Chapter6

Conjoint Analysis, Related Modeling, and Applications

John R. Hauser. Massachuse11s l11s1i1111e o[Technowgy Vilhala R. Rao, Come/I University

Conjoinl analysis has as its roots the need to solve irnportant acade1nic and industry problems. Paul Green's work on conjoint analysis grew oul of his contributions to the theory and practice of mulridimensional scaling (MDS) to address marketing problems, as discussed in Chapter 3. MOS offered the ability to represent consumer multidimensional perceptions and consumer preferences relative 10 an existing se1 of products.

THE DEVl>l,OPMENT O•' CONJOINT ANALYSIS

Recognizing the strengths and weaknesses of MDS, Green sought ways to augment its power. Drawing upon his extensive experience in product development from his days at DuPont, Green sought a means to decompose consumer preforences into the partial contribution (partworth) of product features. In this manner, researchers could not only explain the preferences of existing products, but could •imulate preferences for entirely 11ew products that were defined by feature combinations. Such a method could also be used to decompose perceptions if a percepnial variable - say "ease of use" - was used as the dependent measure rather than ''preference." This would solve the problem of reverse mapping in MOS - the challenge of translating a point from percepmal space into a corresponding point (or set of points) in product· feature space.

This mapping challenge was related to axiomatic work in psychometrics. Author8 such as Luce and Tukey (1964) and Krantz, Luce, Suppes, and Tversky (1971) were exploring the behavioral axioms that would enable a

141

142 Marketing Research 011d M0</tli11t;

decomposition of an overall judgment into ils parts. In a seminal paper (Green and Rao 1971 ), Green drew upon this conjoint measurement theory, adap<ed it to the wlu1ion of marketing and product-development problems, considered carefully the prae1ical mea~urement issue.~. and opened a floodga1c of research opponunilics and applications. (As an indication of the pathbreaking nature of this work, 1he reviewers of the anicle by Green and Rao were quite apprehensive of the value of this approach. Bue, the editor at 1he lime, Professor Ralph Day, had the vision to sec 1he enormous potential for this research menm.)

Conjoint Measurement or Conjoint Analysis

Conjoint measurement offered a theory 10 decompose an ordinal 5C81e of holistic judgment into interval scales for each component anribute. 1bc 1hcory details how lhe transformation depends on 1he satisfaction of various axioms such a.< additivity and independence. However. in rea.l problems we expect that such axioms are approximate at best. The real genius is making appropriate trndeoffs so that real consumers in real market research settings are answering questions from which uS<:ful inl'orm<11ion can be inferred.

In the thiny years since the original conjoint analysis article. researchers in marketing und other disciplines, led by 1he insighc and creativity of Paul Green. have explored these tradeoffs. While valid and interesting intellectual debateS rem.,in today and while the field continues to advance with new in•ighL'>, theory. and methodology. we are left with the legacy of an elegant theory transfonncd into an evolving ~rch stream of great practical impon. Whereas the earlier, axiomatic work is often called conjoint mea.ruremwr. we choose to cull the expanded focus conjoint a11alysis.

Pa ul Green's Contributions

Paul Green himself has contributed almost 100 anicles and books on conjoint nnnlysis. He was there in the beginning and he is there now. He has embraced (or led) new developments including the move to metric measures (Carmone. Green, and Jain 1978). evalun11on< of non-additivity (Green and Devita 1975). hybrid methods to combine data sources and reduce respondent burden (Green 1984), and new c.~tirnation methods such as hierarchical Bayes methods (Lenk et al. 1996). He hu funher led the way with seminal applications such as the applica1ion of conjoint analysis to really new products such as Marriott's Counyard (Wind i:t al. 1989) and the E-Z Pass system (Green, Krieger, and Vavra 1999). It is safe to say that conjoim analysis would not be where it is today without Green's leadership.

In this paper we pay homage to Green by reviewing wme or 1he enorinou> breudth of research in conjoint unnlysis. We highlight :some of the

Conjoint A1wlysi.>, Modeling, Appliratifm.v 143

major 1heoretical and practical issues ttnd we illustrate many of the con1ribu1ion< of the past thirty years.

CONJOINT ANAL \'SIS IS A JOURNEY NOT A DESTINATION

The essence of conjoint analysis is to identify and measure a mapping from more detailed descriptors of a product or service onto an overall measure of the cusiomcl''s evaluation of 1hat produc1. We begin wilh an example from Green's classic paper (wi1h Jerry Wind) thnt was published in the Harvard Bu.sines.r Review (1975). Green and Wind were designing a carpet cleltner and cho"6 to describe tbe carpet cleaners by fi"e features: ---

• c .....,

:::t:::::'' --,., ............ 41 .. 91 - ll.:-Ji'9 MoMy.llock Cninil

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,.

F/~ure fl.I. t.:-.[M!rfnll!ntaJ Design for Carpel Clr.ener From Green and Wind (1975)

144 Marketing Research a11d M(){/ellng

• Jll!Ckage design - one of three levels illustrated in Figure 6-1 • brand name - one of three brand names - K2R, Glory, and Bissell • seal - either the carpet cleaner had a Good Housekeeping seal of

appmval or it did nOI • guarantee - either the carpet cleaner had a money-back guarantee

or it did not • price - specified at the three di~rele le\•els of $1.19, $1.39, and

$ 1.59

Responden~< were gi ven a fractional factorial design of profiles. each of which was described by the levels of the features it contained, and were asked to rank order cards representing the profiles in order to indicate their preferences for the profiles. Because a full 3x3x2x2x3 design would have yielded 108 profiles, they chose a balanced orthogonal design that kept the respondent's ta.'k within reason - each respondent bad to rank but 18 profiles.

