Quantitive models in marketing research

This page intentionally left blank Quantitative Models in Marketing Research Recent advances in data collection and data storage techniques enable marketing researchers to study the characteristics of a large range of transactions and purchases, in particular the effects of household-specific characteristics and marketing-mix variables This book presents the most important and practically relevant quantitative models for marketing research Each model is presented in detail with a self-contained discussion, which includes: a demonstration of the mechanics of the model, empirical analysis, real-world examples, and interpretation of results and findings The reader of the book will learn how to apply the techniques, as well as understand the latest methodological developments in the academic literature Pathways are offered in the book for students and practitioners with differing statistical and mathematical skill levels, although a basic knowledge of elementary numerical techniques is assumed PHILIP HANS FRANSES is Professor of Applied Econometrics affiliated with the Econometric Institute and Professor of Marketing Research affiliated with the Department of Marketing and Organization, both at Erasmus University Rotterdam He has written successful textbooks in time series analysis RICHARD PAAP is Postdoctoral Researcher with the Rotterdam Institute for Business Economic Studies at Erasmus University Rotterdam His research interests cover applied (macro-)econometrics, Bayesian statistics, time series analysis, and marketing research Quantitative Models in Marketing Research Philip Hans Franses and Richard Paap           The Pitt Building, Trumpington Street, Cambridge, United Kingdom    The Edinburgh Building, Cambridge CB2 2RU, UK 40 West 20th Street, New York, NY 10011-4211, USA 477 Williamstown Road, Port Melbourne, VIC 3207, Australia Ruiz de Alarcón 13, 28014 Madrid, Spain Dock House, The Waterfront, Cape Town 8001, South Africa http://www.cambridge.org © Philip Hans Franses and Richard Paap 2004 First published in printed format 2001 ISBN 0-511-03237-4 eBook (Adobe Reader) ISBN 0-521-80166-4 hardback Contents List of figures List of tables Preface Introduction and outline of the book 1.1 Introduction 1.1.1 On marketing research 1.1.2 Data 1.1.3 Models 1.2 Outline of the book 1.2.1 How to use this book 1.2.2 Outline of chapter contents page ix xi xiii 1 6 Features of marketing research data 2.1 Quantitative models 2.2 Marketing performance measures 2.2.1 A continuous variable 2.2.2 A binomial variable 2.2.3 An unordered multinomial variable 2.2.4 An ordered multinomial variable 2.2.5 A limited continuous variable 2.2.6 A duration variable 2.2.7 Summary 2.3 What we exclude from this book? 10 10 12 13 15 18 19 21 24 26 26 A continuous dependent variable 3.1 The standard Linear Regression model 3.2 Estimation 3.2.1 Estimation by Ordinary Least Squares 3.2.2 Estimation by Maximum Likelihood 29 29 34 34 35 v vi Contents 3.3 3.4 3.5 Diagnostics, model selection and forecasting 3.3.1 Diagnostics 3.3.2 Model selection 3.3.3 Forecasting Modeling sales Advanced topics 38 39 41 43 44 47 A binomial dependent variable 4.1 Representation and interpretation 4.1.1 Modeling a binomial dependent variable 4.1.2 The Logit and Probit models 4.1.3 Model interpretation 4.2 Estimation 4.2.1 The Logit model 4.2.2 The Probit model 4.2.3 Visualizing estimation results 4.3 Diagnostics, model selection and forecasting 4.3.1 Diagnostics 4.3.2 Model selection 4.3.3 Forecasting 4.4 Modeling the choice between two brands 4.5 Advanced topics 4.5.1 Modeling unobserved heterogeneity 4.5.2 Modeling dynamics 4.5.3 Sample selection issues 49 49 50 53 55 58 59 60 61 61 62 63 65 66 71 71 73 73 An unordered multinomial dependent variable 5.1 Representation and interpretation 5.1.1 The Multinomial and Conditional Logit models 5.1.2 The Multinomial Probit model 5.1.3 The Nested Logit model 5.2 Estimation 5.2.1 The Multinomial and Conditional Logit models 5.2.2 The Multinomial Probit model 5.2.3 The Nested Logit model 5.3 Diagnostics, model selection and forecasting 5.3.1 Diagnostics 5.3.2 Model selection 5.3.3 Forecasting 76 77 77 86 88 91 92 95 95 96 96 97 99 Contents 5.4 5.5 Modeling the choice between