Duncan K. H. Fong

A Two-Stage Bayesian Model Selection Strategy for Supersaturated Designs

In early stages of experimentation, one often has many candidate factors of which only few have significant influence on the response. Supersaturated designs can offer important advantages. However, standard regression techniques of fitting a prediction line using all candidate variables fail to analyze data from such designs. Stepwise regression may be used but has drawbacks as reported in the literature. A two-stage Bayesian model selection strategy, able to keep all possible models under consideration while providing a level of robustness akin to Bayesian analyses incorporating noninformative priors, is proposed. The strategy is demonstrated on a well-known dataset and compared to competing methods via simulation.

Analysis of a dual sourcing inventory model with normal unit demand and Erlang mixture lead times

Abstract We consider an inventory model where two suppliers are used concurrently to replenish one stock item. The unit demand is assumed to be normally distributed and the supplier lead times are mixtures of Erlang distributions. The lead time distributions need not be identical. This paper presents closed form expressions to evaluate the means and variances of the effective lead times, the probability of no stockout at a fixed reorder level and the potential lost sales. When the lead times are not identical, at a comparable service level, it is possible to achieve a lower average stock level by using unequal order splits. Several data sets are used in the paper to illustrate the method.

Managing Trade-in Programs Based on Product Characteristics and Customer Heterogeneity in Business-to-Business Markets

Trade-in programs are offered extensively in business-to-business (B2B) markets. The success of such programs depends on well-designed and executed trade-in policies as well as accurate prediction of return flow to support operational decisions. Motivated by a real problem facing a high-tech company, this paper develops methods to segment customers and forecast product returns based on return merchandise authorization information. Noisy, yet proven to be valuable, returned quantity signals are adjusted by taking product characteristics and customer heterogeneity into account, and the resulting forecast outperforms two benchmark strategies that represent the high-tech companys current practice and a widely adopted method in the literature, respectively. In addition, our methods can serve as tools for companies to uncover the root causes of return merchandise authorization discrepancy, monitor and analyze customer behavior, design segment-specific trade-in policies, and evaluate the effectiveness and efficiency of trade-in programs on a continuous basis.

A Bayesian approach to the spatial representation of market structure from consumer choice data

This paper is concerned with the spatial representation of market structure calibrated on actual or intended choice data. Previous models developed for that purpose accommodate consumer heterogeneity by estimating parameters for each consumer, typically using the method of maximum likelihood. This approach to heterogeneity avoids assuming any particular distribution of the individual level parameters across the sample, but leads to problems related to the consistency of the estimates, sufficient degrees of freedom, and the validity of asymptotic standard errors and test statistics. Of greater concern is the assumption of independence of the choice observations within the same individual. This assumption is necessary in a maximum likelihood (MLE) framework to make the estimation computationally feasible. However, the marketing and psychology literature (cf. Manrai, 1995; Tversky and Simonson, 1993; Kim et al., forth coming) demonstrates that dependencies among choice alternatives may exist, and negligence to take such covariance into account may lead to inconsistent estimates, reduced predictive validity, and incorrect managerial action. We develop a new multidimensional scaling (MDS) model that estimates spatial market structures from pick-any/J choice data, provides for individual level parameters, and allows for correlations among the choice alternatives across individuals. We provide a Bayesian estimation method that overcomes the traditional problems associated with estimating models with such correlated alternatives. We provide an application to pick-any/J data for various brands of portable telephones. In a comparative analysis, we show that the proposed model outperforms one in which the utilities are assumed to be uncorrelated across choice alternatives.

Revisiting Customer Value Analysis in a Heterogeneous Market

Purpose – Customer value has recently become a primary focus among many strategy researchers and practitioners as an essential element of a firms competitive strategy. Many firms are engaged in some form of customer value analysis (CVA), which involves a structural analysis of the antecedent factors of perceived value (i.e. perceived quality and perceived price) to assess their relative importance in the perceptions of their buyers. Previous CVA research has focused upon using aggregate market or market segment level analyses. The purpose of this paper is to expose the limitations of implementing CVA on either an aggregate or market segment level basis, and propose an alternative individual level approach.Design/methodology/approach – The paper develops an extended hierarchical Bayesian approach for cross‐sectional data with one observation per response unit, which allows for estimation at the individual firm level to make CVA more useful. This paper demonstrates the utility of the proposed Bayesian meth...