When the data collection was comple1e, Green and Wind assumed tll!\t the overall preference was an additive sum of the "panwonhs" of the features, represented each feature by a series of dummy variables, and used rnonotonic regression to estimate the contribution of each feature to overall preference. In this manner, panwonhs were obmined for each respondent, enabling the researchers nexibility to (I) cluster the panworths 10 identify segments and (2) simulate preferences for new products by adding those products to the respondent>' choice sets and re-computing the implied preferences. (Here they assumed that each respondent would purchase !heir most preferred product.)

In the tweniy-seven yeim since this article was published (thiny-one years since the pioneering Green and Rao 1971 anicle), much has changed, but the ~sic structure of the conjoint challenge remains. We organize this short review around the elements pioneered by Green and provide examples of how each element has evolved. Bccau<e of the sheer breadth of today's applicutions, we have space but to highlight the most common examples. TI1e basic elements of our review arc:

• how a product or service is decomposed (additive function of five features in 1975)

• stimuli rep<CSCnlation (cruds in 1975) • methods to reduce respondent burden (orthogonal factorial design

in 1975) • data collection fomiat (rank order of cards in 1975) • estimation (monotonic regression in 1975)

In a field so vast, we can provide but an overview. Our focus is on the measurement and representation of consumer preferences. In the next chapter, Green, Krieger, and Win<I address how conjoint estimates are used in models

Coi1join1 Analysis, Modeling, Applications: 145

to segment the market, identify high-potential product designs, plan product Jines, and forecast purchase potemial. We encourage readers to explore this field further.

Dec<>mposing the Product or Service

There are ac least two considerations in decomposing the product or the service: (l) the elements into which the product is decomposed and (2) the function by which the elemental decomposition is mapped onto overall preference.

ln the carpet-cleaner example, the elemental decomposition was into physical features. This has been the most conm1on application of conjoint analysis in the last thirty years and is the most relevant if the product­development team is facing the decision about \Vhich features to include in a product design. However, conjoint analysis has also been used with more qualitative fean1res such as •·personalness/' "convenience," and ''quality0 of health care, (e.g., Hauser and Urban 197'7). Such applications occur early in the product-development process when the team is trying to understand the basic perceptual positioning of the prnduct or service.

The key consideration in the decomposition is that the elements be as comple.te as feasible, understandable to the respondents, useful to the product­development team, and as separable as feasible. Researchers have used detailed qualit.ati ve intervie\YS, focus . groups, contextual engineering, and lead-user analyses to identify the appropriate clements. In some cases, more elaborate methods are used in which detailed phrases (obtained from customer interviews) are clustered based on similarity or factor-analyzed based on evaluations to identify groups of phrase.s which are then represented by a summary feature (e.g., Green, Cannone, and Pox 1969; Green and McMcnnamin 1973; Griflin and Hauser 1993; Hauser and Koppelman 1979; Rao and Katz. 1971 ).

If the feanires are chosen carefully, then they will satisfy a propeny known as "preferential independence." Basically, two features.Ji and f,, are preferentially independent of the remaini11g features if tradeoffs among/1 and h do not depend upon the remaining features. Preferential independence is extremely important to the researcher because if each set of features is preferentially independent of its complement set, then the (riskless) conjoint function can be represented by an additi,·e (or multiplicative) decomposition (Keeney and Raiffa 1976, Theorem 3.6). Whenever preferential independence is not satisfied, the conjoint function is more difficult 10 e.~timate and interactions among features are nece.~sary, as illustrated for food menus by Green and Devita (1975) and Carmone and Green (1981). There are many decompositional forms and related indepe11dence conditions.

In some cases, the preference is defined over risky features - that is, the features are described by a probability density function rather than simply as

146 Marketing Restarcli anti Modeling

known features. In this case. some researchers have represented the features 11s lotteries und have applied von Neumann-Morgenstern utility mea.,uremcnt {llliashberg 1980: Elia>hberg and Hauser 1985; Hauser and Urban 1979). See Farquhar ( 1977) for a review of related independence conditions and functional forms.

Repre,..,ntation of Stimuli

In the Cllrpet..:leaner example, Green and Wind represented the product profiles by verbal and pictorial descriptions on cards that were then sorted by respondents. Jn the past thirty years, stimu li representations have been limited only the by imagination of the rcseMChers. For example. in the design of the E-Z Pass system, Vavra. Green, and Krieger (1999) sent videolapes and other descriptive materials to respondents so that they fully understood the innovation and its features. Wind et al. ( 1989) used combinations of physical models, photographs, and verbal descriptions. Recently. with the development of the Internet, researchers have begun to exploit the rich multi-media capabilitic.~ of the Web to provide virtual prototypes to Web-based respondents (Dahan nnd Srinivasan 2000). Indeed, this urea of conjoinl analysis is growing rapidly. with many firms providing panels of literally millions of respondcnL< who can respond within days (Buckmann 2000; Dahan and Hauser2002: Gonier 1999; Nadilo 1999).

