Extending Multidimensional Thresholding to Include Categorical Attributes

Multidimensional thresholding (MDT) elicits preferences at the individual level but assumes attribute-level ranges are infinitely divisible, restricting the inclusion of categorical attributes in the design. This article presents a novel framework for including categorical attributes in MDT and outlines a design process to include a single categorical attribute alongside continuous attributes.

The proposed approach involves 4 steps: (1) rank categories of the categorical attribute and use point allocation to score each category, (2) rank the relative importance of scale swings across all attributes, (3) undertake a series of thresholding exercises among continuous attributes, and (4) trade the scale swing in the categorical attribute against partial swings in the continuous attribute ranked 1 place higher. Computational experiments were used to determine the precision with which preference weights for a categorical attribute can be obtained.

The results suggest that a categorical attribute can be included in MDT with modest loss of precision, on average, compared with continuous attributes. The loss of precision is a function of the importance of the scale swing of the categorical attribute, with greater imprecision when the categorical attribute is ranked first. The number of continuous attributes and the number of choice tasks had little influence on precision.

Including a categorical attribute in MDT is feasible and extends the potential application of MDT, particularly if the swing in the categorical attribute is not expected to be the most important attribute for most participants. Future research should test the method in relevant applications.