Bayesia Lab Choice Modeling 1


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We present a new method and the associated workflow for estimating market shares of future products based exclusively on pre-introduction data, such as syndicated studies conducted prior to product launch. Our approach provides a highly practical, fast and economical alternative to conducting new primary research.

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Bayesia Lab Choice Modeling 1

  1. 1. Modeling Vehicle Choice and Simulating MarketShare with Bayesian NetworksA case study about predicting the U.S. market share of the Porsche Panamerausing the Bayesia Market SimulatorWhite Paper 2010/IIStefan Conrady, stefan.conrady@conradyscience.comDr. Lionel Jouffe, jouffe@bayesia.comDecember 18, 2010Conrady Applied Science, LLC - Bayesia’s North American Partner for Sales and Consulting
  2. 2. Simulating Market Share with the Bayesia Market SimulatorTable of ContentsModeling Vehicle Choice and Simulating Market Share with Bayesian Net-works Abstract/Executive Summary 1 Objective 1 About the Authors 2 Stefan Conrady 2 Lionel Jouffe 2 Acknowledgements 2 Introduction 2 Bayesian Networks for Choice Modeling 3 Case Study 4 Porsche Panamera 4 Common Forecasting Practices 6 Tutorial 6 Data Preparation 6 Consumer Research 6 Variable Selection 7 Set of Choice Alternatives 7 Filtered Values (Censored States) 7 Data Modeling 8 Data Import 8 Missing Values 9 Discretization 10 Variable Classes and Forbidden Arcs 12 Unsupervised Learning 13 Simulation 14 Product Scenario Baseline 14 Product Scenario Simulation 16 Substitution and Cannibalization 19 Market Scenario Simulation 20Conrady Applied Science, LLC - i
  3. 3. Simulating Market Share with the Bayesia Market Simulator Limitations 20 Outlook 20 Summary 21 Appendix 22 Utility-Based Choice Theory 22 Multinomial Logit Models 22 Stated Preference Data 23 Revealed Preference Data 23 NVES Variables 23 References 25 Contact Information 26 Conrady Applied Science, LLC 26 Bayesia SAS 26 Copyright 26Conrady Applied Science, LLC - ii
  4. 4. Simulating Market Share with the Bayesia Market Simulator This innovative approach is explained step-by-step in aModeling Vehicle Choice study about the introduction of the new Porsche Panam-and Simulating Market era in the U.S. market. The results con rm that market share simulation with Bayesian networks is feasible evenShare with Bayesian in niche markets that provide relatively few observa- tions.Networks We believe that making this method and the tools acces- sible to practitioners is an important contribution toAbstract/Executive Summary real-world marketing. We are con dent that for manyWe present a new method and the associated work ow companies this approach can yield a step-change in theirfor estimating market shares of future products based forecasting ability.exclusively on pre-introduction data, such as syndicatedstudies conducted prior to product launch. Our ap- Objectiveproach provides a highly practical, fast and economical This tutorial is intended for marketing practitioners, whoalternative to conducting new primary research. are exploring the use of Bayesian network for their work. The example in this tutorial is meant to illustrateWith Bayesian networks as the framework, and by em- the capabilities of BayesiaLab with a real-world caseploying the BayesiaLab and Bayesia Market Simulator study and actual consumer data. Beyond market re-software packages, this approach helps market research- searchers, analysts in many elds will hopefully nd theers and product planners to reliably perform market proposed methodology valuable and intuitive. In thisshare simulations on their desktop computers1 , which context, many of the technical steps are outlined in greatwould have been entirely inconceivable in the past. detail, such as data preparation and the network learn- Market Share Simulation Work ow with BayesiaLab and Bayesia Market Simulator Scenario Market Data from Survey De nition from Analyst Projection Market Model Simulation Modeling Bayesian Network Bayesia Market BayesiaLab Simulator Market Shares1 BayesiaLab and Bayesia Market Simulator can run on a wide range of operating systems, including Windows, OS X,Linux/Unix, etc.Conrady Applied Science, LLC - 1
  5. 5. Simulating Market Share with the Bayesia Market Simulatoring, as they are applicable to research with BayesiaLab in Bayesian networks. BayesiaLab enjoys broad acceptancegeneral, regardless of the domain. in academic communities as well as in business and in- dustry. The relevance of Bayesian networks, especially inThis paper is part of a series of tutorials, which are ex- the context of market research, is highlighted byploring a broad range of real-world applications of Bayesia’s strategic partnership with Procter & Gamble,Bayesian networks. who has deployed BayesiaLab globally since 2007.About the Authors Acknowledgements Strategic Vision, Inc.2 (SVI) has generously made theirStefan ConradyStefan Conrady is the co-founder and managing partner 2009 New Vehicle Experience Survey available as a dataof Conrady Applied Science, LLC, a privately held con- source for this case study. In this context, special thanks go to Alexander Edwards, President, Automotive Divi-sulting rm specializing in knowledge discovery andprobabilistic reasoning with Bayesian networks. In 2010, sion of Strategic Vision.Conrady Applied Science was appointed the authorized We would also like to thank Jeff Dotson3, John Fitzger-sales and consulting partner of Bayesia SAS for North ald4 and Frank Koppelman5 for their ongoing coachingAmerica. Stefan Conrady has many years of marketing, and their valuable comments on this paper. However, allproduct planning and market research experience with errors remain the responsibility of the authors.Mercedes-Benz, BMW Group, Rolls-Royce Motor Carsand Nissan. In the context of these management assign- Finally, Kenneth Train’s6 books and articles have beenments, Stefan has been based in Europe, North America very helpful over the years as we explored the eld ofand Asia. consumer choice modeling.Lionel Jouffe IntroductionDr. Lionel Jouffe is co-founder and CEO of France-based For the vast majority of businesses, market share is a keyBayesia SAS. Lionel Jouffe holds a Ph.D. in Computer performance indicator. Market share is used as a metricScience and has been working in the eld of Arti cial that allows comparing competitive performance inde-Intelligence since the early 1990s. He and his team have pendently from overall market size and its uctuations.been developing BayesiaLab since 1999 and it hasemerged as the leading software package for knowledge In the product planning process, the expected marketdiscovery, data mining and knowledge modeling using share is critical, along with the overall market forecast,2 www.strategicvision.com3 Assistant Professor of Marketing, Vanderbilt University, Owen Graduate School of Management.4 President, Fitzgerald Brunetti Productions, Inc., New York.5 Professor Emeritus, Professor Emeritus of Civil and Environmental Engineering, Robert R. McCormick School of En-gineering and Applied Science, Northwestern University.6 Adjunct Professor of Economics and Public Policy, University of California, Berkeley.Conrady Applied Science, LLC - 2