Have Mc~y on the Respondenu

From 1hc beginning. 1·esearchers have recognized thnt conjoint-analysis estimates are only as good as the dat" from which they are obtained. In the carpet-cleaner example, Green and Wind were concerned with respondent wear-out if respondents were asked to rank 108 product profiles. To avoid such wear-out, they chose an 011hogonal design to reduce the number of prot.les (to 18) that any respondent wo'Uld see. Of course, this design was not without tmdeotTs - an Ol'lh<>gonal design implicitly assumes preferential independence and doe.' not allow any interactions to be estimated. Researchers huve developed many methods to reduce respondent burden, tailored to the information required for the managerial application, the fearnre structure, and respondent task.

We review brieOy a few of the methods that have been proposed. As early as 1978, Carmone, Green. and Jain (p. 300) found that most applicntions dom.inded n doien or more features, but that it was difficu II for custorners to rank more than a doien profiles. Many researchers have documented that the respondents' 1ask can be burdensome and have suggested lhat accuracy degrades as 1he number of queMions increases (Bateson, Rcibstcin, and Boulding 1987; Green, Carroll, and Goldberg 1981, p. 34; Green, Goldberg. and Montemayor 1981, p. 337; Huber et al. 1993: Lenk ct al. 1996, p. 183:

Conjoim Analysis. Modeling, Applimtimis 147

Malhotra 1982, 1986, p. 33; Moore aJid Semenik 1988; Srinivasan and Park 1997, p. 286). When appropriate, eflicient experimemal designs are used so that Lhe respondent need consider only a small fraction of all possible product prolile-~ (Addelrnan 1962; Kuhfeld, Tobias, and Garratt 1994). Tradeoff analysis presents resp<Jndents with two attributes at a time and has them evaluate the reduced sets (Jain et al. 1979; Johnson 1974; Segal 1982). Two stages can be introduced in which respondents eliminate unacceptable products, unacceptable anribmes, or use prior soning tasks to simplify the evaluation task (Acito and Jain 1980; Green, Krieger, and Bansal 1988; Klein 1988; Malhon11 1986; Srinivasan 1988). Hierarchical integration provides a means to measure preferences among higher-level benefits and lhcn again for features that drive !hose benefits (Oppcwal, Louviere, and Timmermans 1994; Wind et al. 1989; Srinivasan and Park 1997).

Many researchers combine these. methods with intensity questions (interval and ratio scales) or with self-explicated tasks (Griffin and Hauser 1993; Hauser and Shugan 1980; Neslin 1981; Srinivasan and Wyner 1988; Wilkie and Pessemier 1973). Other re.<earchen. have simplified the task. In choice-based conjoint analysis (CBC) respondents simply choose one profile each from many sets of profiles (Carroll and Green 1995; Elrod, Louviere, and Davy 1992; Haaijer, Kamakura, rund Wedel 2000; Haaijer et al. 1998; Oppewal, Louviere, and Timmermans 1994; Orme 1999). Hybrid conjoint analysis combines sclf-explica1ed tasks for each respondent with a master design across respondents of profile-based questions (Akaah and Korgaonkar 1983; Green 1984; Green, Goldberg, and Montemayor 1981). Finally, Hiernrchical Bayes (HB) methods improve Lhe predictability of the partworths that have been collected by other means (Lenk ct al. 1996; Johnson 1999; Sawtooth 1999) and thLlS, in theory, cnnble the researcher to obtain estimates with fewer questions.

Each of these methods, when used carefully and respons ibly, reduces the respondents' burden and is feasible in large commercial applications. As this remains an area of active research, wt: expect further developments and, specilicall y, we expect researchers to experiment with many hybrid combinations of these methods.

Formats of Data Collection

Conjoint analysis was born in the belief that 1he data collection method should ask as linle of the respondents as feasible and infer the rest. Like mos! early researchers, Green and Wind asked their respondents 10 rank order the profiles of carpet cleaners. Even the linear-programming methods transfonned overaU rank orders into rank orders among pairs (Srinivasan and Shocker 1973a, 1973b). However, toward the end of the 1970s, both academic and industrial researchers began to notice that respondents could, indeed, provide inler"al, or even ratio, data on preferences among product or service profiles.

148 Marketi1111 Rest(ll'c/1 aiul Modeling

For example, Carmone, Green, and Jain (1978) state: "(in industrial applications) roting scales ... have substituted for strict ranking procedures . ... metric annlysis ... is very robust." In parallel, in their well-known As..,ssor model, Silk and Urban (1978) and Urban and Kaiz (1983) wete using constant-sum·pained-comparisoo prererence measurements for extremely accurate forttMts for new produces. During this period, researchers experimented with many different formats for coUeccing data on preferences.

Research into question formats continu.,. today with new forms, such as contigurntors. being used with success. However, thi' area remains one of stmngly-held beliefs and debates. For example, in their defense of the choicc­bascd (CBC) format. Louviere, Hensher, and Swait (2000) state: "We suggest that i'Csearchers consider transforming ratings data in this wny rather than blindly assuming 1hm m1ings produced by human subjects sutisfy demanding measuremenl properties." Green, Krieger, and Wind (2001) tllke n more two­sided view and. while acknowledging the potential benefits of the formal, suggosl !hill "choice-bm;ed conjoint studies can be n mixed blessing. The respondent's tasks are extensive." Finally, Orme (1999) suggests thai "(CBC) often press the limits of how much information can be succe~sfully evaluated before respondents either quit, glaze over, or sllltt lo employ sub-optimal shortcut methods for making choices."

We do not take a stand on which format is be.5t, pnmarily because each format has it~ strengths and weaknesses and because the researcher should choose the fonn:it carefully as appropriate lo the managerial problem and the stimuli being presented. We instead review five major formats: full-profile, partial-profile. slated preferences (CBC), self-explica1ed preferences, and co11figura1ors.

