Constrained part-worth estimation in conjoint analysis using the self-explicated utility model *

Different structures of across-attribute constraints upon individual-level part-worth estimates in conjoint analysis are derived from self-explicated attribute level evaluations and self-explicated attribute importances. Their appeal is that, although constraints are based upon the (weighted) linearcompensatory self-explicated utility model, part-worths can also reflect alternative models, such as the lexicographic model. Furthermore, they only assume ordinal measures of evaluation and importance. An algorithm, based on alternating least squares and iterative majorization, is provided for computing part-worth estimates subject to the constraints. In an application, part-worths that are subject to across-attribute constraints improve upon the predictive validity of unconstrained part-worths, part-worths subject to within-attribute constraints derived from self-explicated attribute level evaluations, and self-explicated part-worths. Predictive validity is measured by Pearson correlations, percentages of first choice hits, and first choice shares. Comparing different structures of across-attribute constraints, it seems that attribute level evaluation scores that are commensurable across attributes should be weighted before summing them across attributes to obtain overall utilities. In addition, it seems that, despite fine-grained rating scales, algorithms that force equal ratings to have precisely the same value under monotone transformations do less well than those that permit greater variability in the transformation. In the final section, we discuss our results and give suggestions for further research.

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