  6. 6. Simulating Market Share with the Bayesia Market Simulatoras together they de ne the sales volume expectation, “oracles” that allow us to “deliberately reason about thewhich, for obvious reasons, is a key element in most consequences of actions we have not yet taken.” 8business cases. Bayesian Networks for Choice ModelingAs a result, it is critical for decision makers to correctly Using Bayesian networks9 as the general framework forpredict the future market shares of products not yet de- modeling a domain or system has many advantages,veloped. The task of such market share forecasts typi- which Darwiche (2010) summarizes as follows:cally falls into marketing and market research depart-ments, who are mostly closely involved with understand- • “Bayesian networks provide a systematic and localizeding consumer behavior and, more speci cally, the method for structuring probabilistic informationproduct choices they make. about a situation into a coherent whole […]”If we fully understood the consumer’s decision making • “Many applications can be reduced to Bayesian net-process and observed all components of it, we could work inference, allowing one to to capitalize on Bayes-simply generate a deterministic model for predicting ian network algorithms instead of having to inventfuture consumer choices. However, we do not and it is specialized algorithms for each new application.”obvious that many elements contributing to a consumer’s Given the very attractive properties of Bayesian net-purchase decision are inherently unobservable. Despite works for representing a wide range of problem do-our limited comprehension of the true human choice mains, it seems appropriate applying them for choiceprocess, there are a number of tools that still allow mod- modeling as well. In particular, the BayesiaLab softwareeling consumer choice with what is observable, and ac- package has made it very convenient to automaticallycounting for what will remain unknowable. In this con- machine-learn fairly large and complex Bayesian net-text, and based on the seminal works of Nobel-laureate works from observational data.Daniel McFadden7, choice modeling has emerged as animportant tool in understanding and simulating con- Beyond the convenience and speed of estimating Bayes-sumer choice. ian networks with BayesiaLab, there are three fundamen- tal differences in modeling consumer choice with Bayes-Such choice models serve a representation of the “real ian networks compared to traditional discrete choiceworld” and thus become, what Judea Pearl likes to call models.107 Daniel McFadden received, jointly with James Heckman, the 2000 Nobel Memorial Prize in Economic Sciences;McFadden’s share of the prize was “for his development of theory and methods for analyzing discrete choice”.8 A recurring quote from Judea Pearl’s many lectures on causality.9 A Bayesian network is a graphical model that represents the joint probability distribution over a set of random vari-ables and their conditional dependencies via a directed acyclic graph (DAG). For example, a Bayesian network couldrepresent the probabilistic relationships between diseases and symptoms. Given symptoms, the network can be used tocompute the probabilities of the presence of various diseases. A very concise introduction to Bayesian networks can befound in Darwiche (2010).10 A very brief overview about utility-based choice models is provided in the appendix.Conrady Applied Science, LLC - 3
  7. 7. Simulating Market Share with the Bayesia Market Simulator1. Whereas utility-based choice models, such as multi- As a result we obtain a choice probability as a function nomial logit models (MNL), will “ atten” the vector of product and consumer attributes. of attribute utilities into a single scalar value, Bayes- In order to obtain a product’s projected market share, we ian networks do not inherently restrict all the di- then need to simulate choice probabilities across all mensions relating to choice. For example, learning a Bayesian network on observed vehicle choices might product scenarios and across all individuals in the popu- lation under study. For this speci c purpose Bayesia SAS reveal that fuel economy and vehicle price are sub- has developed the Bayesia Market Simulator, which uses ject to tradeoff, while safety is a nonnegotiable basic requirement for the consumer. Correctly recognizing the Bayesian networks generated by BayesiaLab. Both tools will play a central role in this case study. such dynamics are obviously critical for making predictions about future consumer choices. Case Study2. Bayesian networks are nonparametric and therefore To illustrate the entire market share estimation process do not require the speci cation of a functional form. with Bayesian networks, we have derived a case study No assumptions need to made regarding the form of from the U.S. auto industry. More speci cally, we will links between variables. Potentially nonlinear pat- model consumer choice behavior in the high-end vehicle terns are therefore not an issue for model estimation market based on 2009 survey data. This is an interesting or simulation. point in time, as it precedes the launch of the new Por- sche Panamera in model year 2010 (MY 2010), which3. Bayesian networks are inherently probabilistic and will be the focus of our study. as such there is no need to specify an error term. An error would be needed in a traditional choice model Porsche Panamera to make it non-deterministic.4. In BayesiaLab all computations are natively discrete and therefore no transformation functions, such as logit or probit, are needed. Given that we are deal- ing with discrete consumer choices, this all-discrete approach is an advantage.For our case study we use BayesiaLab 5.0 ProfessionalEdition to learn a Bayesian network from consumerchoices in the form of stated preference (SP) or revealed After the highly successful Cayenne, a four-door luxurypreference (RP) data.11 ,12 The learned Bayesian network SUV, the Panamera is Porsche’s second vehicle with fourallows us to compute the posterior probability distribu- doors. Clearly in uenced by the legendary 911’s styling,tion in each choice situation, including hypothetical the Panamera is offers sports-car looks and performanceproduct alternatives (and even hypothetical consumers). while comfortably accommodating four passengers. It11 The properties of Stated Preference (SP) and Revealed Preference (RP) data are explained in the appendix.12 Although we focus here exclusively on machine-learning consumer behavior, within the BayesiaLab framework wecan also utilize expert knowledge about consumer behavior. For instance, vehicle dealers and their salespeople will haveextensive knowledge about how consumer behave in the showroom. A special Knowledge Elicitation module inBayesiaLab can formally capture such expertise and build a new Bayesian network from it or augment an existing one.Knowledge Elicitation with BayesiaLab will be the subject of a separate tutorial to be published in the near future.Conrady Applied Science, LLC - 4
  8. 8. Simulating Market Share with the Bayesia Market Simulatorenters a segment with well-established contenders, such Beyond these traditional premium sedans, there are athe Mercedes-Benz S-Class13 , the BMW 7-series14 and number of less conventional products that one can as-the Audi A815, shown below in that order. sume to be in the Panamera’s competitive eld as well. The coupe-like Mercedes-Benz CLS16 would probably fall into this category. Finally, the new Panamera may draw customers away from Porsche’s own product offerings, such as the Cay- enne17 , an effect that is often referred to as “product substitution” or “product cannibalization.” It is not our intention to speculate about potential product interactions, but rather to attempt learning from13 MY 2010 shown14 MY 2009 shown15 MY 2009 shown16 MY 2010 shown17 MY 2009 shownConrady Applied Science, LLC - 5
