Combining sources of preference data

Journal of Econometrics 89 (1999) 197—221

Combining sources of preference data David Hensher , Jordan Louviere
, Joffre Swait* Graduate School of Business, The University of Sydney, Sydney, NSW 2006, Australia
Department of Marketing, The University of Sydney, Sydney, NSW 2006, Australia  Advanis Inc., 12 W. University Ave., C205, Gainesville, FL 32601, USA  College of Business Administration, University of Florida, FL, USA

Abstract This paper brings together several research streams and concepts that have been evolving in random utility choice theory: (1) it reviews the literature on stated preference (SP) elicitation methods and introduces the concept of testing data generation process invariance across SP and revealed preference (RP) choice data sources; (2) it describes the evolution of discrete choice models within the random utility family, where progressively more behavioural realism is being achieved by relaxing strong assumptions on the role of the variance structure (specifically, heteroscedasticity) of the unobserved effects, a topic central to the issue of combining multiple data sources; (3) particular choice model formulations incorporating heteroscedastic effects are presented, discussed and applied to data. The rich insights possible from modelling heteroscedasticity in choice processes are illustrated in the empirical application, highlighting its relevance to issues of data combination and taste heterogeneity.  1999 Elsevier Science S.A. All rights reserved. JEL classification: C25 Keywords: Choice data combination; Choice models; Stated preference; Heteroscedasticity; Discrete Regression; Qualitative Choice Models

1. Introduction Economists have traditionally focused on the actual market behaviour of economic agents for both theory inspiration and testing. Despite this traditional

* Correspondence address: Advanis Inc., 12 W. University Ave. C205, Gainesville, FL 32601, USA. E-mail: Joffre—[email protected] 0304-4076/99/$ — see front matter  1999 Elsevier Science S.A. All rights reserved. PII: S 0 3 0 4 - 4 0 7 6 ( 9 8 ) 0 0 0 6 1 - X

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interest (e.g., Lancaster, 1996; McFadden, 1981) in what the literature terms revealed preference (RP) data, there are compelling reasons why economists also should be interested in stated preference (SP) data. SP data involve choices by the same economic agents, but evoked in hypothetical markets for reasons such as these: 1. Firms need to model demand for new products with new attributes or features for which there is no RP history, and/or for which one cannot safely forecast by analogy to existing products. 2. Key RP explanatory variables may exhibit little or no variability, and/or be highly collinear. Often collinearity arises from two interrelated sources: (a) market technology, which drives correlations among some product attributes and limits ranges over which they vary; and (b) market forces, which encourage competitors to offer similar attribute levels, or at least restricts ranges on certain attributes. Market forces also encourage negative correlations between attributes for a given efficient frontier, hence, some attributes may be perfectly correlated and/or linear combinations of other attributes, which can lead to identification problems. 3. As markets evolve and change, attributes previously not present may be introduced to influence choices. For example, PCs offer many new features unavailable five years ago, and these features not only may drive current choices but also may appeal to different market segments. 4. Often RP data fail to satisfy model assumptions and/or contain statistical quirks. Even with more powerful statistical tools and models, one imposes maintained assumptions to analyse data. Failure to satisfy assumptions often leads to bias, which may be ameliorated with SP data or a combined RP/SP data strategy. 5. In contrast to RP data, SP data may be less time and money intensive to collect. 6. Some products are not traded in real markets, and although RP data can be used for indirect inference in some cases, such as ‘travel cost’ methods used to model environmental impacts (Englin and Cameron, 1996), RP data often do not exist (see Hanemann and Kanninen, 1997). By definition, RP data help illuminate preferences within existing or recent past market and technology structures. Although SP data may also be useful in this way, they provide insights into how preferences are likely to respond to shifts in technological frontiers. The latter use of SP data is exploited by many academic and applied researchers, and often plays a key role in informing corporate and marketing strategy. That is, understanding and predicting consumer responses to new product introductions, line extensions, etc., involve modelling likely demand and cannibalisation effects, identifying appropriate target markets, segments, etc. Such strategic decisions typically involve

