MaxDiff Priority Estimations with and without HB-MNL
Abstract
Maximum difference (MaxDiff) is a discrete choice modeling approach widely used in marketing research for finding utilities and preference probabilities among multiple alternatives. It can be seen as an extension of the paired comparison in Thurstone and Bradley–Terry techniques for the simultaneous presenting of three, four or more items to respondents. A respondent identifies the best and the worst ones, so the remaining are deemed intermediate by preference alternatives. Estimation of individual utilities is usually performed in a hierarchical Bayesian (HB)-multinomial-logit (MNL) modeling. MNL model can be reduced to a logit model by the data composed of two specially constructed design matrices of the prevalence from the best and the worst sides. The composed data can be of a large size which makes logistic modeling less precise and very consuming in computer time and memory. This paper describes how the results for utilities and choice probabilities can be obtained from the raw data, and instead of HB methods the empirical Bayes techniques can be applied. This approach enriches MaxDiff and is useful for estimations on large data sets. The results of analytical approach are compared with HB-MNL and several other techniques.
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