Fu/I-Profile E1•a/11ation.<

Full-profile s1imuli are similar to those in Figure (>. I. Each product is described by 1he levels of 1he features. that ii contains. The respondent e-0n be asked 10 rank order nil stimuli or 10 provide a metric ruling of ench stimulus. Jn some hybrid methods, the experimental designs arc blocked across resp<>ndcnL,. Full-rrofile analysis remains the most common form of conjoint analysis and has the advantage that the respondent evalumes each profile holistically nod in the context of all other stimuli. Its weakness is that the respoodent'< burden grows dramatically with the number of profiles that mus! be ranked or roted.

Panial-Profile Ew1/uarions

Whenever preferential independence is satisfied, perhap~ approximately, tradeoffs among a neduced set of features do not depend upon 1he levels of the other features. In this case. responden1s can evaluate partial profiles in which

Conjou11 A1111/y.<i.r, Modeling, Applications 149

some of the features arc explicit and the ocher fea1ures are assumed constan1. While the number of stimuli can vary from 1wo 10 many, two siimuli are most common. Allhough !he respondent can lbe asked only to choose among the partial profiles, ii ;. common to obtain an in1erv11J evaluation of the profiles. Figure 6-2a illuqra1es a pairwise partial,profile evaluation in which the respondent is asked to provide a metric roting to indicate his or her strength of preference. Jn fixed designs. the partial stimuli arc chosen from a partial design. Recently, there has been signi fican1 research on the most eflicieni mnnner in which to choose the partial profiles (e.g .. KuhlCld, Tobias, and Oan-•11 1994).

Because partial profiles are well sui1ed to presentation on CQmpu1er monilors. researchers ha\'C developed adaptive methods in which then• set of partial profiles presented to respondents is b:cw:d on the answers to the preceding n· I secs of partial profiles. The best-known exnmple of such adoptive selection of partial profiles is Johnson's ( 1987) adaptive conjoin! analysis (ACA). In ACA, respondents are first a.'kcd a sec of self-explicated questions (see below) 10 es1ablish initial estimates of importances. Then, onlinary-least·squarcs (OLS) regres,ioo. based on the initial importances and the preceding n-1 metric paired-comparison que>tions, provides imermedime estimates of the part worths of each feature and level. The 11"' pair of profiles are chosen so thnl they are a.< equal as fea•ible in terms of estimated preference - a procedure known as utility balance. ACA bas proved robust in prnc:tice and is, perhaps, the second most common form of conjoint analysis. Reccnlly, researchers have re..:s1imated the panworths obtained from ACA with Hierarchicul Bayes (HB) methods. (That is, OLS estimates the intermediate partworths that are used to select questions, hu~ once the data collection is complete, the panwonhs are re~~1ima1ed wi1h HB.) HB appears 10 be qui1e effective when fev.'Cr questions arc nsked of each respondent than are 1ypical in 1he standard ACA in1en1icw.

The advanlnge of ACA is that 1he que,Lions are chosen for high ittfomtation conlcnl. However, becau!;e ii is OLS-based, ACA has 1he potemial for endogeneity bias, lhat is, the 11" question. and hence the n'' set of independent vanables. depend upon the ansv.ers. and hence the errors. in the lirst ti· I questions. furthermore, 1he util i1y-balance crite.rion suggests 1hat this bias is always upward and is greater for foaturc.< that have higher (lnie) par1worths (Hauser. Simester, and Tuul>ia 2002). However, to date. there has been no research to establish whether or nOI this 1heore1ical bias is managerially relevant.

Recently, new methods for adap1ivc queslion selection have been proposed thai are not 01..S based and, instead, choose questions 10 minimize tho uncertainty in pammcler es1im:uion. In these "polyhedral" 1oothoci~. each question constrains the feasible 'el of partworths. Multiple c.onstrain1s imply that the set of panwonhs is a multi-dimensional polyhedron in partworth· space. The polyhedron is approximated with an ellipsoid and the longest axis

15-0 Mari<Lting R<search and Mod.ting

of ibe ellipsoid provides the means to <elect the next question. Spec11ically, 1f 1he question vector is selected parallel to the longest axis. then the consiraints imposed by the next answer are perpendicular to that axis and are most likely to result in the srnalle•t new polyhedron. In addition, 1his question vec1or is most likely 10 lt:lld to constraints that intersect the feasible polyhedron. In this manner, the questions reduce the set of fea.,ible panW011hs as rapidly as

(a) Partial Prolil• (Melli< Pairs)

Question

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FigMr~ ~1a ond h. Rxamplr:s orDaUt·Collttdon l< .. ornuitN From Touhl11, Sin~ter, Hi!uli<:r, and Dahan 2003; Toubia. Hauser. ~d Sinie.h~r (2fl0"'\\

Conjoint Analysis, Modeling, Applications 151

possible. In initial applications and simulations, these question-select methods appcil! superior to OLS-bascd utility- balance estimates (Toubia, Simester, Hauser, and Dahan 2003). These methods are available as stand-alone options (e.g., FastPace) and are now offered as an option within ACA. In addition, other major suppliers are developing polyhedral-based methods.