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significant uncertainties, which motivated initial and continuing interest in SP methods and models in marketing. These observations therefore suggest that RP and SP data sources have complementary strengths and weaknesses which potentially can be exploited to enhance understanding of preference processes. Thus, not surprisingly, interest in combining RP and SP choice data (and, more generally, preference data) has been growing steadily in transportation, marketing and resource economics since 1991 (e.g. Ben-Akiva and Morikawa, 1991; Swait and Louviere, 1993; Adamowicz et al., 1994, 1996). Therefore, the objectives of this paper are to: 1. review and discuss some key developments and advances in this stream of research; 2. present a select set of model specifications that incorporate different error structure assumptions, which lie at the heart of the data combination process, and discuss their associated parameter estimation and testing issues; 3. exemplify the types of insights that may be obtained from data combination exercises, via an empirical illustration; and 4. present and discuss conclusions and research implications arising from this stream of research.

2. Decision making and choice behaviour 2.1. Conceptual framework The marketing discipline has developed a working model of consumer decision making that is loosely structured as follows. Consumers first become aware of needs and/or problems, and then search for information about products/services that could satisfy their need(s)/solve their problems. As consumers learn about products, product attributes and attribute levels, and associated uncertainties, they form beliefs about products. Eventually, they have sufficient information to form a decision strategy (or utility function) for valuing and trading off various product attributes. Once consumers have beliefs or priors about attributes possessed by product alternatives, they develop preference orderings for products; and depending upon budget and/or other constraints or considerations, decide whether to purchase/choose, and if they purchase/choose, which one or more alternatives, in what quantities, how often, etc. Fig. 1 formalises the stages which consumers go through to form utilities or values and compare products to form overall (holistic) preferences for available sets of alternatives. The stages form a series of interrelated processes, which are consistent with economic theory and random utility operationalisation of decision processes. Importantly, the conceptual framework shows that one can ‘mix and match’ measures from different stages in the process to explain choice

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Fig. 1. Functional relationships implied by the framework.

behaviour. In this way, explanatory variables at one stage can serve as instruments or ‘proxy’ variables for measures at other stages, which can reduce specification errors and/or improve estimation efficiency. The framework also suggests that choices can be explained by direct observation/measurement of physical product attributes and/or managerial actions like advertising expenditures or price promotions (the vector X), but such direct estimation may obscure important intermediate processes and/or overlook the potential role of intermediate models and measures. The advantage of the latter integration is that one can explain choice behaviour in terms of 1. 2. 3. 4. 5.

individual characteristics/differences (Z’s), physically observable and measurable (engineering) variables (X’s), psychophysical variables (beliefs/product positions) (S’s), part-worth utility measures (v’s), or holistic measures of each alternative’s utility (»’s).

SP methods primarily have been used to model processes involved in stages 2—6, although it is worth noting that there has been an enormous amount of research in psychology and neurophysiology involving stage 1 (called psychophyics, or mapping physical reality into perceptions). Econometricians are probably less familiar with SP methods and models used to study, explain and model these intermediate processes. Thus, a brief overview of SP methods and models seems apropos. Our review emphasises SP methods and models in marketing, and concentrates on recent research on combining sources of preference data to enhance our ability to explain and model the links implied in Fig. 1.