Model-Based Segmentation Featuring Simultaneous Segment-Level Variable Selection

The authors propose a new Bayesian latent structure regression model with variable selection to solve various commonly encountered marketing problems related to market segmentation and heterogeneity. The proposed procedure simultaneously performs segmentation and regression analysis within the derived segments, in addition to determining the optimal subset of independent variables per derived segment. The authors present comparative analyses contrasting the performance of the proposed methodology against standard latent class regression and traditional Bayesian finite mixture regression. They demonstrate that their proposed Bayesian model compares favorably with these traditional benchmark models. They then present an actual commercial customer satisfaction study performed for an electric utility company in the southeastern United States, in which they examine the heterogeneous drivers of perceived quality. Finally, they discuss limitations of the research and provide several directions for further research.

A Bayesian Vector Multidimensional Scaling Procedure for the Analysis of Ordered Preference Data

Multidimensional scaling (MDS) comprises a family of geometric models for the multidimensional representation of data and a corresponding set of methods for fitting such models to actual data. In this paper, we develop a new Bayesian vector MDS model to analyze ordered successive categories preference/dominance data commonly collected in many social science and business studies. A joint spatial representation of the row and column elements of the input data matrix is provided in a reduced dimensionality such that the geometric relationship of the row and column elements renders insight into the utility structure underlying the data. Unlike classical deterministic MDS procedures, the Bayesian method includes a probability based criterion to determine the number of dimensions of the derived joint space map and provides posterior interval as well as point estimates for parameters of interest. Also, our procedure models the raw integer successive categories data which ameliorates the need of any data preprocessing as required for many metric MDS procedures. Furthermore, the proposed Bayesian procedure allows external information in the form of an intractable posterior distribution derived from a related dataset to be incorporated as a prior in deriving the spatial representation of the preference data. An actual commercial application dealing with consumers’ intentions to buy new luxury sport utility vehicles are presented to illustrate the proposed methodology. Favorable comparisons are made with more traditional MDS approaches.

Forecasting the Penetration of a New Product--A Bayesian Approach

We adopt a Bayesian approach to forecast the penetration of a new product into a market. We incorporate prior information from an existing product and/or management judgments into the data analysis. The penetration curve is assumed to be a nondecreasing function of time and may be under shape constraints. Markov-chain Monte Carlo methods are proposed and used to compute the Bayesian forecasts. An example on forecasting the penetration of color television using the information from black-and-white television is provided. The models considered can also be used to address the general bioassay and reliability stress-testing problems.

Ranking and estimation of related means in the presence of a covariate : a Bayesian approach

Abstract Choosing the largest of several means can be a demanding problem, especially in the presence of a covariate. A hierarchical Bayesian approach to ranking and selection, as well as estimation of related means in the presence of a covariate, is considered. For the multiple slopes model we compute, in addition to the posterior means and standard deviations of the parameters, the posterior probabilities that each mean, at a given value of the covariate, is the largest. The vector of posterior probabilities thus obtained provides an easily understandable answer to the selection problem. Although calculation of the posterior probabilities may involve four-dimensional numerical integration in the difficult unbalanced design and unknown variance case, an efficient Monte Carlo method of evaluation has been developed and is given in the article. By reanalyzing a well-known data set on the breaking strength and thickness of starch films, we illustrate how our Bayesian approach produces meaningful conclusions...

A hierarchical bayesian procedure for two-mode cluster analysis

This manuscript introduces a new Bayesian finite mixture methodology for the joint clustering of row and column stimuli/objects associated with two-mode asymmetric proximity, dominance, or profile data. That is, common clusters are derived which partition both the row and column stimuli/objects simultaneously into the same derived set of clusters. In this manner, interrelationships between both sets of entities (rows and columns) are easily ascertained. We describe the technical details of the proposed two-mode clustering methodology including its Bayesian mixture formulation and a Bayes factor heuristic for model selection. We present a modest Monte Carlo analysis to investigate the performance of the proposed Bayesian two-mode clustering procedure with respect to synthetically created data whose structure and parameters are known. Next, a consumer psychology application is provided examining physician pharmaceutical prescription behavior for various brands of prescription drugs in the neuroscience health market. We conclude by discussing several fertile areas for future research.