Probabilistic Preferences Composition in the Classification of Apparel Retail Stores

Abstract

This paper employs the probabilistic composition of preferences to classify stores by their operational efficiency. Probabilistic composition of preferences is a multicriteria analysis methodology based on the transformation of assessments by multiple attributes into probabilities of choice. The numerical initial measurements provide estimates for location parameters of probability distributions that are compared to measure the preferences. The probabilities of choice according to each attribute separately are aggregated according to probabilistic composition rules. A classification of two sets of stores into five classes is performed.

MaxDiff Choice Probability Estimations on Aggregate and Individual Level

“…Variousmethodsofbusinessanalyticsarewidelyappliednowadaysforsolvingpracticaldecisionmakingproblemsandfindingutilitiesandchoiceprobabilitiesamongmultiplealternatives(e.g., Wang, 2014;Ribeiro,Meza,&Sant'Anna,2015;Ye&Li,2015;Huie,2016;Firat,Akan,Ersoy,Gök,&Ünal 2017).Amongthem,oneoftheoftenusedapproachistheso-calledMaximumDifference(MaxDiff) method, also known as Best-Worst Scaling (BWS), which is a modern prioritization technique introducedbyJ. Louviere(1991),anddevelopedfurtherinnumerousworks(e.g.,Marley&Louviere, 2005Lusk&Briggeman,2009;Flynn,2010;Scarpa,Notaro,Louviere,&Rafaelli,2011;Louviere, Lings,Islam,Gudergan,&Flynn,2013;YooandDoiron,2013;Hawkins,Marley,Heathcote,Flynn, Louviere,&Brown,2014).MaxDiffcanbeconsideredasanextensionofscalingtechniquesbased onpairedcomparisoninThurstoneandBradley-Terrymodels (Thurstone,1927;BradleyandTerry, 1952;David,1988;Lipovetsky2007,2008.Thediscretechoicemodel(DCM)isimplementedin MaxDiffforestimationoftheutilityparametersandchoiceprobabilitiesinmultinomial-logit(MNL) approach (McFadden,1973(McFadden, ,1981McFaddenandRichter,1990;Louviere,Hensher,&Swait,2000;Train,2003;Orme,2010;Lipovetsky,2011Lipovetsky, ,2014Lipovetsky, ,2015.InMaxDiffrespondentsanswerwhichof severalitems(usually,about4or5ofthose)presentedineachofseveralsubsets(couldbeabouta dozenormoreofthem)isthebestoneandwhichistheworstone.Thetasksaregiveninabalanced designwhereeachitemisshownacrossallrespondentsasimilarnumberoftimes.BWSestimationof individualutilitiesisusuallyperformedinthehierarchicalBayesianMNLprocedureandtheresults areaggregatedbyrespondentstoobtainthechoiceprobabilitiesforeachofthecompareditems,but otherapproacheshavebeenalsodeveloped.…”