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Discrete choice modeling (DCM) is nowadays one of the main tools for estimating preferences among multiple alternatives widely used in applied economics and psychology, transportation and management, social and marketing research. Estimation of the utility parameters and choice probabilities is usually performed via the multinomial-logit (MNL) modeling originated by McFadden (1973, 1981) and further developed in numerous works (McFadden and Richter, 1990; Louviere, Hensher, & Swait, 2000; Train, 2003; Orme, 2010). One of the most popular techniques based on DCM is the Best-Worst Scaling (BWS), also called Maximum Difference (MaxDiff) which is a modern marketing research approach to evaluation probability of choice among many compared items. This method has been proposed by Louviere (1991, 1993), and developed in various works (Marley and Louviere, 2005; Bacon, Lenk, Seryakova, & Veccia, 2007, 2008). BWS can be seen as extension of scaling by Thurstone and Bradley-Terry models from paired comparisons (Thurstone, 1927; Bradley and Terry, 1952; David, 1988; Lipovetsky and Conklin, 2004; Lipovetsky, 2008) to simultaneous comparisons among three and more items in a balanced plan where each item is represented approximately the same number of times across the sample, and the respondents indicate which items are the best and worst, with following estimation of choice probabilities in MNL by various available software or analytically (Louviere, Flynn, & Marley, 2015; Marley, Flynn, & Louviere, 2008; Marley, Islam, & Hawkins, 2016; Lipovetsky and Conklin, 2014a, 2014b; Lipovetsky, 2018).
Maxdiff has become a very popular method in marketing research, and for more adequate practical applications it can be adjusted to the real-world situations of absence of some compared items from the shelfs during consumers’ shopping. It can occur by various reasons, and the aim of this paper is to tune general MaxDiff choice probabilities to a scenario of the items unavailability. Additionally, to it we consider a possible increase of the items preference due to the influence of the word-of-the-mouth, e.g., via spread and impact of opinions in social networks. The presented approaches are innovative and were not yet been described in the literature on best-worst scaling or applied in MaxDiff prioritization.
In order to perform such adjustments, we consider the following techniques. In the recent work by Blanchet, Gallego, & Goyal (2016) the choice models of several kinds were described as Markov chains (e.g., Bellman, 1960) with states corresponding to the items and transition probabilities defined by the preferences among the items, and this approach was applied to assortment optimization. As assumed in that work, if a product/item is not available, a customer substitutes the most preferred by another item, and such sequential transitions can be described by Markov chain model, where arriving probability equals the MNL choice values, while transitional probabilities are defined as the inflated probabilities re-estimated by exclusion of each item from their set.