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2.2. Brief overview of SP methods and models The SP methods and models literature is large and spread over several fields, but psychology and marketing arguably contain the material likely to be of most interest to econometricians. Although there are many SP paradigms, we focus on work related to random utility theory (RUT) choice models. RUT was first proposed by Thurstone (1927) as a way to model choices of pairs of alternatives. McFadden (1974) extended RUT to the multiple choice case, although fixed (as opposed to random) utility multiple choice models were developed earlier (e.g., Luce, 1959; Restle, 1961; Rushton, 1969). Academic marketing’s interest in SP models primarily is concentrated in two research streams: (a) conjoint analysis (CA) and related work on modelling consumer tradeoffs and preferences (e.g., Green and Wind, 1971; Green and Srinivasan, 1978, 1990; Louviere, 1974, 1988a, 1994, 1995); and (b) behavioural decision theory (BDT) in marketing, psychology and economics, which seeks deeper understanding of process and more behaviourally realistic models of decision processes (e.g., Meyer et al., 1984; Kahneman and Tversky, 1979, 1984; Keller, 1993). It is fair to say that much BDT research is incompatible with RUT, and has little intellectual commonality with research on modelling preferences in econometrics and economics; consequently, we focus on the first research stream. Conjoint analysis and related techniques are used to measure and model consumer tradeoffs, preferences and choices. The origins of these methods are axiomatic conjoint measurement, utility theory and risky decision making (e.g., Krantz and Tversky, 1971; Krantz et al., 1971; Machina, 1987), but few papers in this stream in marketing involve risky decision making (e.g., Louviere, 1988a). As well, great emphasis has been placed on practical application and prediction instead of process explanations (but see Lynch, 1985); hence, much of the published work in marketing eschews behavioural theory in favour of ad hoc statistical methods. However, conjoint analysis recently has been recast in a more behavioural framework consistent with RUT and RUT-based choice models (Louviere, 1988b, 1994, 1995). This more recent stream of research comprises the remainder of our overview, but we first briefly explain conjoint analysis as typically practiced by marketing academics and professionals. CA is a family of preference elicitation procedures that involves the following series of design and analysis steps: (a) identification (to the extent possible) of an underlying set of product attributes that drive choice in particular applications, (b) assignment of levels to each attribute to represent ranges of likely variation expected during a period of interest, (c) use of experimental design techniques to combine attribute levels into multi-attribute descriptions or ‘product profiles’, (d) evaluation of the product profiles by consumers sampled from a target market of interest (usually evaluating profiles on rating scales), (e) analysis of

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each sampled consumer’s profile rating data to estimate individual-specific models (usually via OLS regression) and (f) using the resulting equations to predict the choices expected for various scenarios of policy interest (usually predicting that alternatives with the highest predicted regression scores will be chosen). There are many variations on this general theme, including more recent methods that employ multiple choice experiments and use RUT-based discrete choice models to analyse the resulting data and make predictions using microsimulation methods (Louviere and Woodworth, 1983; Louviere, 1994), but the preceding description is fairly close to the mark. To date little academic research in marketing concerned with CA or BDT has evinced interest in developing formal links with theory in economics and/ or real market behaviour, although lip service sometimes is paid to Lancaster (1966) product characteristics framework by CA adherents. In contrast, research into preference elicitation procedures consistent with RUT has tried to forge such conceptual and empirical links (e.g., Louviere and Hensher, 1983; Louviere and Woodworth, 1983; Hensher and Louviere, 1983; Louviere, 1988a,b; Louviere, 1994, 1995; Hensher, 1994; Swait and Louviere, 1993; Swait et al., 1993; Adamowicz et al., 1994, 1996). Indeed, since the early 1980s marketing and transportation researchers steadily have increased our understanding of the links between traditional RP models and measures and their SP counterparts. In fact, it is now fair to say that these links are reasonably well understood, and that (with some exceptions) it is possible to design research to obtain SP data that parallel RP data in most details. By way of contrast, traditional CA and much of BDT research involves evaluation or decision tasks that bear little resemblance to choice situations faced by real consumers. For example, traditional CA typically relies on elicitation tasks that involve one-at-a-time ratings of product profiles. Such tasks may indeed elicit preferences, but they have no counterpart in consumer behaviour in real markets. Similarly, many BDT tasks involve the study of obtuse lowdimensional gambles, which often have only vague connections to real market choices. Researchers involved in the development and application of RUTbased preference elicitation methods, on the other hand, often seek to develop experiments and tasks that resemble their real market counterparts in as many essential details as possible. This has led to the development of new design theory for these types of discrete multiple choice problems (e.g., Louviere and Woodworth, 1983; Huber and Zwerina, 1996). Thus, it is fair to say that at the present time the primary difference between more traditional RP econometric methods and models and the more recent RUT-based SP methods and models is primarily the data generation processes. Specifically, RUT-SP theory and analysis methods are identical to those that underlie the econometric analysis of cross-sectional and longitudinal discrete choices or other preference data consistent with RUT (e.g., ordered outcomes,

