Comments on Conjoint Analysis with Partial Profiles

At the outset, I am pleased to comment on the 2004 article by Bradlow, Hu, and Ho (BHH), who tackle an important problem in conjoint analysis research. Their model hypothesizes that subjects learn from the patterns of levels of nonmissing attributes in partial profiles and impute values to the missing values in a particular (current) profile by using the patterns of attributes in the candidate profile and in the previously presented profiles. Although BHH’s terminology is somewhat unusual, they divide the total set of attributes selected for the conjoint study into three subsets: (1) attributes that have no missing information in all the profiles presented (i.e., omnipresent [OM]), (2) attributes that contain no missing information in the current profile (presence manipulated [PM] and nonmissing or nonmissing PM), and (3) attributes that contain missing information (PM and missing or missing PM). The difficulty with this classification is that the set of attributes designated as OM is also manipulated in the conjoint study and can contain missing information. Bradlow, Hu, and Ho’s method of imputation yields probabilities that the missing attribute takes one of two levels and is a generalization of the extant methods. The prior methods are ignoring the missing attribute problem, inferring the missing attribute level from the most recently presented profile, and averaging the value for the missing attribute with the values for the attribute in the previously presented profiles. The method of BHH generalizes such notions and uses the information on the attribute with the missing level (missing PM), the information on other attributes with missing information (nonmissing PM), and the information on attributes that have no missing information in the profiles (OM). The authors rely on a construct of experience count to impute probabilities for the two levels in their generalized model. Bradlow, Hu, and Ho employ a Bayesian framework to estimate the several parameters of the proposed model and show that the proposed learning models perform better than the extant approaches in handling missing levels in the empirical example. My subsequent comments pertain to four issues: (1) other ways to conceptualize the problem; (2) managerial aspects of the procedure that BHH suggest; (3) the role of price in solving the problem; and (4) a data collection procedure for partial profiles, which may obviate the imputation problem. In addition, I raise a few minor points with respect to the article.