  9. 9. Simulating Market Share with the Bayesia Market Simulatorrevealed consumer behavior in a very formal way with TutorialBayesian networks. In this tutorial we will explain each step from dataIn order not to prematurely restrict our consumer choice preparation to market share simulation using BayesiaLabset, we have de ned a broad set of competitors for our and Bayesia Market Simulator, according to the follow-purposes and included all non-domestic luxury vehicles18 ing outline:(including Light Trucks) priced above $75,000.19 1. Data preparation (external)What was certainly a very real task for Porsche’s product 2. BayesiaLab:planning team in recent years, i.e. predicting the Panam-era market share, now becomes the topic of our case a. Data importstudy and tutorial. Our objective is to predict what mar-ket share the Panamera will achieve without conducting b. Data modelingany new research, strictly using RP data from before the 3. Baseline product scenario generation (external)product launch. 4. Bayesia Market Simulator:Common Forecasting PracticesAlthough we have no knowledge of the speci c forecast- a. Network importing methods at Porsche, we know from industry experi-ence that volume and market share forecasts are often b. De nition of scenariosdetermined through a long series of negotiations20 be- c. Market share simulationtween stakeholders, typically with an optimistic market-ing group on one side and a skeptical CFO on the other. NotationWhile expert consensus may indeed be a reasonable heu-ristic for business planning, the lack of forecasting for- To clearly distinguish between natural language,malisms is often justi ed by saying that forecasting is at software-speci c functions and study-speci c variableleast as much art as it is science. names, the following notation is used:The authors believe strongly that there is great risk in • BayesiaLab and Bayesia Market Simulator functions,relying too heavily on “art”, which is inherently non- keywords, commands, etc., are shown in bold type.auditable, and have therefore been pursuing easily trac- • Variable/node names are capitalized and italicized.table, but scienti cally sound methods to support mana-gerial decision making, especially in the context of fore- Data Preparationcasting. With this in mind, this very formal and struc-tured forecasting exercise was consciously chosen as the Consumer Researchtopic of the tutorial. This tutorial utilizes the 2009 New Vehicle Experience Survey, a syndicated study conducted annually by Strate- gic Vision, Inc., which surveys new vehicle buyers in the18 We followed the SVI segmentation and included “Luxury Car”, “Premium Coupe”, “Premium Convertible/Roadster”and “Luxury Utility” in our selection.19 The $75,000 threshold was chosen as it marks the lower end of the Panamera price range.20 As an interesting aside, these negotiations are usually Markovian in nature, i.e. the starting point of today’s negotia-tion only depends on the outcome of the previous negotiation.Conrady Applied Science, LLC - 6
  10. 10. Simulating Market Share with the Bayesia Market SimulatorU.S. This study is widely used in the auto industry and it cles actual buyers did consider and which vehicles theyserves one of the primary market research tools. NVES disposed in the context of their most recent purchase.23contains over 1,000 variables and close to 200,000 re- As mentioned in the case study introduction, we includedspondent records. In large auto companies, hundreds of “Luxury Car”, “Premium Coupe”, “Premiumanalysts typically have access to NVES, most oftenthrough the mTAB interface provided by Productive Ac- Convertible/Roadster” and “Luxury Utility” 24 in the choice set and we further restricted it by excluding allcess, Inc. (PAI).21 domestic vehicles and vehicles priced below $75,000. ForVariable Selection this segment of assumed Panamera competitors we haveCompared to traditional statistical models, Bayesian approximately 1,200 unweighted observations in thenetworks require much less “care” in terms of variable 2009 NVES, which, on a weighted basis, re ect ap-selection, as overparameterization is generally not an proximately 25,000 vehicles purchased in 2009.issue. So, although we could easily start with all 1,000+ Filtered Values (Censored States)variables, for expositional clarity we will initially select Although in BayesiaLab we can be less rigorous regard-only about 50 variables22 from the following categories, ing the maximum number of variables, we still need towhich we assume to capture relevant characteristics ofboth the consumer and the product: be conscious of the information contained in them. For instance, we need to distinguish unobserved values1. Vehicle/product attributes, e.g. brand, segment, num- from non-existing values, although at rst glance both ber of cylinders, transmission, drive type, etc. appear to be “simple” missing values in the database.2. Consumer demographics, e.g. age, income, gender, etc. BayesiaLab has a unique feature that allows treating non-existing values as Filtered Values or Censored States.3. Vehicle-related consumer attitudes, e.g. “I want to look good when driving my vehicle”, “I want a basic, no-frills vehicle that does the job,” etc. To explain Filtered Values we need to resort to an auto- motive example from outside our speci c study. We as-Set of Choice Alternatives sume that we have two questions about trailer towing.Beyond variable selection, we must also de ne the set of We rst ask, “do you use your vehicle for towing?”, andchoice alternatives and assume which vehicles a potential then, “what is the towing weight?” If the response to thePanamera customer would consider. Not only that, but rst question is “no”, then a value for the second onewe also need to make sure that all choice alternatives for cannot exist, which in BayesiaLab’s nomenclature is athe Panamera’s choice alternatives are included. For in- Filtered Value or Censored State. We actually must notstance, if we included the Porsche Cayenne in the choice impute a value for towing weight in this case and insteadset, then the Mercedes-Benz M-Class and the BMW X5 Filtered Value code will indicate this special condition.should be included too, and so on. One might argue thatthe vehicle purchase might be an alternative to a kitchen On the other hand, a respondent may answer “yes”, butrenovation or the purchase of a boat. Expert knowledge then fail to provide a towing weight. In this case, a trueis clearly required at this point as to how far to expand value for the towing weight exists, but we cannot ob-the choice set. Furthermore, SVI’s NVES can also help us serve it. Here it is entirely appropriate to impute a miss-in this regard as it contains questions about what vehi-21 www.paiwhq.com22 A list of all variables used is given in the appendix. It should be noted that even 50 variables would create a majorcomputational challenge with MNL models.23 Martin Krzywinski’s visualization tool, Circos, is highly recommended for the interpretation of cross-shopping behav-ior: According to SVI’s segment de nition.Conrady Applied Science, LLC - 7
  11. 11. Simulating Market Share with the Bayesia Market Simulatoring value, as we will explain as part of the Data Importprocedure.To indicate Filtered Values to BayesiaLab, we will needto apply a study-speci c logic and recode the relevantvariables in the original database. Most statistical soft-ware package have a set of functions for this kind oftask.For example, in STATISTICA this can be done with theRecode function. The table displayed in the Data Import wizard shows the individual variables as columns and the respondent re- cords as rows. There are a number of options available, such as for Sampling. However, this is not necessary in our example given the relatively small size of the data- base. Clicking the Next button prompts a data type analysis, which provides BayesiaLab’s best guess regarding the data type of each variable.Alternatively, this recoding logic can also be expressed Furthermore, the Information box provides a brief sum-with the following pseudo code: mary regarding the number of records, the number of missing values, ltered states, etc.IF towing=yes THEN towing weight=unchangedIF towing=no THEN towing weight=FV (Filtered Value)A simple Excel function will achieve the same and it isassumed that the reader can implement this without fur-ther guidance.Although Filtered Values are very important in manyresearch contexts, hence the emphasis here, our casestudy does not require using them.Data ModelingData ImportTo start the analysis with BayesiaLab, we rst import the For this example, we will need to override the defaultdatabase, which needs to be formatted as a CSV le.25 data type for the Unique Identi er variable, as eachWith Data>Open Data Source>Text File, we start the value is a nominal record identi er rather than a numeri-Data Import wizard, which immediately provides a cal scale value. We can change the data type by highlight-preview of the data le. ing the Unique Identi er column and clicking the Row25 CSV stands for “comma-separated values”, a common format for text-based data les. As an alternative to this im-port format, BayesiaLab offers a JDBC connection, which is practical when accessing large databases on servers.Conrady Applied Science, LLC - 8