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complete rankings, joint continuous-discrete and other selection problems, etc.). Perhaps more importantly, recognition of this isomorphism between methods and models used to obtain and analyse RUT-based RP and SP data has spurred academic and applied interest in combining sources of preference data (e.g., Morikawa, 1989; Ben-Akiva and Morikawa, 1991; Swait and Louviere, 1993; Swait et al., 1993; Swait et al., 1994; Adamowicz et al., 1994, 1996; Hensher and Bradley, 1993; Louviere, 1994, 1995). This recent research interest and the resulting paradigm associated with it are the focus of our paper, and are discussed in Section 3. The isomorphism of RUT-based RP and SP data has evolved from advances in RUT-based SP choice modelling theory and methods. Although it is well established that RUT-based discrete choice SP models can be estimated from experiments involving choices among pairs of options (e.g., Thurstone, 1927), a more general experimental basis was established only recently in marketing and transport. Specifically, Louviere and Woodworth (1983) in marketing, and Hensher and Louviere (1983) in transport pioneered a general approach to design and analyse discrete choice experiments based on McFadden’s (1974) extension of RUT to the multiple choice case. More recently, there has been further progress on design theory for SP choice experiments (e.g., Hensher and Barnard, 1990; Anderson and Wiley, 1992; Bunch et al., 1996; Huber and Zwerina, 1996), but much more research is needed. In particular, the design issues in choice experiments are (a) identification, (b) precision, (c) realism and (d) cognitive limitations. Identification refers to the possible forms of utility functions that can be identified (tested) from a given experiment under a maintained hypothesis about a choice model form (e.g., Multinomial Logit, Multinomial Probit). Precision refers to the efficiency of the estimates, given a functional form and maintained choice model hypothesis. Realism is the degree to which the experiment mirrors real marketplace choices, and cognitive limits refers to complexity and task demands. Typically, one tries to maximise identification, minimise standard errors, and maximise realism subject to management of complexity at levels that do not compromise data quality (see Swait and Adamowicz, 1997). Naturally, applied work requires compromise among these objectives. Choice experiments are particular types of experimental designs that take identification and precision into account. A choice experiment consists of one or more sets of mutually exclusive, competing choice alternatives, which can be designed sequentially or simultaneously (Louviere, 1988a, 1994), the latter being far more common than the former: E Sequential design: First, designs one or more sets of choice alternatives (often product profiles as in CA) with desirable utility function identification properties, and then assigns them to choice sets such that choice model properties and desired levels of precision are satisfied. For example, if one wishes to

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study how consumers choose from choice sets that consist of a fixed set of three competing options in a particular market, one could develop a sequential design as follows: (a) design three statistically equivalent sets of P total product profiles (attribute level combinations), (b) place each set of P profiles in three separate ‘urns’ and (c) simultaneously sample one profile randomly from each urn without replacement to create P total choice sets with three choice options. If the number of sets is sufficiently large, asymptotic properties of particular discrete choice models should be satisfied; and taken as a whole, the choice sets should have desirable statistical properties. This approach is relatively easy to implement, but cannot insure identification or precision levels without large numbers of sets. E Simultaneous design: If there are N choice alternatives, and each has M attributes with exactly ¸ levels, one can design experiments that satisfy the statistical properties of the most general member of the logistic regression family (i.e., ‘Mother Logit’ — McFadden et al., 1977) by treating all attributes of all alternatives as a collective factorial (i.e., ¸+,) and selecting the smallest orthogonal main-effects design from the full factorial. This insures that the marginals (i.e., alternative-specific and/or generic parameters) are orthogonal within and between choice alternatives, which satisfies the necessary and sufficient conditions to estimate the parameters of a Mother Logit model. Mother Logit models include ‘cross-effects’ of attributes of one alternative in the utility function of a second alternative, thus allowing violations of the IID property of RUT choice models (Louviere and Woodworth, 1983; McFadden, 1981). Such a design allows one to estimate own-attribute and cross-attribute effects independently, which in turn allows one to relax the IID assumption in the basic MNL model derivation and permits estimation of more complex model forms. There are other ways to design choice experiments (e.g., 2, designs, Louviere and Woodworth, 1983), but the above encompasses much of the state of the art. Generally speaking, designs differ in (a) ability to capture utility function complexity (i.e., non-linearities and/or non-additivities), (b) number of alternatives, (c) number of attributes per alternative and (d) types of IID violations accommodated (Louviere and Woodworth, 1983; Louviere, 1988a,b; Louviere, 1994, 1995; Carson et al., 1994). It is fair to say that research on the design of RUT-based choice experiments is in its infancy, and although much has been learned, much more research is needed to fully illuminate properties of designs and develop optimally efficient designs for a wide variety of non-IID error choice processes. Specifically, there now exist a variety of ways to design choice experiments consistent with simple MNL choice processes, and progress has been made in the design of more complex experiments which relax IID error assumptions. However, little work is available to guide design selection for particular problems, because choice models are non-linear, and design

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optimisation requires a priori knowledge of true probabilities. That is, we know that certain types of designs are consistent with various choice process models like MNL. However, we do not yet understand how statistically efficient such designs may be for particular applications, nor how to optimise these designs for particular applications except in limited circumstances involving small numbers of alternatives and attributes (see Bunch et al., 1996; Carson et al., 1994).