(c) Selr·expll<atod Qu<>Stions

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Figure ~2c 1u1d d. Examples ofData·Collection Format!> Fro111 Toubia, Siincslcr. Hauscr. and Dahan (2003): Toubia. Hauser. and Sin.ester {2003)

152 Mt1rl<eting Research aml Modeling

Stated Prefertnus

In 1974 McFadden provided a random u11li1y inle.rpreialion of the logil model, renewing in1cre.~1 in disaggregate choice models in transpona1ion demand analysis and in economerrics. lrt random utilily models (RUM). 1he rcspc>ndenr's utilil)' is represented as a (usually linear-in-thc-parnnieters) combinal ion of produc1 or service fearures, plus an error lerm. Then, based on the dis1ribu1ional assumptions that are made about lhe error term, a researcher can calculnle the probabiliry Lhut n produc1, defined by ils features, is purchased. Por example. if 1be error lerrns are independent Gumbel extreme value mndom variables. then we ob1.ain the logiL model. If !he error terms are muhivariate normal, we obtain the probi1 model. Initially, such RUM were cstumlcd ba.<ed on observing (I) the product feamres of existing produc~< and (2) lhc choices made by individual consumers. Because such panwonhs are "revealed" by the marketplace such models became known as '"re\•c.aled preference models."

While RUM models have many advantages, !hey suffer from sample selection bias when the set of ex isling products represenls art cl'ficienr frontier of lhc pnlducl space. Very often, l!he darn upon which RUM are based is highly collinear. If a new product "s1rc1ches" a feature not currently in 1he data., predictions are diflicull. Thus, RUM models have been extended to sU\lcd preferences in which the researcher creates product profiles 10 span the set of feature combinations. The respondent's task is redefined ns a choice among product profiles (cf. Louviere, Hen~her. and Swait 2000). In this form. RUM models ha\'C all the charac1erist.ics of coojoint analysis, except thal !he data collection fonnal is varied. (See Figure 6-2b.) Specifically, rather 1han mnking or rating the full product profiles, respondents are asked 10 choose one pl'ofi lc from each choice sel. Each respondent sees muhiple choice sets and, usually, 1he expcrimentul design is completed across many respondents. A nul 1 produc1 is often included in 1hc choice sets so 1ha1 forecasts can be calibrated. The pan worths are estimated either with standard RUM analysis (logil or probi1) or. increasingly, with Hierarchical Bayes estimmion.

Unlike OLS estimation. the experimental design thal maximizes efficiency depends upon the parameters of the model, e.g., the panwonhs. Thus. recem papers have explored ··aggregate customization" in which data ""' collected with an initia.I experimental design. parameters an: estimated, and the experimental design is re-opiimiL.ed. See. for example, Huber and Zwerina ( 1996), Arora and lluber (2001). and Sandor and Wedel (2001).

More recenily, polyhedrnl methods h;l\'e been cx1cnded 10 ~ie choic°' based format and provide a means lo customize experimental designs wirhi n respondenls. Early research suggests 1hat, for some levels ol' heterogeneity and for some levels of unccrininty lhc polyhedral melhods produce experimental designs thal Jcoo 10 beuer es1ima1es than those obUlined by aggregate cu,1omiza1ion (Toubio, Simesier. and Hauser 2003).

Co11joilit Analysis, Modeling, Applicario1i.s 153

Self·explicated Methods

In the carpet-deaner example, Green and Wind ~!losed each l'espoodeot's preferences imo partwonhs which represented the values of the various levels of the carpet-cleaner features. However. it is possible to compose preferences by asking respondents questions about the features themsel ves. Such compositional methods require two types of questions. Fll'St, the respondent must provide the relative value of each level within a feature and, second, provide the relative value of the features. Figure 6-2c provides examples of the latter.

In 1heory, it should be difficult for respondents to provide such judgments, but empirical experience suggests that they are quite accurate. For example, one conjoint method, Casemap, relies emirely on self-explicated judgments and has prMen to predict well (Bucklin and Srinivasan 199 1; Srinivasan 1988; Srinivasan and Wyne1· 1988). For an interesting review of self-explicated models, see Wilkie and Pessemier ( 1973) and for a comparison of alternative formats, see Griffin and Hauser (l 993).

Self-explicated methods have also proven powerful when used in conjunction with decompositional methods. For example, Green has used self· explicated methods effectively in hybrid conjoint analysis - a method in which each respondent's self-explicated partworths modify overall pa11wonhs that are e~timated with an experimental de.sign that is blockecJ across respondents. ACA, reviewed earlier, is another hybrid in which self· explicated and metric partial profile datn are combined effectively to enhance accuracy.

Configurators

Configurators represent a relatively recent form of conjoint-analysis data. With configurators, the respondent is gjven the choice of all levels of all features and uses a Web interface to selecl his or her prefen'ed set of fearures. For example, at Dell.com potential computer purchasers "configure" their machine by choosing memory, processor speed, peripherals, and other features. Figure 6-2d is an example of a configurator for laptop computer bags. The form of data C-Ollection is relatively new. Applications include Franke and von Hippcl (2002), Liechcy, Ramaswamy, and Cohen (2001), Urban and Hauser (2002) and von Hippe! (2001).

Estimation Methods

Be<:auso Green and Wind a.~ked their respondents to rank order the eighteen carpet-cleaner profiles, the natural choice for estimation was monotonic regression. Since 1975, re.searchers have expanded greatly the

154 Marlwri11g Research and Modeling

repertoire of estimation tools. We review here five classes of es1irnation methods.