  12. 12. Simulating Market Share with the Bayesia Market SimulatorIdenti er check box, which changes the color of the of discrete distributions, means-imputation typically alsoUnique Identi er column to beige. introduces a bias. There are other, better techniques, which typically demand signi cant computational effortAlthough it is not imperative to maintain a Row Identi- and thus often turn out like a labor-intensive standalone er, and we could instead assign the Not Distributed project rather than being just a preparatory step.status to the Unique Identi er variable, it can be quitehelpful for nding individual respondent records at a Without going into too much detail at this point,later point in the analysis. BayesiaLab can estimate all missing values given the learned network structure using the Expectation Maxi-As the respondent records in the NVES survey are mization (EM) algorithm. As a result, we obtain a com-weighted, we need to select the Weight by clicking on the plete database without “making things up.” In tradi-Combined Base Weight variable, which will turn the tional statistics, the equivalent would be to say that nei-column green. ther the mean nor the variance of the variables is af- fected by the imputation process. Continuing in our data import process, the next screen provides options as to how to treat the missing values. Clicking the small upside-down triangle next to the vari- able names brings up a window with key statistics of the selected variable, in this case Age Bracket.Missing ValuesIn the context of data import, it is important to point outhow missing values are treated in BayesiaLab. The na-tive, automatic processing of missing values reveals aparticular strength of BayesiaLab.In traditional statistical analysis, the analyst has tochoose from a number of methods to handle missing The very basic functions of ltering, i.e. case-wise dele-values in a database, but unfortunately many of them tion, and mean/modal value imputation are available.have serious drawbacks. Perhaps the most common However, at this point, we can take advantage ofmethod is case-wise deletion, which simply excludes re- BayesiaLab’s advanced missing values processing algo-cords that contain any missing values. Casually speaking, rithms. We will select Dynamic Completion, which willthis means throwing away lots of good data (the non- continuously “ ll in” and “update” the missing valuesmissing values) along with the bad (the missing values). according to the conditional distribution of the variable,Another method is means-imputation, by which any as de ned by the current structure of the networks.missing value is lled in with the variable’s mean. Inevi- However, as our network is not yet connected and hencetably, this reduces the variance of the variable and thus does not have a structure, BayesiaLab will draw from thehas an impact on its summary statistics, which is clearlyundesirable considering the intended analysis. In the caseConrady Applied Science, LLC - 9
  13. 13. Simulating Market Share with the Bayesia Market Simulatormarginal distribution of each variable to “tentatively”establish placeholder values for each missing value.A screenshot from STATISTICA, where we have donemost of the preprocessing, shows the marginal distribu-tion of the Age Bracket variable in the form of ahistogram.26 By clicking on the Type drop-down menu, the choice of discretization algorithms appears. Selecting Manual will show a cumulative graph of theThe missing Age Bracket values will be drawn from this Purchase Price distribution, and we can see that it rangesmarginal distribution and are used as placeholders, until from $75,000 to $180,000.28we can use the structure of the Bayesian network to rees-timate our missing values. As Dynamic Completion im-plies, BayesiaLab performs this on continuous basis inthe background, so at any point we would have the bestpossible estimates for the missing values, given the cur-rent network structure.DiscretizationThe next step is the Discretization and Aggregation dia-logue, which allows the analyst to determine the type ofdiscretization, which must be performed on all continu-ous variables.27 We will use the Purchase Price variableto explain the process. Highlighting a variable will showthe default discretization algorithm while the graphpanel is initially blank. We could now manually select binning thresholds by way of point-and-click directly on the graph panel. This26 The normal curve in the histogram is just for illustration purposes. BayesiaLab always uses the actual discrete distri-bution, not a parametric approximation.27 BayesiaLab requires discrete distributions for all variables.28 $75,000 was previously selected as the lower boundary for this particular vehicle segment. $180,000 was the highestreported price in NVES.Conrady Applied Science, LLC - 10
  14. 14. Simulating Market Share with the Bayesia Market Simulatormight be relevant, if there were government regulationsin place with speci c vehicle price thresholds.29For our purposes, however, we want to create price cate-gories that are meaningful in the context of our vehiclesegment and ve bins may seem like a reasonable start-ing point. The resulting bins appear much more suitable to describeClicking Generate Discretization will prompt us to select our domain.the type of discretization and the number of desired in-tervals. Without having a-priori knowledge about thedistribution of the Price variable, we may want to startwith the Equal Distances algorithm.The resulting view shows the generated intervals and byclicking on the interval boundaries we can see the per- We will proceed similarly with the only other continuouscentage of cases falling into the adjacent intervals. variable in the database, i.e. Age Bracket. Note For choosing discretization algorithms beyond this example, the following rule of thumb may be helpful: • For supervised learning, choose Decision Tree. • For unsupervised learning, choose, in the order of priority, K-Means, Equal Distances or Equal Frequencies. Clicking Finish completes the import process and 49 variables (columns) from our database are now shown as blue nodes in the Graph Panel, which is the main win-We learn from this that our bottom two intervals contain dow for network editing.89% of the cases, whereas the top two intervals containjust under 5% of the cases. This suggests that we maynot have enough granularity to characterize the bulk ofthe market towards the bottom end of the price spec-trum. Perhaps we also have too few cases within the toptwo intervals. So we will generate a new discretization,now with four intervals, and select KMeans as the typethis time.29 The now-expired luxury tax for passenger cars in the U.S. would be an example for such a policy.Conrady Applied Science, LLC - 11