3. The theory of choice data combination 3.1. The fundamental identification problem: inseparability of taste and scale It is well known that the scale of the estimated parameters and the magnitude of the random component in all choice models based on random utility theory (RUT) are linked (see, e.g., Hensher and Johnson, 1981; Ben-Akiva and Lerman, 1985; Anderson et al., 1992). Let º "» #e , GO GO GO

(1)

where º is the unobserved, latent utility consumer q associates with alternative GO i, » the systematic, quantifiable proportion of utility involving observables of GO alternatives and consumers, and e is the random or unobservable effects GO associated with the utility of alternative i and consumer q. All RUT-based choice models are derived by making assumptions about the distribution of the random effects. Imbedded in all RUT choice models are scale parameters, which are inversely related to the variance of the random component and not identifiable separately from taste parameters. The imbedded scale parameters are a consequence of the distributions assumed. For example, the multinomial logit (MNL) choice model is derived from Eq. (1) by assuming that the e are IID Gumbel distributed. The Gumbel scale GO parameter j*0 is inversely proportional to the standard deviation of the random component (p "nj\6\). The full expression of the MNL choice GO probability is exp (j» ) exp (jbX ) GO " GO , P " GO exp (j» ) exp (jbX ) HZ!L HO HZ!O HO

(2)

where P is the choice probability of alternative i for consumer q, the systematic GO utility » "bX , and b is the vector of taste parameters. Ben-Akiva and GO GO Lerman (1985, Chapter 5) discuss the MNL model in detail and show that the parameter vector estimated from a given source of RUT-conformable preference data is actually (jb), which presents one with an identification problem. A given

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set of data yields some value of j, which can be normalised to a constant (e.g., unity). The analysis proceeds as if (jb) were the taste parameters. A similar identification problem exists for other generalised extreme value (GEV) choice models, such as Nested MNL, tree extreme value and ordered GEV (McFadden, 1981; Small, 1987, 1994), binary logit and probit models, and even MNP (multinomial probit) (e.g., Hausman and Wise, 1978; Daganzo, 1980; Bunch, 1991; Keane, 1995). Such identification problems arise because choice models specify a structural relationship between a categorical response and a latent variable (i.e. utility). Similar to structural equation models involving latent variables (e.g. LISREL), both origin and variance (i.e., ‘scale’) of the latent variable(s) must be specified to identify utility function parameters. Morikawa (1989) noted that the basic scale identification problem applied to a single preference data source, but ratios of j’s in two or more sources of data were identified, which led to sequential (Swait and Louviere, 1993) and simultaneous (Morikawa, 1989; Ben-Akiva and Morikawa, 1991; Hensher and Bradley, 1993; Bhat, 1995) estimation methods for combining RP and SP data sources. Suppose there are K preference data sources to be combined. The estimation problem above involves imposing an equality restriction on the taste parameters of the K preference data sources (i.e. b "2"b "b), and estimation of  ) K!1 additional scale parameters (j ,2, j ). That is, one scale parameter is  ) fixed, say j "1, and the K!1 other parameters are inverse variance ratios  relative to the reference (fixed) data source. The corresponding unrestricted model frees taste parameters and scale factors for the K data sources by estimating (j b ), k"1,2, K. The null hypothesis is taste invariance across I I data sources, after permitting variance/reliability differences, which can be tested using a likelihood ratio statistic, as we later discuss. Increasing recognition of the scale parameter’s role spawned several research streams, most notably (a) ‘data fusion’ in travel demand modelling (e.g., Morikawa, 1989; Ben-Akiva and Morikawa, 1991; Hensher and Bradley, 1993; Swait et al., 1994), and (b) combining, comparing and testing process differences in sources of preference data (e.g., Swait and Louviere, 1993; Louviere et al., 1993; Bradley and Daly, 1994; Louviere, 1994; Louviere, 1995; Swait and Adamowicz, 1997). The latter stream views scale (variance) as an integral feature of behavioural processes, whereas data fusionists seem to see scale as a nuisance