Reg~ssion·Baud Methods

TI1e bnsic conjoint problem is to eMimllle the panwonhs that best explain the overall preference judgments made by re-<p<mdents. If the preference judgment is an approximately intcrvnl senle, then the partwonhs c.m be represented by dummy variables and ordinary least-squares (OLS) regression is a nnturnl and relntively straightforward means with which to estimate the partworths.1 If the data are only monotonic. then the least·squares criterion is replaced with a "stress" criterion. Further. if there are known constraints, such as the constraint that a lower price is preferred 10 a higher price, then such constraints can be added to either the metric or monotonic regn:...,ions. One panicularly interesting form of regre.<sion is the Linmap algorithm (Srinivasan and Shocker 1973a. 1973b). In Linmap. the profile ranks are convened lo pairwiM: ranks and the r.,,'Ulting inequality constraints are noted. A linear loss function is dclincd such that any violations or the constraints are weighted by the mngnimde of the violation and ru linear program is used to minimize the sum or these violations. Not only has Linmap proven accurate in a number of applications, but it provides a natural structure to handle constraints.

The advantages of tbe regression-based methods are their simplicity and the wide availability of software with which to perform estimation» tr all the appropriate normality assumptions are ""tislied, lben regression may be the most efficient. Howe'"'· regre&Sion requires at least as many observations as parameters. This prc.<ents a real challenge with large conjoint designs (many features and levels}. In some cases respondent fatigue suggests much smaller designs. Even \Vhen the number of observations exceeds the number of parameters, the number of degrees of freedom may not be sufficielll for good estimat ion. Fonunately, researchers have mitigated this problem by combining data from self-explicated preferences with data from either full- or panial·profile methods (Green 1984; Johnson 1987). Such hybrid methods have been used very successfully in large conjoint applications (e.g .. Wind et al. 1989).

Rcurdorn·Utiliry Mathis

When the data are choice-based (CBC), researchers have turned 10

random-utility models (RUM). The basic idea is that the assumption of utility maximization combined with distributional a.~sumplions on the unobserved errors implies a known function thlll maps the partworlh levels onto the probabilities that each prolile is chosen from a given choice set. Many specificmions of RUM lend themselves nicely to maximum-likelihood estimation (MLE). The most conunon models are the logil model (Gumbel

Conjoint Analysis, Modeling, Applicatimu 155

errors), the probit model (multivariate nonnal errors), and the nested-logit model (genernlized extreme value errors). See Ben-Akiva and Lerman (1985), Louviere, Hensher, and Swait (2000), or McFadden (2000).

The advantages of RUM models are that they are derived from transparent assumptions about utility maximization, Lhat they lend themselves naturaUy to efficient MLE estimation, that estimation software is widely available, and that they are a natural means to estimate partworths from choice-based data. Not only have they proven accurate, but Louviere, Hensher and Swait (2000) review sixteen empirical studies in marketing, transportation, and environmental valuation in which stated-choice models (CBC) provide estimates similar 10 those obtained by revealed preference choice models.2 The disadvantage of the RUM models is that, prior 10 HB estimation, the number of choice observations required for partworth es Li mation was too Jarge to obtain practical es6rnates for e.ach respondent. Most experimental designs are blocked. across respondents. However, like regression-based hybrids, this, 100, can be mitigated with lhc judicious use of self-explicated imporcances (Ter Hofstede, Kim, and Wedel 2002).

Hierarchical Bayes Estilna1ion

One of the greatest practical challenges in conjoint analysis is to get sufficient data for partworth estimates with relacively few questions. This leads to tension in the experimental desigit. The researcher would like partworth estimates for each respondent so that (I) he or she could captu1'e the heterogeneity of preferences, (2) design a product line, and (3) segment the market if necessary. On the other nand, if the respondent is asked too many questions, the respondent might become fatigued and either quit the interview, especially in Web-based formats, or provide data that are extremely noisy.

Hierarchical Bayes (HB) estimation add~sses this tension in at least three ways. First, HB recognizes that the researcher's goals can be achieved if he or she kno"vs Lhe disuibu1ion of partw<>rths. Second, \vhile consumer,.; ar~ heterogeneous, there is information in Lhc populalion distribution that can be used to constrain the estimates of the partworths for each respondent. And, third, prior information and beliefs can be used effectively. In addition, the philosophy is changed slightly. T.he researcher does not attempt to estimarc point-values of the paitwo11hs, but endeavors 10 fully characterize the uncertainty about those estimates (mean and posterior distribution).

The basic idea behind HB is quite simple. For each respondem, the uncertainty about that respondent's pal't worths is characterized by a known distribution. However, the parameters of that distribution are themselves distributed across the population (hence the hierarchy). We then establish prior beliefs and update those beliefs based on the data and Bayes theorem. The challenge is that the e<Juations do nor lend themselves to simple

156 Marketing Research and Modeling

analytical solmions. Fo11unntely, with the aid of Gihhs sampling and the Metropolis Hastings Algorithm, it is feasible to obtain updates for the specified parameters (Allenby and Rossi 1999; Arora, Allenby, and Ginter 1998; Johnson 1999; Lenk et al. J 996; Liechty, Ramaswamy, and Cohen 2001; Sawtooth Software 1999). HB estimates have proven quite accurate in simulation and in empirical applications (Andrews, Ansari, and Currim 2002; Lenk et al. 1996, Toubia et al. 2003). Hierarchical Bayes estimates appear particularly useful for situations in which the paJ1woJ1hs are relatively homogeneQus and/or there is significant response errors (Toubia, Simester, Hauser, and Dahan 2003; Toubia, Hauser. and Simester 2003).