  15. 15. Simulating Market Share with the Bayesia Market Simulator we are in P(Age < 45 | Number of children under 6 = 2). Hence we focus the learning algorithm on the area of interest, i.e. product attributes vis-à-vis mar- ket attributes. 2. We must not learn the dependencies between the product variables themselves because they would simply re ect today’s product offerings and their contingencies, e.g. P(Vehicle Segment=“4-door se- dan” | Brand=“Porsche”)=0. We do want to under- stand what is available today, but we certainly do not want to encode today’s product scenarios asThe six nodes on the far left column re ect product at- constraints in the network. Instead, we want to betributes (green), the second-from-left column shows ten able to introduce new scenarios, which are notdemographic attributes (yellow) and all remaining nodes available the right represent 33 vehicle-related attitudes (red).This initial view represents a fully unconnected Bayesian To focus learning in a speci c area, we need to take annetwork. indirect approach and tell BayesiaLab “what not to learn.” So, to prevent the algorithm from learning theAlso, to simplify our nomenclature, we will combine the product-to-product variable relationships, we will “for-demographic attributes (yellow) and the vehicle-related bid” such arcs.attitudes (red) and refer to them together as “Market”variables (now all red). We rst create a Class by highlighting all product nodes then right-clicking them. From the menu, we then select Properties>Classes>Add.Variable Classes and Forbidden ArcsOne is now tempted to immediately start with Unsuper-vised Learning to see how all these variables relate toeach other.However, there are two reasons why we need to intro-duce another step at this point:1. Our mission is to model the interactions between When prompted for a name, we can choose something products variables on the one side and market vari- descriptive, so we give this new Class class the label ables on the other, so we can see the consumer re- “Product”. sponse to products. For instance, we are more inter- ested in learning P(Transmission= “Manual” | Atti- tude = “Driving is one of my favorite things”) thanConrady Applied Science, LLC - 12
  16. 16. Simulating Market Share with the Bayesia Market Simulator As a result, these Forbidden Arc relationships will appear in the Forbidden Arc Editor and will remain there unless we subsequently choose to modify them.Having introduced this Class of node, we can now veryeasily manage Forbidden Arcs. More speci cally, wewant to make all arcs within the Class Products forbid-den. A right-click anywhere on the Graph Panel opensup the menu from which we can select Edit ForbiddenArcs. We are also reminded about the presence of Forbidden Arcs by the symbol in the lower right corner of the screen. Unsupervised Learning Now that the learning constraints are in place, we con- tinue to learn the network by selecting Learning>Asso- ciation Discovering>EQ.30In the Forbidden Arc Editor, we can select the ClassProduct both as start and end. The resulting network may appear somewhat unwieldyWe now repeat the above steps and also create Forbid- at rst glance, but upon closer inspection we can see thatden Arcs for the Market variables. arcs exist only between Product variables (green) and Market variables (red), which is precisely what we in- tended by establishing Forbidden Arcs.30 EQ is one of the unsupervised learning algorithms implemented in BayesiaLab. Koller and Friedman (2009) provide acomprehensive introduction to learning algorithms.Conrady Applied Science, LLC - 13
  17. 17. Simulating Market Share with the Bayesia Market Simulator ing the baseline scenario is described in the following section. Product Scenario Baseline The idea is that all available product con gurations were manifested in the market in 2009 and thus captured in the 2009 NVES.33 It still requires careful consideration as to how many Product variables should be included to generate the baseline product scenario. We want to create a type ofHowever, we will not analyze this structure any further, coordinate system, that allows us to identify productsbut rather use it solely as a statistical device to be used in through their principal characteristics. For instance, thethe Bayesia Market Simulator. We simply need to save following attributes would uniquely de ne a “Mercedes- Benz S550 4Matic”:the network in its native xbl le format, so the BayesiaMarket Simulator can subsequently import it. • Brand=“Mercedes-Benz”Simulation • Engine Type=“V8”With the Bayesia Market Simulator we have the ability • Drive Type=“AWD”to simulate “alternate worlds” for both the Productvariables as well as for the Market variables. In most • Transmission=“Automatic”applications, however, marketing analysts will want toprimarily study new Product scenarios assuming the • Segment=“High Premium”34Market remains invariant, meaning that consumer • Price=“>$85,795 AND <= $99,378”demographics and attitudes remain the same.31 Relating consumer attributes and attitudes to these indi-It will be the task of the analyst to de ne new product vidual product attributes, rather than to the vehicle as ascenarios, which will need to include all products as- whole, will then allow us to construct hypotheticalsumed to be in the marketplace for the to-be-projected products during our simulation. To stay with the Mer-timeframe, in our case 2010.32 As many products carry cedes example, we could de ne a new product by settingover from one year to the next, e.g. from model year the engine type to “V6” and changing the price to “<2010 to model year 2011, it is very helpful to use the $85,795”.currently available products as a baseline scenario, uponwhich changes can be built. Quite simply, we need to It is easy to imagine how one can get the number oftake inventory of the product landscape today. In the permutations to exceed the number of consumers. Forcurrent version of Bayesia Market Simulator this step is instance, in the High Premium segment, we could furtheryet not automated, so a practical procedure for generat- differentiate between short wheelbase and long wheel-31 The year-to-year invariance assumption of the market has been challenged by many marketing executives during themost recent recession. In this context, many media headlines also proclaimed a paradigm shift in consumer behavior.The authors have believed - then as well as now - that more has remained the same than has changed in terms of con-sumer attitudes.32 For expositional simplicity, we make no distinction between model year and calendar year.33 In our example, we judge this to be a reasonable simpli cation, even though a small number of automobiles at thevery top end of the market, e.g. the Rolls-Royce Phantom, may not be captured in the survey.34 Using the Strategic Vision segmentation nomenclature, “High Premium” de nes a large four-door luxury sedan.Conrady Applied Science, LLC - 14
  18. 18. Simulating Market Share with the Bayesia Market Simulatorbase versions, which would increase the number of base-line product scenarios. We want to nd a reasonablebalance between product granularity and the ratio ofconsumers to product scenarios, although we cannotprovide the reader with a hard-and-fast rule.Pricing is obviously a very important part of the productscenario con guration and here we are confronted with This will export all variables and all records, includingthe reality that no two customers pay exactly the same values from previously performed missing value imputa-for the identical product, and the survey data makes this tions. The output will be in a semicolon-delimited textvery evident. Furthermore, there are numerous product le, which can be easily imported into Excel or any sta-features outside our “coordinate system”, e.g. an op- tistical application, such as SPSS or STATISTICA. Thetional $6,000 high-end audio system, that would materi- purpose of loading this into an external application is toally affect the price point of an individual vehicle, but manipulate the database to extract the unique productwhich would not move the vehicle into a different cate- combinations available in the market.gory from a consumer’s perspective. With options, anS550 can easily reach a price of over $100,000. Still we In Excel this can be done very quickly by deleting allwould want such a high-end S550 to be grouped