Abstract
Statistical and decision-making techniques for solving prioritization problems are described. These approaches include the analytic hierarchy process (AHP) of the multi-attribute decision-making and its extension to the statistical modeling and testing, scaling techniques of priority estimation, maximum difference models, identification of key drivers in regression, and other methods. The described techniques have been widely applied and proved to be helpful for identification and ordering the most important items in solving various marketing research and decision-making problems.
Introduction
In the previous reviews (Lipovetsky, 2021a,b,c, 2022a,b), modifications and regularizations of linear, logistic, and multinomial regressions, multivariate statistical analysis, and special methods of data modeling, classification, and prediction were described. The current work discusses methods developed for decision-making in solving prioritization problems, e.g., comparing the alternatives and finding which items or variables are the most important players or drivers for the problem or process in the project under consideration. One of these approaches is the Analytic Hierarchy Process (AHP) of the multi-attribute decision-making and group decision-making, with extensions to statistical modeling and testing. Other approaches include the scaling techniques of preference evaluation in Thurstone, Bradley-Terry, maximum difference models, and also identification of key drivers in regression and supplementary methods. These techniques were checked in solving various marketing research problems and proved to be useful for identification and ordering the most important items for managerial decisions.
Analytic Hierarchy Process
The Analytic Hierarchy Process (AHP) and its generalization to the Analytic Network Process (ANP) were originated by Thomas Saaty and developed in multiple works. These methods are based on the pairwise comparison of the alternatives by their quotients elicited from the respondents by different criteria. The local priority vectors are found as the main eigenvectors which can be combined into the global vector of preferences. Properties of the priority vectors in these methods are described in (Lipovetsky, 2010, 2011a,b, 2013a). Combined estimation of the global priority vector simultaneously by all criteria and alternatives is considered in (Lipovetsky, 1996). Fuzzy AHP with
Scaling techniques
Scaling methods are based on pairwise comparison of items by the found frequencies of their preferences. The priorities among the items are estimated by different models, including Thurstone, Bradley-Terry, the best-worst or maximum difference techniques. Thurstone scaling in different approaches is considered in (Lipovetsky & Conklin, 2004a; Lipovetsky, 2007a,b, 2013b). Bradley–Terry choice probability evaluations in several techniques, including the maximum likelihood, eigenproblem solution, and Chapman-Kolmogorov equations for the steady-state probabilities are described in (Lipovetsky, 2008a). Comparison of the AHP with Thurstone scaling, Bradley-Terry-Luce, and Markov stochastic modeling is performed in (Lipovetsky & Conklin, 2001, 2003).
The Best-Worst Scaling (BWS), also known as the Maximum Difference (MaxDiff) was originated by Jordan Louviere and has become one of the main models of choice and prioritization among multiple alternatives. It is an extension of the pair comparison techniques for the simultaneous presentation of several items to respondents who identify the best and the worst items, with estimation of utilities performed by multinomial-logit modeling. Several methods of solving such problems are considered in (Lipovetsky & Conklin, 2014, 2015b; Lipovetsky, 2021c). Solutions based on the complex utility in discrete choice modeling, and BWS prioritization method based on D. Kahneman’s System 1 approach to the process of decision making are given in the works (Lipovetsky, 2018, 2019). Combined application of the AHP and BWS scaling approaches for big data is discussed in (Lipovetsky, 2016).
Game theory, key driver analysis, and other techniques
Combinatorial technique of the total unduplicated reach and frequency (TURF) is well-known in marketing research for finding preferences among many products. For a better estimate of the consumer preferences, a tool from the cooperative game theory, namely, the Shapley value, was suggested in (Conklin & Lipovetsky, 2005; Lipovetsky, 2022b). Possibilities of antagonistic and bargaining games for optimal decisions were discussed in (Lipovetsky, 2007c). In marketing research on customer satisfaction and loyalty analyses for detecting optimal marketing strategy, the Shapley value and Kano theory were implemented for identification of key drivers (Conklin et al., 2004). Considering predictors in regression modeling as players in a game theory permits to find the variables contribution and to formulate Shapley value regression which identifies and orders the key drivers of the model (Lipovetsky, 2021a). Decision making methods based on the variables’ importance in the regression, discriminant, logistic, and Bayesian sensitivity-specificity analyses are studied in (Lipovetsky & Conklin, 2004b, 2015c, 2020).
Some other techniques of decision making include multi-mode eigenproblem for data analysis (Lipovetsky & Tishler, 1994; Lipovetsky, 1994, 2022a), deciding on circular priorities (Burnovski & Lipovetsky, 1995), and the aesthetic preference (Lipovetsky & Lootsma, 2000). Comparison among different patterns of priority estimation is given in (Lipovetsky, 2008b).
Conclusion
A wide range of methods for decision making and prioritization is presented. The described techniques have been developed and employed in real marketing research projects. They can be useful in socio-economics and other fields as well.