This paper analyzes customer product-choice behavior based on the recency and frequency of each customer's page views on e-commerce sites. Recently, we devised an optimization model for estimating product-choice probabilities that satisfy monotonicity, convexity, and concavity constraints with respect to recency and frequency. This shape-restricted model delivered high predictive performance even when there were few training samples. However, typical e-commerce sites deal in many different varieties of products, so the predictive performance of the model can be further improved by integration of such product heterogeneity. For this purpose, we develop a novel latent-class shape-restricted model for estimating product-choice probabilities for each latent class of products. We also give a tailored expectation-maximization algorithm for parameter estimation. Computational results demonstrate that higher predictive performance is achieved with our latent-class model than with the previous shape-restricted model and common latent-class logistic regression.
Latent-class (or mixture) regression @cite_14 @cite_1 is a traditional form of latent-class modeling @cite_2 @cite_36 . It is aimed at classifying a sample into latent classes and simultaneously forming a regression model within these classes. There are two main algorithms for maximum likelihood estimation of latent-class regression models: the Newton--Raphson algorithm @cite_28 and the EM algorithm @cite_35 @cite_30 . While these models are frequently used in marketing and business research to represent consumer heterogeneity, we apply latent-class modeling to the classification of a wide variety of products on e-commerce sites. For this purpose, we develop a latent-class model for estimating the product-choice probabilities that satisfy monotonicity, convexity, and concavity constraints. To the best of our knowledge, none of the existing studies have considered a latent-class model under such a variety of shape restrictions. We also demonstrate that our latent-class model is superior to latent-class logistic regression @cite_31 @cite_26 @cite_20 in terms of predictive performance based on clickstream data.
@cite_30 @cite_35 @cite_14 @cite_26 @cite_36 @cite_28 @cite_1 @cite_2 @cite_31 @cite_20
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The first unified account of the theory, methodology, and applications of the EM algorithm and its extensionsSince its inception in 1977, the Expectation-Maximization (EM) algorithm has been the subject of intense scrutiny, dozens of applications, numerous extensions, and thousands of publications. The algorithm and its extensions are now standard tools applied to incomplete data problems in virtually every field in which statistical methods are used. Until now, however, no single source offered a complete and unified treatment of the subject.The EM Algorithm and Extensions describes the formulation of the EM algorithm, details its methodology, discusses its implementation, and illustrates applications in many statistical contexts. Employing numerous examples, Geoffrey McLachlan and Thriyambakam Krishnan examine applications both in evidently incomplete data situations-where data are missing, distributions are truncated, or observations are censored or grouped-and in a broad variety of situations in which incompleteness is neither natural nor evident. They point out the algorithm's shortcomings and explain how these are addressed in the various extensions.Areas of application discussed include: Regression Medical imaging Categorical data analysis Finite mixture analysis Factor analysis Robust statistical modeling Variance-components estimation Survival analysis Repeated-measures designs For theoreticians, practitioners, and graduate students in statistics as well as researchers in the social and physical sciences, The EM Algorithm and Extensions opens the door to the tremendous potential of this remarkably versatile statistical tool. Despite the importance of data mining techniques to customer relationship management (CRM), there is a lack of a comprehensive literature review and a classification scheme for it. This is the first identifiable academic literature review of the application of data mining techniques to CRM. It provides an academic database of literature between the period of 2000-2006 covering 24 journals and proposes a classification scheme to classify the articles. Nine hundred articles were identified and reviewed for their direct relevance to applying data mining techniques to CRM. Eighty-seven articles were subsequently selected, reviewed and classified. Each of the 87 selected papers was categorized on four CRM dimensions (Customer Identification, Customer Attraction, Customer Retention and Customer Development) and seven data mining functions (Association, Classification, Clustering, Forecasting, Regression, Sequence Discovery and Visualization). Papers were further classified into nine sub-categories of CRM elements under different data mining techniques based on the major focus of each paper. The review and classification process was independently verified. Findings of this paper indicate that the research area of customer retention received most research attention. Of these, most are related to one-to-one marketing and loyalty programs respectively. On the other hand, classification and association models are the two commonly used models for data mining in CRM. Our analysis provides a roadmap to guide future research and facilitate knowledge accumulation and creation concerning the application of data mining techniques in CRM. Preface Jacques A. Hagenaars and Allan L. McCutcheon Part I. Introduction: 1. Latent class analysis Leo A. Goodman 2. Basic concepts and procedures in singe- and multiple-group latent class analysis Allan L. McCutcheon Part II. Classification and Measurement: 3. Latent class cluster analysis Jeroen K. Vermunt and Jay Magidson 4. Some examples of latent budget analysis and its extensions Peter G. M. van der Heijden, L. Andries van der Ark and Ab Mooijaart 5. Ordering the classes Marcel Croon 6. Comparison and choice Ulf Bockenholt 7. Three-parameter linear logistic latent class analysis Anton K. Formann and Thomas Kohlmann Part III. 8. Use of categorical and continuous covariates in latent class analysis C. Mitchell Dayton and George B. Macready 9. Directed loglinear modelling with latent variables Jacques A. Hagenaars 10. Latent class models for longitudinal data Linda M. Collins and Brian P. Flaherty 11. Latent markov chains Rolf Langeheine and Frank van de Pol Part IV. Unobserved heterogeneity and non-response: 12. A latent class approach to measuring the fit of a statistical model Tamas Rudas 13. Mixture regression models Michael Wedel and Wayne S. DeSarbo 14. A general latent class approach to unobserved heterogeneity in the analysis of event history data Jeroen K. Vermunt 15. Latent class models for contingency tables with missing data Christopher Winship, Robert D. Mare and John Robert Warren Appendices Index. In the present paper the linear logistic extension of latent class analysis is described. Thereby it is assumed that the item latent probabilities as well as the class sizes can be attributed to some explanatory variables. The basic equations of the model state the decomposition of the log-odds of the item latent probabilities and of the class sizes into weighted sums of basic parameters representing the effects of the predictor variables. Further, the maximum likelihood equations for these effect parameters and statistical tests for goodness-of-fit are given. Finally, an example illustrates the practical application of the model and the interpretation of the model parameters. Marketing scholars commonly characterize market structure by studying the patterns of substitution implied by brand switching. Though the approach is useful, it typically ignores the destabilizing role of marketing variables (e.g., price) in switching behavior. The authors propose a flexible choice model that partitions the market into consumer segments differing in both brand preference and price sensitivity. The result is a unified description of market structure that links the pattern of brand switching to the magnitudes of own- and cross-price elasticities. The approach is applied in a study of competition between national brands and private labels in one product category.