with columns unrelated to the product con guration, whichthe standard S550. Thus it is important to de ne reason- leaves us with just the product price brackets that cover the price spectrum of eachvehicle and minimize model fragmentation.During the Data Import stage, BayesiaLab has discre-tized all continuous numerical values, including Price,and created discrete states. If these discrete states areadequate considering the price positioning and pricespectrum of the vehicles under study, we can now lever-age this existing binning for generating all currentproduct scenarios and select Data>Save Data. In Excel 2010 (for Windows) and Excel 2011 (for Mac), there is a very convenient feature, which allows to quickly remove all duplicates, which is exactly what we want to achieve. We want to know all the unique product con gurations currently in the market.In the subsequently appearing dialogue box, we need toselect Use the States’ Long Name. It is important thatUse Continuous Values is not checked, otherwise we willlose the discretized states of the Price variable. This leaves use with a table of approximately 100 unique product scenario combinations available at the time of the survey.Conrady Applied Science, LLC - 15
  19. 19. Simulating Market Share with the Bayesia Market SimulatorTo make these unique product scenarios available for Upon loading we will see the principal interface of thesubsequent use in the Bayesia Market Simulator, we need Bayesia Market Simulator. On the left panel, all nodes ofto save the table as a semicolon-delimited CSV le. This the network appear as variables. We will now need tois important to point out, as most programs will save separate all variables into Market Variables and ScenarioCSV les by default as comma-delimited les. Variables by clicking the respective arrow buttons. In our case, the aptly named Market variables are the MarketProduct Scenario Simulation Variables in BMS nomenclature and Product variablesNow that we have the Bayesian network describing the are the Scenario Variables.overall market (as an xbl le) as well as the baselineproduct scenarios (as a csv le), we can proceed to openthe Bayesia Market Simulator. All variables must be allocated before being able to con- tinue to Scenario Editing. This also implies that Product variables, which are not to be included as Scenario Vari-Clicking File>Open will prompt us to open the xbl net- ables, must be excluded from the Bayesian network le we previously generated with BayesiaLab. If necessary, we will return to BayesiaLab to make such edits As we are working with RP data, every record in our database re ects one vehicle purchase, i.e. “reveals” one choice, and therefore we need to leave the Target Vari- able and Target State elds blank. These elds would only be used in conjunction with SP data, which includes a variable indicating acceptance versus rejection. Clicking Scenario Editing opens up a new window. We can now manually add any product scenarios we wish to simulate. Given the potentially large number of scenar- ios, it will typically be better to load the baseline product scenarios, which were saved earlier.Conrady Applied Science, LLC - 16
  20. 20. Simulating Market Share with the Bayesia Market Simulator Upon successful import, all baseline product scenarios will appear in the Scenario Editing dialogue.We can do that by selecting Offer>Import Offers.We now select to open the semicolon-delimited CSV lewith the baseline product scenarios. It is very importantthat the CSV le is formatted precisely as speci ed, forinstance, without any extra blank lines.In case there are any import issues, it can be helpful toreview the CSV le in a text editor and to visually in-spect the formatting. The analyst can now add any new product scenarios or delete those products, which are no longer expected to be in the market.35 By clicking Add Offer an additional scenario will be added at the bottom of the product sce- nario list. In the case of long product scenario lists, this may require scrolling all the way down. Clicking on the product attributes of any scenario prompts drop-down menus to appear with the available35 To maintain expositional simplicity, we have added all Panamera versions for the entire year 2010 and not changedany other product scenarios. It should be pointed out that the V6 version of the Porsche Panamera was introduced onlyin mid-2010. BMW has also launched an additional six-cylinder version of the 7-series as well as AWD variants, whichare not re ected in the simulation. Finally, Jaguar has released a new XJ in 2010, while that year marked the runout ofthe old-generation Audi A8.Conrady Applied Science, LLC - 17
  21. 21. Simulating Market Share with the Bayesia Market Simulatorattribute states, e.g. RWD or AWD.36 This also allows to done by associating the original database, from whichchange attributes of existing products, according to the the network was learned, or by creating a new, arti cialanalysts requirements. one that re ects the joint probability distribution of the learned Bayesian network. The latter can be achieved by selecting Database>Gener- ate. It is up to the analyst to determine the size of the data- base to be generated. Although there is no xed rule, too small of a database will limit the observability of prod- ucts with a very small market share.For our case study, we will add the following versions ofthe Panamera as new product scenarios:• Panamera (V6, RWD) Alternatively, we can also associate the original database,• Panamera 4 (V6, AWD) which contains the survey responses. In our case, the original database contains 1,203 records, which is very• Panamera S (V8, RWD) reasonable in terms of computational requirements.• Panamera 4S (V8, AWD) Once a database is associated, clicking the Simulation button will start the market share estimation process.• Panamera Turbo (V8 Turbo, RWD)To characterize all of them as large 4-door luxury se-dans, which is the key distinction versus previous Por-sche products, we will assign the “High Premium” at-tribute to them.Once this is completed, we need to obtain a databasethat represents the consumer base, on which these newproduct scenarios will be “tried out”. This can either be36 RWD and AWD stands for rear-wheel drive and all-wheel drive respectivelyConrady Applied Science, LLC - 18
  22. 22. Simulating Market Share with the Bayesia Market Simulator Simulated High Premium Market Shares ($75,000+) 1% 12% 21% Audi BMW 3% Jaguar Lexus 10% Mercedes Porsche 53% As can be seen from the results, the Porsche Panamera’s predicted market share appears to be compatible with the reported running rate for calendar year 2010, which was available at the time of writing. Unfortunately, weWith the given complexity of our network and around do not know how this compares to Porsche’s expecta-100 product scenarios, the simulation should take no tions, but the Panamera seems to be quite successfullonger than 30 seconds on a typical desktop computer. overall.Upon completion, the simulation results will appear in Substitution and Cannibalizationthe form of a pie chart and a table. One can go back and The fully simulated database can also be saved as areview the scenarios by clicking the Scenario Editing semicolon-delimited CSV le, which will allow reviewingbutton. the choice probability for each product scenario by indi- vidual consumer in a spreadsheet. We can literally examine the new, simulated choices record-by-record and see which customers have made the switch to the Panamera. Applying conditional for- matting to the spreadsheet can also be very helpful. TheThe aggregated simulated market shares can also be cop- above screenshot, for example, shows a selection of ac-ied from the results table and pasted into Excel or anyother application for further editing and presentation tual Mercedes buyers, who would either consider or pick the Porsche Panamera in this simulation. High choicepurposes. An example is provided below, showing the probabilities are shown in shades of red, while near-zerosimulated market shares of the brands under study in theHigh Premium segment. probabilities are depicted in dark blue.Conrady Applied Science, LLC - 19
