as additive and distributive rules. Because the axiomatic approach is effective in rejecting inappropriate functional forms, we argue that it should complement rather than replace the empirical fitting diagnostic approaches.