data augmentation for latent variables in marketing

i DATA AUGMENTATION FOR LATENT VARIABLES IN MARKETING DISSERTATION Presented in Partial Fulfillment of Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Ling-Jing Kao, B.A., M.S. * * * * * The Ohio State University 2006 Dissertation Committee: Dr. Greg M. Allenby, Adviser Dr. H. Rao Unnava Dr. Thomas Otter Approved by ___________________________________ Adviser Business Administration Graduate Program ii ii ABSTRACT Latent variable models are an important aspect of consumer research whenever the determinants of behavior are an important aspect of study. The purpose of this thesis is to develop a new method of error augmentation to deal with latent variable models of heterogeneous, non-linear consumer behavior for two issues commonly encountered in marketing. The first issue relates to a consumer’s purchase decision driven by a time- varying latent behavior process. The second issue relates to consumer preferences affected by multiple unobserved factors. This thesis comprises three essays. The first issue is addressed in the first and the second essays, and the second issue is addressed in the third essay. The new method of error augmentation is applied to estimate models proposed in this thesis. The new method of error augmentation is needed because, in the proposed models, the observed discrete choices do not have a direct correspondence to the errors. The proposed models would be difficult to estimate without the new approach. The first essay develops a new method of error augmentation for state-space models of economic behavior where the observed behavior is related to a latent variable whose temporal variation is described by a state equation. The proposed state-space model is applied to analyze a consumer’s purchase and resignation decisions in a membership club. iii The result indicates that increasing inter-arrival time between shipments can lead to longer customer longevity and greater sales. The second essay investigates an alternative method of modeling customer inter- purchase times. A state-space model is proposed to investigate the possibility to model inter-purchase times as an independent variable. The results indicate that the proposed state-space model can accurately describe customer behavior when the specification of the state equation is plausible for the data. In the third essay, a demand model is developed to address three issues in choice modeling. The first issue relates to the effects of multiple treatments for data collected in a pre-post study. The second issue relates to a marketing action of line extension that is widely adopted in marketing practice. The last issue relates to consumer decisions of brand-pack and no-choice for consumer packaged goods at the level of stock-keeping unit. Data from a leading consumer packaged goods company are used to study changes in consumer preferences and sensitivities in a simulated shopping environment. The results indicate that consumers’ reactions to media are very heterogeneous. Media can make some consumers have extreme preferences, and make preferences of some consumers become more homogeneous. This thesis contributes marketing literature by developing a new method of error augmentation for latent variable models that cannot be estimated by standard approaches. The new method of error augmentation is illustrated by three different marketing applications in this thesis. The state-space model proposed in the first and the second essays can be extended to study consumer learning or consumer searching behavior. The iv demand model proposed in the third essay can be extended to study consumer preference changes in multiple stages. v Dedicated to my parents Tsung-Ching Kao and Yu-Hsiu Hsu vi ACKNOWLEDGMENTS I wish to express sincere thanks to my advisor, Dr. Greg M. Allenby, for the time and effort he put into my doctoral education. You are an outstanding scholar. You have been a responsible facilitator, gatekeeper, and protector in my graduate study as well as a wonderful friend in my life. I have learned tremendously from you. I also want to thank you for the challenges and frustrations you give to me in research. These challenges and frustrations make me think a lot about my life and myself. It makes me be tougher and stronger in the road of pursuing my dream. Without these challenges and frustrations, I will still be a child spoiled by people around me. This training process of doctoral education has installed me a dedication to rigor in research. Without your mentoring, I could not have succeeded in my doctoral journey. My appreciation is also extended to the other members of my dissertation committee, Dr. H. Rao Unnava and Dr. Thomas Otter. I want to thank them for providing guidance and support during my dissertation research and during my time at Ohio State. I thank the other marketing faculty at Ohio State for their enduring support to my doctoral education. I want to thank current and past Ph.D. students particularly Jaehwan Kim, Yancy Edwards, Tim Gilbrid, Sandeep Chandukala, and Jeff Dotson for their support and friendship. vii I also want to thank Cindy Coykendale and Lisa Gang for providing invaluable help on all administrative details. I want to thank Tim Renken and June Hahn for providing data for my dissertation. My dissertation cannot be completed on time without the help form Curtis Smith in the department of computing and communication services. I want to thank you for setting up R environment in Unix servers for me. I could not have started or completed my doctoral studied without the support of my family. My parents Tsung-Ching Kao and Yu-Hsiu Hsu always stand by for me with strong faith while I pursued my dreams and for being patient with, believing in, and walking with me. I also appreciate my brothers and sister, Yu-Sui, Kuo-Ting, and Hsin- Chih, for their overwhelming concern and encouragement. Finally, I would like to give my special thank to Dr. Chih-Chou Chiu in National Taipei University of Technology for his invaluable friendship and encouragement along the way. I thank you to stand by for me and listen to me while I was in