four brands Advanced topics 5.5.1 Modeling unobserved heterogeneity 5.5.2 Modeling dynamics 5.A EViews Code 5.A.1 The Multinomial Logit model 5.A.2 The Conditional Logit model 5.A.3 The Nested Logit model vii 101 107 107 108 109 110 110 111 An ordered multinomial dependent variable 6.1 Representation and interpretation 6.1.1 Modeling an ordered dependent variable 6.1.2 The Ordered Logit and Ordered Probit models 6.1.3 Model interpretation 6.2 Estimation 6.2.1 A general ordered regression model 6.2.2 The Ordered Logit and Probit models 6.2.3 Visualizing estimation results 6.3 Diagnostics, model selection and forecasting 6.3.1 Diagnostics 6.3.2 Model selection 6.3.3 Forecasting 6.4 Modeling risk profiles of individuals 6.5 Advanced topics 6.5.1 Related models for an ordered variable 6.5.2 Selective sampling 112 113 113 A limited dependent variable 7.1 Representation and interpretation 7.1.1 Truncated Regression model 7.1.2 Censored Regression model 7.2 Estimation 7.2.1 Truncated Regression model 7.2.2 Censored Regression model 7.3 Diagnostics, model selection and forecasting 7.3.1 Diagnostics 7.3.2 Model selection 7.3.3 Forecasting 7.4 Modeling donations to charity 7.5 Advanced Topics 133 134 134 137 142 142 144 147 147 149 150 151 155 116 117 118 118 121 122 122 123 124 125 125 129 130 130 viii Contents A duration dependent variable 8.1 Representation and interpretation 8.1.1 Accelerated Lifetime model 8.1.2 Proportional Hazard model 8.2 Estimation 8.2.1 Accelerated Lifetime model 8.2.2 Proportional Hazard model 8.3 Diagnostics, model selection and forecasting 8.3.1 Diagnostics 8.3.2 Model selection 8.3.3 Forecasting 8.4 Modeling interpurchase times 8.5 Advanced topics 8.A EViews code 8.A.1 Accelerated Lifetime model (Weibull distribution) 8.A.2 Proportional Hazard model (loglogistic distribution) 158 159 165 166 168 169 170 172 172 174 175 175 179 182 Appendix A.1 Overview of matrix algebra A.2 Overview of distributions A.3 Critical values 184 184 187 193 Bibliography Author index Subject index 196 202 204 182 183 is to see these as measuring the effect of xi on the choice for brand A relative to brand B The next step now concerns the specification of the distribution of "i 4.1.2 The Logit and Probit models The discussion up to now has left the distribution of "i unspecified In this subsection we will consider two commonly applied cumulative distribution functions So far we have considered only a single explanatory variable, and in particular examples below we will continue to so 54 Quantitative models in marketing research However, in the subsequent discussion we will generally assume the availability of K þ explanatory variables, where the first variable concerns the intercept As in chapter 3, we summarize these variables in the  ðK þ 1Þ vector Xi , and we summarize the K þ unknown parameters to K in a ðK þ 1Þ Â parameter vector The discussion in the previous subsection indicates that a model that correlates a binomial dependent variable with explanatory variables can be constructed as Pr½Yi ¼ 1jXi Š ¼ Pr½yÃi > 0jXi Š ¼ Pr½Xi þ "i > 0jXi Š ¼ Pr½"i > ÀXi jXi Š ¼ Pr½"i ð4:12Þ Xi jXi Š: The last line of this set of equations states that the probability of observing Yi ¼ given Xi is equal to the cumulative distribution function of "i , evaluated at Xi In shorthand notation, this is Pr½Yi ¼ 1jXi Š ¼ FðXi Þ; ð4:13Þ where FðXi Þ denotes the cumulative distribution function of "i evaluated in Xi For further use, we denote the corresponding density function evaluated in Xi as f ðXi Þ There are many possible choices for F, but in practice one usually considers either the normal or the logistic distribution function In the first case, that is ! Z Xi z2 pffiffiffiffiffiffi exp À dz; ð4:14Þ FðXi ... put forward in articles in, for example, Marketing Science, the Journal of Marketing Research, the Journal of Consumer Research and the International Journal of Research in Marketing For that... and marketing research Quantitative Models in Marketing Research Philip Hans Franses and Richard Paap           The Pitt Building, Trumpington...This page intentionally left blank Quantitative Models in Marketing Research Recent advances in data collection and data storage techniques enable marketing researchers to study the