A generalized ordinal finite mixture regression model for market segmentation

Abstract Model-based market segmentation analyses often involve an ordinal dependent variable as ordinal responses are frequently collected in marketing research. In the Bayesian segmentation literature, there are models for an interval- or ratio-scaled dependent variable but there is not any general model for an ordinal dependent variable. In this manuscript, the authors propose a new Bayesian procedure to simultaneously perform segmentation and ordinal regression with variable selection within each derived segment. The procedure is robust to outliers and it also provides an option to include concomitant variables that allows the simultaneous profiling of the derived segments. The authors demonstrate that the practice of treating ordinal responses as interval- or ratio-scales to apply existing Bayesian segmentation procedures can lead to very misleading results and conclusions. Through simulation studies, the authors show that the proposed procedure outperforms several benchmark Bayesian segmentation models in parameter recovery, segment retention, and segment membership prediction for such data. Finally, they provide a commercial business customer satisfaction empirical application to illustrate the usefulness of the proposed model.

[1]  C. Mallows,et al.  A Method for Comparing Two Hierarchical Clusterings , 1983 .

[2]  D. V. van Dyk,et al.  Partially Collapsed Gibbs Samplers , 2008 .

[3]  John Roberts,et al.  From academic research to marketing practice: Exploring the marketing science value chain , 2014, How to Get Published in the Best Marketing Journals.

[4]  Wayne S. DeSarbo,et al.  Model-Based Segmentation Featuring Simultaneous Segment-Level Variable Selection , 2012 .

[5]  Ajay Jasra,et al.  Markov Chain Monte Carlo Methods and the Label Switching Problem in Bayesian Mixture Modeling , 2005 .

[6]  S. Frühwirth-Schnatter Estimating Marginal Likelihoods for Mixture and Markov Switching Models Using Bridge Sampling Techniques , 2004 .

[7]  Michel Wedel,et al.  Concomitant Variable Latent Class Models for Conjoint Analysis , 1994 .

[8]  Ernst Wit,et al.  Probabilistic relabelling strategies for the label switching problem in Bayesian mixture models , 2010, Stat. Comput..

[9]  T. J. Mitchell,et al.  Bayesian Variable Selection in Linear Regression , 1988 .

[10]  Irwin Guttman,et al.  Conversion of ordinal attitudinal scales: An inferential Bayesian approach , 2012 .

[11]  Miguel A. Juárez,et al.  Model-Based Clustering of Non-Gaussian Panel Data Based on Skew-t Distributions , 2010 .

[12]  J. S. Rao,et al.  Spike and slab variable selection: Frequentist and Bayesian strategies , 2005, math/0505633.

[13]  David S. Leslie,et al.  A tutorial on bridge sampling , 2017, Journal of mathematical psychology.

[14]  A. Pettitt,et al.  Marginal likelihood estimation via power posteriors , 2008 .

[15]  D. Madigan,et al.  A method for simultaneous variable selection and outlier identification in linear regression , 1996 .

[16]  Michel Wedel,et al.  Leveraging Missing Ratings to Improve Online Recommendation Systems , 2006 .

[17]  Simon J. Blanchard,et al.  Implementing Managerial Constraints in Model-Based Segmentation: Extensions of Kim, Fong, and DeSarbo (2012) with an Application to Heterogeneous Perceptions of Service Quality , 2013 .

[18]  S. Frühwirth-Schnatter,et al.  Bayesian inference for finite mixtures of univariate and multivariate skew-normal and skew-t distributions. , 2010, Biostatistics.

[19]  Stef van Buuren,et al.  MICE: Multivariate Imputation by Chained Equations in R , 2011 .

[20]  Greg M. Allenby,et al.  The Dimensionality of Customer Satisfaction Survey Responses and Implications for Driver Analysis , 2013, Mark. Sci..

[21]  Geoffrey J. McLachlan,et al.  Robust mixture modelling using the t distribution , 2000, Stat. Comput..

[22]  C. Biernacki,et al.  Degeneracy in the maximum likelihood estimation of univariate Gaussian mixtures with EM , 2003 .

[23]  Giovanni Montana,et al.  A Bayesian mixture of lasso regressions with t-errors , 2014, Comput. Stat. Data Anal..

[24]  S. Chib,et al.  Bayesian analysis of binary and polychotomous response data , 1993 .

[25]  Mary Kathryn Cowles,et al.  Accelerating Monte Carlo Markov chain convergence for cumulative-link generalized linear models , 1996, Stat. Comput..

[26]  Xiao-Li Meng,et al.  SIMULATING RATIOS OF NORMALIZING CONSTANTS VIA A SIMPLE IDENTITY: A THEORETICAL EXPLORATION , 1996 .

[27]  George B. Macready,et al.  Concomitant-Variable Latent-Class Models , 1988 .

[28]  Chun Yu,et al.  Robust mixture regression using the t-distribution , 2014, Comput. Stat. Data Anal..

[29]  Rick L. Andrews,et al.  Retention of latent segments in regression-based marketing models , 2003 .

[30]  B. Weijters,et al.  The effect of rating scale format on response styles: the number of response categories and response catgory labels , 2010 .

[31]  B. Lindsay,et al.  Bayesian Mixture Labeling by Highest Posterior Density , 2009 .

[32]  C. Hennig Breakdown points for maximum likelihood estimators of location–scale mixtures , 2004, math/0410073.

[33]  E. George,et al.  Journal of the American Statistical Association is currently published by American Statistical Association. , 2007 .