  23. 23. Simulating Market Share with the Bayesia Market SimulatorIt is equally interesting to examine which Porsche buyers Upon editing the market segments, the simulation can bewould pick the Panamera over their current vehicle rerun to obtain the new market share results.choice. Limitations This approach can simulate product and market scenar- ios consisting of variations of con gurations, which can be observed with suf cient sample today. However, the impact of entirely new technologies cannot be simulated on this basis. As a result, projecting the market share of the all-electric Nissan Leaf38 would not possible, whereas estimating the share of a hypothetical three-row BMW crossover vehicle would be feasible. In all cases, it re- quires the analyst’s expert knowledge and judgment to determine the adequacy and equivalency of product at- tributes observable today.Not surprisingly, our simulation suggests high probabili-ties of Panamera choice for several current Cayenne Outlookowners. One is tempted to take this a step further and There exist several natural extensions to the presentedcalculate a rate of cannibalization. In this particular sur- methodology, however it would go beyond the scope ofvey, however, the sample size is too small to attempt do- this paper to present them. A brief summary shall suf ceing so. Otherwise, such a computation would be simple for now and we will go into greater detail in forthcom-arithmetic. ing case studies in this series:Market Scenario Simulation 1. Beyond learning from data, we can use expertAlthough experimenting with product scenarios is ex- knowledge to create or augment Bayesian networks.pected to be the primary use of the Bayesia Market BayesiaLab offers a Knowledge Elicitation module,Simulator, it is also possible to change the market scenar- which formally captures expert knowledge and en-ios. codes it in a Bayesian network. In absence of market data, this is an excellent approach to have decisionFor example, this can be used to simulate the impact of makers collectively (and formally correct) reasonpolicy changes. One could hypothesize that legislation about future states of the world.would prohibit or severely penalize ownership of vehi-cles of a certain size or of a speci c engine type in urban 2. We can extend the concept of product attributes toareas.37 consumers’ product satisfaction ratings. This will allow estimating the market share impact as a func- tion of changes in consumer ratings. For instance, an automaker could reason about the volume im- pact from a vehicle facelift, which is expected to raise the consumer rating of “styling”. 3. The product cannibalization or substitution rate can be estimated based on the simulated choice behav- ior, given that there is suf cient sample size. So, for most mainstream products, this seems to be realistic.37 Given the draconian restrictions on motorists in Central London, this example is presumably not very far-fetched.38 The all-electric Leaf was launched by Nissan in the U.S. in December of 2010.Conrady Applied Science, LLC - 20
  24. 24. Simulating Market Share with the Bayesia Market Simulator4. With the ability to study consumer choice at the model level, we can also aggregate these results to the segment level. Alternatively, using a less granular approach, we can model the entire market at the segment and brand level, which would allow study- ing market changes at a larger scale.5. Beyond simulating “hard” policy changes affecting the market, e.g. excluding a product class from a certain geography, we can also use BayesiaLab to simulate new populations with small changes in average consumer attitudes versus the originally surveyed population. For instance, such an arti - cially modi ed population could be more environ- mentally conscious and one could apply opinions prevalent on the West Coast to the whole country. Bayesia Market Simulator can then generate new market shares based on these new hypothetical market conditions.SummaryBayesiaLab and Bayesia Market Simulator are unique intheir ability to use Bayesian networks for choice model-ing and market share simulation. The presented work- ow provides a comprehensive method for simulatingmarket shares of future products based on their keycharacteristics, without requiring new and costly ex-periments.As a result, BayesiaLab and Bayesia Market Simulatorallow using a vast range of existing research for marketshare predictions. Given the signi cant resources manycorporations have allocated over many years to conduct-ing consumer surveys, these BayesiaLab tools offer anentirely new way to turn the accumulated research datainto practical market oracles.Conrady Applied Science, LLC - 21
  25. 25. Simulating Market Share with the Bayesia Market SimulatorAppendix vance how individual product and consumer attributes relate to these unobservable utilities. However, there areUtility-Based Choice Theory methods that allow us to estimate these unknown vari-In today’s choice modeling practice, utility-based choice ables and, based on this knowledge, they allow us totheory plays a dominant role. predict choice in the future. One such method is brie y highlighted in the following.1. The rst concept of utility-based choice theory is that each individual chooses the alternative that Multinomial Logit Models yields him or her the highest utility. In the domain of choice modeling, MultiNomial Logit models (MNL) have become the workhorse of the indus-2. The second idea refers to being able to collapse a try, but here we only want to provide a cursory overview, vector describing attributes of choice alternatives so the reader can compare the approach presented in the into a single scalar utility value for the chooser. For case study with current practice. instance, a vector of attributes for one choice alter- native, e.g. [Price, Fuel Economy, Safety Rating], MNL models provide a functional form for describing would translate into one scalar value, e.g. [5], spe- the relationship between the utilities of alternatives and ci c to each chooser. the probability of choice.The following example is meant to illustrate both: For instance, using an MNL model for a choice situation with three vehicle alternatives, Altima, Accord andFor Consumer A: Camry, the probability of choosing the Altima can be expressed as:• Utility of Product 1: [Price=$25,000, Fuel Economy=25MPG, Safety Rat- exp(VAltima ) ing=4 stars] = 7 ✓ Pr(Altima) = exp(VAltima ) + exp(VAccord ) + exp(VCamry )• Utility of Product 2: [Price=$29,000, Fuel Economy=23MPG, Safety Rat- VAltima in this case stands for the utility of the Altima ing=5 stars] = 5.5 alternative. The utilities VAltima, VAccord, and VCamry are a function of the product attributes, e.g.For Consumer B: VAltima = β1 × Cost Altima + β 2 × FuelEconomyAltima + β 3 × SafetyRatingAltima• Utility of Product 1: [Price=$25,000, Fuel Economy=25MPG, Safety Rat- As we can observe tangible attributes like vehicle cost, ing=4 stars] = 4 fuel economy and safety rating, and we can also observe who bought which vehicle, we can estimate the unknown• Utility of Product 2: parameters. Once we have the parameters, we can simu- [Price=$29,000, Fuel Economy=23MPG, Safety Rat- late choices based on new, hypothetical product attrib- ing=5 stars] = 7.5 ✓ utes, such as a better fuel economy for the Altima or a lower price for the Camry.This concept implies that consumers make tradeoffs,either explicitly or implicitly, and that there exists an The parameters of MNL models can be estimated bothamount x of “Fuel Economy” that is equivalent in utility from “stated preference” (SP) data, i.e. asking consumersto an amount y of “Safety”. The reader may reasonably about what they would choose, and “revealed prefer-object that not even a fuel economy of 100MPG would ence” (RP) data, i.e. observing what they have actuallymake it acceptable to drive a vehicle that is rated very chosen. There are numerous variations and extensionspoorly on safety. to the class of MNL models and the reader is referred to Train (2003) and Koppelman (2006) for a comprehen-Also, we do not know a priori what the utility values are sive introduction.nor can we measure them. Neither do we know in ad-Conrady Applied Science, LLC - 22