 Note that MNL models predict random choice as jP0, and a step function as jPR (see Ben-Akiva and Lerman, 1985). This general behaviour applies to all choice model specifications.  Let each data source have ¸ taste parameters. Under the null hypothesis, K parameter vectors can be represented in R* as vectors of different lengths dictated by differences in reliability (i.e. more reliable measures correspond to longer vectors) superimposed upon one another. The practical importance of this is that an ¸ component graph of two coefficient vectors that differ only in reliability (variance) should plot as a scatter of points around a straight line passing through the origin. The (positive) slope of this line is the ratio of the respective scale parameters.

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parameter that must be taken into account to estimate true quantities of interest (i.e. taste parameters). The latter stream also holds a more catholic view of preference data combinations and comparisons, such as RP with RP and SP with SP, compared with the data fusionists’ typical interest in joining RP and SP data sources. The key insight that precedes both streams, however, is the role that the error structures of different preference data sources play when combining them. Real decision processes are better described if the analyst recognises the behavioural meaning of traditional statistical constructs such as variance and covariance, scale and taste weights. For example, relaxing the constant error variance assumption on the indirect utility of each alternative in a choice set allows one to avoid this key limitation of MNL models by using variance properties to satisfy a common set of statistical assumptions and combine data from different sources (Morikawa, 1989; Hensher and Bradley, 1993; Swait and Louviere, 1993). Different data collection processes may influence choice variability differentially, and if this is not recognised, may confound the real behavioural role of observed and unobserved influences on choice. The latter can be captured by appropriate specification of the error variance structure. For example, the variance of each alternative can be specified as a function of task complexity (Swait and Adamowicz, 1997) or respondent characteristics which proxy the ability to understand tasks (Bhat, 1996; Hensher, in press). Thus, to summarise: a general view of the data combination problem recognises and accounts for error structure differences between data sources when testing for (or imposing) taste invariance across data sources. Up to this point, the literature has concentrated on modeling the differential variances (i.e. heteroscedasticity) within and between sources (see references above) when combining multiple data sets. The recognition of the role of heteroscedasticity in this research stream has made it synonymous with the concept of combining sources of preference data. 3.2. Some alternative ways to handle heteroscedasticity in choice models A hierarchy of models is evolving to progressively relax some testable assumptions imposed on the error term in utility function (1). We discuss some possible ways to relax the homoscedasticity assumption with respect to e when GO combining sources of preference data, and relax certain other restrictions often imposed on choice models. Our discussion focuses on examples from the GEV family of discrete choice models (all variants of MNL) for cross-sectional choice data, but the general principles and concepts apply equally well to other choice models and data types. 3.2.1. Random effects heteroscedastic extreme value model The constant variance assumption can be relaxed by specifying a more complex choice model called the heteroscedastic extreme value (HEV) model.

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Allenby and Ginter (1995), Bhat (1995) and Hensher (in press) recently estimated HEV models from single-data sources, and Hensher (1998) jointly estimated one from SP and RP data. Assume the utility function is given by Eq. (1), but that errors are independently, but not identically, distributed over alternatives according to a Type I Extreme Value (or Gumbel) density function f (t)"exp (!t)exp (!exp (!j t)), !R(t(R, (3) G G where the j are the respective scale parameters. The errors are, therefore, G independent and heteroscedastic. If the decision rule is maximal utility, then the choice probabilities are given by 