The details of HB estimation are beyond the scope of this paper. However, we note that HB estimation has been applied to all forms of conjoint analysis tfata collection. For example, although ACA uses a form of OLS for intermediate estimates and FastPace uses analytic-center methods for intermediate estimates, both have used HB successfully 10 re-estimate part worths after all data have been collected.

Direcl Computation Based on Self-Explicated /111poru111ces

In methods such as Casemap, tJie partworths are computed directly. In addition, as discussed above, such direct computations can be combined with other fonns of estimation.

Es1imario11 Based 011 New Oplimization Meth0<ls

ln the last few years, researchers have recognized the power of new optimization methods. These optimization methods run extremely fast on today's computers and provide the means to do extensive computations between questions (for intennediate estimates) or after all the data arc collected (for revised estimates). Th~rc are many such approaches. We review three.

A1ialy1ic~ce111er estinzation. \Vhen there are fe\ver que.stions than there are partwo11hs to be estimated, the questions can be viewed as constraints on the parameter space. The resulting feasible region is a multidimensional polyhedron. One estimate is the center of the polyhedron. Such estimates arc justified based (>n either uniform priors or the proven (local) robustness of equally-weighted models (Dawes and Con·igan 1974; Einhorn 197 1; Huber 1975; Moore and Semenik 1988; Srinivasan and Park 1997). Although computing the true center of a polylnedmn i• computationally inrmctable, the analytic center provides an extremely close approximation and can he computed rapidly (Freund 1993; Ne.1terov and Nemirovskii 1994; Sonncvend I985a, J985b; and Vaidja 1989).l Furthermore. for state-preference data, tbe analytic-center is analogous to a maximum-likelihood criterion. For the

Ca11joi111 A1111/ysis, Modeling, Applicati,,ns 157

specific algorithm, and methods to handle response error.; for metric-pairs data, see Toubia, Simester, Hauser, and Dahan (2003). For methods based on stated-preference data. see Toubia, Hauser, and Simester (2003). Simulations suggest that AC estimation is quite accurate and provide$ relative advantages when the partworths are heterogeneous and/or response errors are not too large. It is particularly usefu l for estimates when there are fewer questions than there are parameters.

Suppart·vec1or machi11es. One challenge in conjoint has been the specification of the preference function. If each pair or features is not preferentially independent of its complernem set, then the preference function is not separable. However, estimating all interactions often requires more data than are feasible to collect. Evgeniou, Boussios, and Z1charia (2002) propose a solution using support-vector machi'1es (SVM). SVMs are common in machine learning and artificial intelligence. The basic idea is to create new variables to represent both interactions and non-linearities, bur to write the function as linear in its parameters. This leads to a large number of parameters to be estimated. However, SVM machines control for this complexity either by imposing a conslraint on the sum of squares of the linear parameters or using this sum of squares in the objective function. A quadm1ic program then identifies the key par-41ne1ers. Early applications suggest strong promise for the method.

Genetic algorithms. Conjoint analysis identifies high-potential product concepts by first estimating t11e partworths of the features of those products. Recently, researchers have experimemed with genetic algori1hms to identify those product concepls directly (Affinnova.com). As in conjoint analysis, each product is represented by its features and these fea111res are reinterpreted as "genes." A respondent is shown a representative set of concepts, each of which is a set of genes. The respondent rates the product on a three-point scale (g=n, yellow, red). This rating detennines the likelihood that the product concept will "reproduce" into th.e n)'Xt generntion. TI1en, fol lowing a genetic a.lgorithm, new progeny concepts are generated based on the genes of 1heir parents. These progeny concepts a.-e shown 10 further respondents and the process continues until the populatio11 stabilizes on a small set of product concepts.

CONJOINT ANALYSIS IS ALIVE, WELL, AND GROWING

Little could anyone have known, when Green pioneered conjoin! analysis, that the field would grow to be what it is today. Theory and practice have exploded to address a myriad of issues. But the journey is not over; indeed it has just begun. We arc conlident that the field will continue to be as vibrant for many years to come. With this vibr-.1ncy come challenges. We J'eview a

158 Marketing Research 01ul Modeling

few of those challenges here, arrJnged! by pragmatic issues, conceptt11tl issues, and methodological issues.

Pragmatic Issues

Conj oint analysis ha.'> solved many managerial problems and will continue to do $0. Such applications encourage a focus on both expanding 1he frontier of capabi lities and 011 ttadeoffs along that frontier. Some of these pragmatic issues include the following:

l. Analysis of tradeoffs between complexity of analysis, cost and difficulty of data collection, and managerial application. Currently, no method dominates in all situations with each method providing both str·engths and weak.nesses. To date there is no comprehensive theory to guide decisions among methods.

2. Matching analysis methods to new fonns of data collection, including Web-based methods, rich multimedia representations, configurmors (e.g., Dell.com) and computational applets that run during data collection. With more computing power available during data col1ection, ne\v heuristics, ne\v 1nethods, and ne\v representations are nO\\.' te:tsible.

3. Meta-analyses of the varied applications under a variety of managerial problems, e.g., tourism, entertainment, health maintenance, gambl ing, development of complex products and syslcms, legal disputes, and corporate acquisitions. There arc literally hundreds, perhaps thousands, of applications completed each year. Meta-analyses of these applications could raise interesting research hypotheses.

4. Comparative empirical studies of the reliability and validity including internal validity, convergent vaJjdity, and external validity. Jt is common to test internal \•alidity (e.g., holdoul profiles), btit much less common to test external validity. More importantly, there is ample opportunity to test the comparative strengths of the various methods.

