A History of Conjoint Paul GreenUniversity of Pennsylvania Joel HuberDuke University Rich JohnsonSawtooth Software

A History of Conjoint The psychometric roots of conjoint The development of ACA The development of choice models The application of conjoint

Psychometric Dream To be able to build an axiomatic system of preferences akin to those in the physical sciences Requires interval scales over which mathematical operations are meaningful People have difficulty making numerically meaningful estimates

Psychometric solution People can give preference orderings for compound or conjoint objects If you prefer a trip to Victoria for $1000 over a trip to Philadelphia for $500 implies that Victoria is worth at least $500 more than Philadelphia A number of such statements can produce asymptotically interval utility scales for cities and money

Typical Early Conjoint Measurement Individuals rank order profiles Profiles developed from full factorials Test consistency with axioms: additivity, cancellation If test is passed, use monotone regression or LINMAP to estimate partworth utilities

Early conjoint results People regularly violated the assumptions There was little correspondence between predictive accuracy and order violations The rank order task was more difficult but no more effective than a rating task Despite theoretical failure the derived utility functions predicted well

Paul Greens Orientation He knew the psychometricians and was instrumental in developments in multidimensional scaling as well as conjoint He came from Dupont and was concerned with managerial problems.

Paul Greens Paradigm Shift Full factorial Orthogonal arrays Ordinal estimation Linear estimation Focus on tests Focus on simulations Conjoint measurement Conjoint analysis

Our debt to Psychometricians A focus on individual preferences The use of full profile stimuli Simple main-effects models Psychometricians tried to axiomatize behavior, we tried to predict it Their task largely failed, but with their help ours has been surprisingly successful

A Tradeoff Matrix

A Respondents Preferences

A Tradeoff Matrix

The Evolution of Choice-Based Conjoint Why choices are better than ratings Problems with early linear choice models McFaddens development of logit Louvieres adoption of logit for experimental choice sets Hierarchical Bayes as the best way to account for heterogeneity

Why choices over ratings? Choice reflects what people do in the marketplace Choice defines the competitive context Managers can immediately use the implications of a choice model People will answer choices about almost anything

What is wrong with choices? Little information in each choice Analysis requires aggregation across respondents Linear model does not work Simple logit does not account for heterogeneity

Whats wrong with linear probability model? Violates homoskediasticity assumptions Produces predictions greater than zero of less than one Assumes the marginal impact of a market action is the same regardless of initial share

Which brand benefits most from a promotion or shelf tag? 1.A soft drink with 5% share of its market 2.A soft drink with 50% of its market 3.A soft drink with 95% of its market

Typical sigmoid curve showing impact of effort on share

Marginal impact of effort depends on share

Aggregate Logit Has the correct marginal properties But becomes undefined for choice probabilities of zero or one Ln (p/(1-p) is undefined where p=0 or 1 Worse, it become very large for probabilities close to one and very small for probabilities close to zero

McFaddens 1976 breakthrough Builds choice from a random utility frameworkerrors are independent Gumbel MLE criterionmaximize probability actual choices occur given parametershas no problem with zeros or ones Critical statistics are defined and asymptotically consistent

Louviere and Woodworth (1983) choice-based experimental designs Applied to experimental design (stated choices) as opposed to actual choices Permitted predictions to alternatives that did not exist and teased out otherwise correlated characteristics in the marketplace Orthogonal arrays were adapted to create choice designs

The red bus, blue bus problem Suppose people choose 50% red bus and 50% cars What happens to share if you add a blue bus that has is the same as the other bus? Logit says 33% for each Logic says 50% cars, 50% red and blue bus Logit assumes proportionality, but similar items need to take share from similar ones

Modeling heterogeneity resolves differential substitution People choose car or bus, then choose bus color Generally, businesses need to estimate shares for items that strongly violate proportionality –Demand for a new or revised offering –Estimate impact of revised offering on own and competitors

Ways to modify logit to accept differential substitution Include customer parameters in the aggregate utility function Car use is correlated with income, include income as a cross term Problem 1: there can be many cross terms Problem 2: demographics are poor at predicting choices

Latent class Heterogeneity is reflected in mass points where responses are assumed to be consistently logit within those points Latent class produces the partworth values and the weights for each class Neat ideaused in Sawtooths ICE program Did not work as well as HB

Random Parameter Logit Assumes that logit parameters are distributed over the population Sample enumeration over the population produces share estimates that are strongly non-proportional Works well, but sensitive to the assumption of the aggregate distribution Requires a new analysis or cross terms for subset analysis

Hierarchical Bayes Estimates both aggregate distribution and individual distributions Individual means serve well in choice simulators, just like those from choice- based conjoint Very efficient, need only as many choices per person as you have parameters

Why HB works It is robust against overfitting It is also less affected by assumptions about the aggregate distribution Its magic has little to do with Bayesian philosophy Random parameter logit plus estimate at the individual level results in identical solution

Lessons HB permits choice-based conjoint to be as user friendly as ratings-based conjoint Choices are not always the best input, but where they are, we can now accommodate them We naturally tend to use models with which we are most familiar, but progress is marked with unfamiliar victors