depression. You have tremendous influence on my decision of pursuing doctoral degree. Your humanity and personality have inspired me to contribute myself to our society and people in the world. viii VITA November 29, 1974 Born – Taipei, Taiwan 1997 B. A., Business Administration Fu-Jen Catholic University, Taipei, Taiwan 2001 M. S., Statistics Texas A&M University, College Station, TX, USA 2001-present Graduate Teaching and Research Associate, The Ohio State University FIELDS OF STUDY Major Field: Business Administration Specialization: Marketing ix TABLE OF CONTENTS Page Abstract ii Dedication v Acknowledgements vi Vita viii List of Tables xi List of Figures xii Chapters: 1. Introduction 1 2. Data augmentation and latent variable models 6 3. Essay 1: Estimating State-Space Models of Economic Behavior: A Hierarchical Bayes Approach 12 3.1 Introduction 12 3.2 State-space models for economic behavior 14 3.2.1 Model estimation 17 3.2.2 Model identification 24 3.3.3 Simulation study 26 3.3 Direct marketing application 27 3.4 Estimation results 30 3.5 Discussion 32 3.6 Conclusion remarks 33 4. Essay 2: A State-Space Model of Purchase Timing for Direct Marketing 46 4.1 Introduction 46 4.2 Model development 48 4.3 Data and model specification 51 4.3.1 State-space model specification 52 4.3.2 Inter-purchase time model specification 53 4.4 Parameter estimates and predictive results 54 4.5 Discussion 56 5. Essay 3: Modeling Media Interactions and Preference Change in Panel Data 64 5.1 Introduction 64 [...]... supply company engaged in business-to-business selling in the United States The second dataset is from a direct marketing company specializing in cosmetics, shampoo, toothpaste and food supplements selling in Taiwan The performance of the proposed model is compared to a traditional inter-purchase time model, with results supporting the proposed model in the business-tocustomer dataset which comprises... data augmentation and choice model with latent variables is discussed, and a new variant of data augmentation is introduced In Chapter 3, the first essay “State-Space Model for Economics Behavior” is included The second essay “A State-Space Model of Purchase Timing for Direct Marketing is presented in Chapter 4 Chapter 5 presents the third essay “Modeling Media Interactions and Preference Change in. .. represent stochastic variation of latent inventory The result indicates that the proposed method provides a flexible framework for analyzing economic models of behavior in marketing The second essay investigates an alternative method of modeling customer interpurchase times In traditional models of direct marketing, inter-purchase times are treated 3 as dependent variables whose model parameters are... represented by a linear compensatory model For example, household inventories non-linearly affect brand preference and purchase timing in the presence of diminishing marginal returns When inventories are not observed, complications arise in estimating demand models because the data are serially dependent unless restrictive assumptions are made about specific inventory levels at each point in time Likewise,... preferences for goods can exhibit temporal changes when inventions such as learning take place Complications arise in tracking latent preference changes at the individual-level because of the relatively short panel lengths present in marketing application The purpose of this thesis is to develop methods of dealing with heterogeneous, non-linear models of behavior for problems commonly encountered in marketing. .. customers In this essay, models that treat purchase timing as an independent variable are explored A latent inventory model is developed according to the assumption that purchases are triggered by inventories below a threshold value The specification of this model is different from the model for the membership data in the first essay, and is explored using two direct marketing datasets The first dataset... directly The method of data augmentation suggests introducing a latent variable z to estimate p(θ|y,z) By integrating out z from p(θ|y,z), the posterior distribution p(θ|y) can be obtained The implementation of data augmentation method is straight forward in a Bayesian framework since Bayesian views all the unknown variables as parameters The estimation can be processed by drawing z and θ from their... auto-correlated errors The method of data augmentation involves the introduction of latent variables into a hierarchical model to simplify computation The augmented variable for the binomial probit model is a latent continuous variable, which, if positive, indicates that the binomial realization is equal to one: ⎧1 if zt ≥ 0 yt = ⎨ ⎩0 if zt < 0 (3.5) zt = α + ε t , ε t ~ N (0,1), for t = 1, 2, ,T (3.6) The associated... by investigating changes in consumer preference and sensitivities in a 4 simulated shopping environment The purpose of this study is to explore the effect of brand extension, the impact of media on the likelihood of purchasing a new brand, and changes in consumer preferences and sensitivities to marketing stimuli The reminder of this thesis is organized as follows In Chapter 2, the literature of data. .. estimating the full covariance matrix as if there are no absent dimensions Different from the application of error augmentation in marketing literature, the method of error augmentation developed in this dissertation is implemented with the procedure of checking the consistency of observed decisions and the decision rule that gives arise of the observed decision The latent variables- the state variables in . for the membership data in the first essay, and is explored using two direct marketing datasets. The first dataset is from an office supply company engaged in business-to-business selling in. i DATA AUGMENTATION FOR LATENT VARIABLES IN MARKETING DISSERTATION Presented in Partial Fulfillment of Requirements for the Degree Doctor of Philosophy in the Graduate School. represented by a linear compensatory model. For example, household inventories non-linearly affect brand preference and purchase timing in the presence of diminishing marginal returns. When inventories