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Abstract:
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Maximum Difference (MaxDiff), also known as Best-Worst Scaling, is a discrete choice technique widely known in marketing research for finding utilities and probabilities among multiple items. It is an extension of paired comparisons in Thurstone and Bradley-Terry techniques for the simultaneous presenting of three or more items to respondents. A respondent identifies the best and the worst ones, and estimation of individual utilities can be performed in Hierarchical Bayesian (HB) multinomial-logit (MNL) modeling. MNL can be presented via 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 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 the empirical Bayes techniques can be applied. This method enriches MaxDiff and is useful for estimations for big data. The results of analytical approach are compared with HB-MNL and several other techniques.
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