5. Methods to handle larger numbers of features, especially, for use in the new product development processes. Complex products such as automobile.~ and office equipment (e.g., copiers) often require consumer information on hundreds of features. More importantly, the fuzzy from end of product development is focused on screening large nun1bers of pocentiaJ features to identify opportunities. New methods such as HB, polyhedral methods. and hybrid methods have greatly expanded the data collection capabilities of conjoint analysis. But industry demands continue for even larger numbers of features and levels.

Conjoint Analysis, Modeling, Applications 159

Conceptual Issues

It is common in any scientific field that new applications and new challenges spawn new 1heory. This is cenainly true in the field of conjoin! analysis. We cite here but a few of 1he conceptual issues.

I. One of 1he mos1 hotly debated issues in the fie ld is the relative merits of the various darn-collection methods. We see substantial oppo1tunities for an underlying theory coupled with empirical tesls t.o explore which situations favor one or more of the various forms of data collection including full-prolile ratings, (metric) paired comparison data, self-explicated data, and (quanta!) stated preference.

2. Price plays a special role in consumer preferences. It is not a feature of a product per se, but rather that which the consumer pays in return for features. It can be a signal, interact with the price..; of other produc1s. and be a straLegic weapon. See, for example, Rao and Sattler (2000) and Foutz, Rao, and Yang (2002). Among the many price-related issues are:

a. Effects of reference points on partworth measurement and evaluation

b. Relative accuracy of price parrwonhs (across methods and data collection) and their relationship to pticing decisions

3. Conjoint analysis provides an exacting measurement of consumer preferences, but to desjgn a product or set marketing variables a firrn musl often do so in light of the actions and pOlCnlial acLions of its competitors. We arc now beginning to see e.quilibrium (or non-equilibrium) models, which include the reactions of firms, competitors, and customers, coupled lo conjoint analyses. One example is Kadiyali, Sudhir. and Rao (2001).

4. Conjoint analysis is based On measurements that inform respondent~ about product features. However, in real markets such information diffuse.~ and does not happen instantaneously. Thus, we expect further development of methods rhat combine the diffusion of information among customers with models of how customers will choose based on that information and with models of how markets will evolve.

S. Conjoin! analysis is based on consumer measurement. But consumer rneasuremenl n1eans real consu1ners ru1s,vering questions about potential beliavior in situations that may differ from the situation of the measurement. This opens opportunities for research on learning, wear--0ul, self-percept.ion biases, and other phenomena such as task presentation and task order.

160 Marketing Research amt Modeling

Methodological Issues

As application and theory advance, so will methodology. Today we can handle larger designs, with more complex rnsks . and more relevant stimuli. These advancements will continue. Among the methodological issues are:

1. With the advent of Web-ba.~cd interviewing, each consumer can be asked multiple types of questions. We can also imagine studies in which the type of question is varied across respondents. Hybrid method~ such as Green's Hybrid Conjoint Analysis and Johnson's Adaptive Conjoint Analysis have been successful. We anticipate further exploration of hyhrid methods that combine data from multiple data sources.

2. A related issue is the use of information from other respondents to inform each responde:nt' s partworth estimates. This includes methods such as:

a. Hyb1id Conjoinl approache.~ b. Hierarchical Bayes methods c. Classical Bayes methods to combine population data with

individual respondent estimation. d. Use aggregate market shares and product archeology( e.g.,

see the models proposed by Berry. Levinsohn, and Pakcs I 995, L 998).

3. Improved methods for adaptive data collection based on data from either prior resporadents (aggregate customization). prior questions, or both.

4. Many new methods have been proposed in the last few years. There are ample researcll opportunities to evaluate these many methods including:

a. Support-vector machines for higher-level interactions b. Genetic algorithms for question design c. Data tries for adaptive full profile casks d. Polyhedral question design for CBC and for metric paired

co1nparisons e. Analytic cen(er estimation f. Neural net\\IOrks for improved estimation g. Genetic programming methods for analysis (Ko1..a 1992) h. Bayesian methods to "listen in" on trusted Internet

agents. 5. And, finally. managers are always seeking insight with which to

make cost vs. benefit tradeoffs. This includes the analysis of the value of sample information 10 effect tradeoffs between the cost of a study and the value of the study. This is particularly relevant in the early stages of product development.

Conjoint Arl(J/y>i.., Modeling, Applico1io11s 161

CONCLUDING THOUGHTS

Thiny years ago, in the rime before lime, or at least before lhe PC, he took peo in hand and scribbled a few equal ions. Conjoin! analysis was born. Looking back, we can simply say 1ha1 we've come a long way, bul 1ha1 lhc journey con1inucs. And Paul Green will continue to lead the way.

NOTllS

1 Naturally. thctc Is dependence among the dummy variables foe a fc:awre. One value can be SCI llrbitrnril)'.

2 By Jimilar. we me1n simihar nlalnY ~.rues or1hc pan"''Ol'ths. Stated-preference partWC111hs may llCC>d 10 be """"led for choire predoruoou If lhcy on: to provide Ille wne prediction< ,., rcl'<31cd·prcf_,.,, models (1..ou•iere. J lensher. and Swait 2000~ h depend• oa Ille a:pplication.

1 The analydc center ii; lhe poin1 tbot minint.ius !he geo1nl!lric ITIC81) of lbc dislances to lhc fr1ce5 of Ille polyhedron.

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