  26. 26. Simulating Market Share with the Bayesia Market SimulatorStated Preference Data cal for a much broader audience. Although ELM hasStated preference data typically comes from experiments, successfully removed the burden of manual coding,i.e. consumer surveys or product clinics. In this context, countless iterations of speci cation and estimation re-conjoint experiments have become a very popular choice main a very time-consuming task of the analyst.elicitation method and a wide range of tools have been NVES Variablesdeveloped for this particular approach. In conjoint stud- The following variables from the 2009 Strategic Visionies, consumers would typically be given a set of arti -cially generated product choices along with their attrib- NVES were included this case study:utes, from which preference responses are then elicited. • UNIQUE IDENTIFIERThere are many variations of this method that all at-tempt to address some of the inherent challenges related • Combined Base Weightto dealing with responses to hypothetical questions. • New Model Purchased - Make/Model/Series (AlphaThe Sawtooth software package has become de-facto Order)industry standard for such conjoint studies.39 • New Model Purchased - BrandRevealed Preference Data • New Model Purchased - Region OriginIn contrast to SP data, revealed preference data is purelyderived from passive observations. As the name implies, • New Model Segmentthe consumer choice is revealed by their actual behaviorrather than by their stated intent in a hypothetical situa- • Segmentation 2tion. A key bene t is that it is typically easier and more • Type Of Transmissioneconomical to obtain passive observations than to con-duct formal experiments. A conceptual limitation of RP • Number Of Cylinders (VIN)data relates to the fact that non-yet-existing products canobviously not be chosen by consumers in the present • Drive Type (VIN)market environment. Thus simulating market shares of • Fuel Typehypothetical products requires “assembling” them fromcomponents and attributes of products, which are al- • Genderready available in the market. This inherently limits theexploration of entirely new technologies, which have • Marital Statuslittle in common with the technologies they may replace. • Age BracketStudies based on RP data have become very popular for • Children Under 6researching travel mode choice, as is also documented ina large body of research. In market research related to • Children 6 To 12CPG products or durable goods, using RP data is some-what less common. • Children 13 To 17We speculate that one of the reasons for the lack of • Total Family Pre-Tax Incomepopularity outside the world of academia is the absence • Ethnic Groupof easy-to-use software packages. Only recently, with therelease of Easy Logit Modeling (ELM)40 , specifying and • Location Of Residenceestimating multinomial logit models has become practi-39 A wide range of tools is available from Sawtooth Software, Inc., Easy Logit Modeling is available from ELM-Works, Inc., ELM can estimate models based onboth RP and SP data, although we only mention it in the RP context.Conrady Applied Science, LLC - 23
  27. 27. Simulating Market Share with the Bayesia Market Simulator• Customer Region Classi cation #1 • My choice of vehicle re ects my personality• I Seek Variety in My Life • I want a vehicle that says a lot about my success in life / career• Im Curious and Open to Experiences • I will switch brand for features or price• Luxury is Not Important Unless it Has Purpose • There are lots of different brands of vehicles that I• I Enjoy Expressing Myself Creatively would consider buying• I See Life as Full of Endless Possibilities • I prefer sofa-like comfort over a cockpit-like interior• Driving is one of my favorite things to do • I want a vehicle that provides the quietest interior• I really dont enjoy driving • I want to look good when driving my vehicle• Whenever I get a chance, I love to go for a drive • I want my vehicle to stand out in a crowd• When I drive for fun, I mainly prefer to relax and lis- • I would pay signi cantly more for environmentally ten to music or talk friendly vehicle• I want vehicles that provide that open-air driving ex- • Price is most important to me when buying a new perience vehicle• I prefer a vehicle that has the capability to outperform • Purchase Price (100s) others• I prefer vehicles that provide superior straight ahead power• I prefer vehicles that provide superior handling and cornering agility• I prefer a balance of comfort and performance• I prefer vehicles that provide the softest, most com- fortable ride quality• I just want the basics on my vehicle - no extras• Value equals balance of costs, comfort & performance• I prefer vehicles that project a tough and workmanlike image• Vehicles are a tool or a part of the gear in an active outdoors lifestyle• I Want to be able to tow heavy loads• I want to be able to traverse any terrain• I want the most versatility in my interior• I want a basic, no frills vehicle that does the jobConrady Applied Science, LLC - 24
  28. 28. Simulating Market Share with the Bayesia Market SimulatorReferencesBarber, David. “Bayesian Reasoning and Machine Learn- ing.”———. Bayesian Reasoning and Machine Learning. Cambridge University Press, 2011.  Darwiche, Adnan. “Bayesian networks.” Communica- tions of the ACM 53, no. 12 (12, 2010): 80.  Koller, Daphne, and Nir Friedman. Probabilistic Graphi- cal Models: Principles and Techniques. The MIT Press, 2009.  Koppelman, Frank, and Chandra Bhat. “A Self Instruct- ing Course in Mode Choice Modeling: Multinomial and Nested Logit Models.” January 31, 2006.Krzywinski, M., J. Schein, I. Birol, J. Connors, R. Gascoyne, D. Horsman, S. J. Jones, and M. A. Marra. “Circos: An information aesthetic for com- parative genomics.” Genome Research 19, no. 9 (6, 2009): 1639-1645.  Neapolitan, Richard E., and Xia Jiang. Probabilistic Methods for Financial and Marketing Informatics. 1st ed. Morgan Kaufmann, 2007.  Pearl, Judea. Causality: Models, Reasoning and Infer- ence. 2nd ed. Cambridge University Press, 2009.  Spirtes, Peter, Clark Glymour, and Richard Scheines. Causation, Prediction, and Search, Second Edition. 2nd ed. The MIT Press, 2001.  Train, Kenneth. Qualitative Choice Analysis: Theory, Econometrics, and an Application to Automobile Demand. 1st ed. The MIT Press, 1985.  Train, Kenneth E. Discrete Choice Methods with Simula- tion. Cambridge University Press, 2003.  Conrady Applied Science, LLC - 25
  29. 29. Simulating Market Share with the Bayesia Market SimulatorContact Information Copyright © 2010 Conrady Applied Science, LLC and Bayesia SAS.Conrady Applied Science, LLC All rights reserved.312 Hamlet’s End WayFranklin, TN 37067 Any redistribution or reproduction of part or all of theUSA contents in any form is prohibited other than the follow-+1 888-386-8383 • You may print or download this document for your personal and noncommercial use only.Bayesia SAS6, rue Léonard de Vinci • You may copy the content to individual third parties for their personal use, but only if you acknowledgeBP 119 Conrady Applied Science, LLC and Bayesia SAS as the53001 Laval CedexFrance source of the material.+33(0)2 43 49 75 69 • You may not, except with our express written sion, distribute or commercially exploit the Nor may you transmit it or store it in any other web- site or other form of electronic retrieval system.Conrady Applied Science, LLC - 26