P " “ F(j )[» !» #e ]j f (j e ) de . (4) GO H GO HO GO G G GO GO H$G \ The derivation of this expression is given in Bhat (1995) and Hensher (in press). The HEV model nests the more restrictive MNL, and is sufficiently flexible to allow differential cross-elasticities among all pairs of alternatives, while avoiding the a priori identification of mutually exclusive market partitions in a nested MNL structure. It is parsimonious compared to MNP, adding only J!1 parameters to the covariance matrix compared to an additional [J(J!1)/2]!1 in the more general MNP model (J is the total number of alternatives in the universal choice set). The computational burden is much less than for MNP, as only a one-dimensional integral (independent of the number of alternatives) is evaluated (MNP evaluates a (J!1)-dimensional integral). Importantly, and in contrast to MNP, the HEV model is easy to interpret and its behaviour intuitive (Bhat, 1995). Hensher (in press) suggested that HEV be used to identify appropriate partitionings of MNL models into nested structures, obviating the search for structure in nested MNL partitions. Nested forms of MNL can accommodate systematic dependencies among unobserved effects that drive violations of the independence of irrelevant alternatives (IIA) property in MNL models. HEV is not closed form, but is appealing because a nested model consistent with the HEV profile of j is easy to apply without the numerical integration of expresG sion (4) (see Hensher and Bradley, 1993). HEV models can be specified for multiple data sources, jointly estimated using a FIML approach to produce a set of alternative-specific j’s across both RP and SP choice sets, by normalising on an arbitrarily selected alternative.  The probabilities must be evaluated numerically because there is no closed-form solution for this single-dimensional integral. The integral can be approximated (e.g., by Gauss—Laguerre quadrature, Press et al., 1986), and computational experience suggests a 68 point approximation can accurately reproduce taste parameter estimates (Greene, 1996).

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3.2.2. Parametrised heteroscedastic MNL model Theory can be developed to explain heteroscedasticity structures in preference data of the type described in Eq. (1). For example, advertising exposures may lead to more (or less) variability in the choice behaviour of a population, depending on content. Such effects are captured partially by random effects specifications of scale parameters, but the source of variability is not explicit. It can be made explicit in parametrised heteroscedastic MNL (PHMNL) models (Swait and Adamowicz, 1997; Swait and Stacey, 1996). The PHMNL model scale parameters are given by j "exp (tZ ), GO GO

(5)

where t is a parameter row-vector and Z are covariates associated with the GO individual and the alternative. PHMNL choice probabilities are given by exp (j bX ) GO GO . P " GO exp (j bX ) HZ!O GO HO

(6)

The parameters to be estimated are b and t. PHMNL nests the MNL if t"0. As with the HEV model described previously, PHMNL allows complex crosssubstitution patterns among alternatives, the general structure of which must be specified via Z . GO Swait and Adamowicz (1997) hypothesised that SP task complexity and RP choice environment (e.g., market structure) influence levels of variability in preference data. They also proposed a way to characterise complexity and/or choice environment, which was supported in several SP and the one RP data set utilised. Their complexity measure was constant across alternatives, hence, scale parameters in their model varied across individuals and SP replications, instead of alternatives. They also found that differences in complexity between preference data sources impacted ability to combine RP and SP data. Swait and Stacey (1996) applied PHMNL to scanner panel choice data, allowing variances (i.e. scales) to vary by person, alternative and time period as a function of brand, socio-demographic characteristics, interpurchase time, state dependence, etc. They showed that accounting for non-stationarity of the variance in terms of the explanatory variables Z enhanced panel behaviour GO insights and significantly improved fits relative to models with fixed covariance matrices (e.g., MNL, nested MNL and MNP models).  If scale factors are constant across alternatives the PHMNL model can be derived from a heteroscedasticity argument (Swait and Adamowicz 1997). If scale factors are alternative-specific, it can be derived as a special case of the tree extreme value model (Daly, 1987; McFadden, 1981; Hensher, 1994; Swait and Stacey, 1996). In either case, the final expression for the choice probability is given by (6).

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3.3. Summary Two models were proposed and discussed to relax the constant variance assumption of basic MNL using random effects or parametrised variance functions. Variants of these and other categorical response models can be formulated to deal with specific heteroscedastic violations. The contribution of this discussion was to illustrate general principles of controlling for heteroscedasticity in choice models, a major consideration in combining data sources.

4. Empirical example To make the concepts of the previous sections more concrete, we focus on a data combination exercise involving two sources of data on choices of freight shipper. We use this exercise to examine the impact of error heteroscedasticity within and between data sources, and implications for data combination. 4.1. Description of the data source Data were collected from a random sample of firms located in a single city in North America. A random sample of 500 individuals who made freight shipper choice decisions for their firms in that city were contacted by phone to solicit participation in a follow-up mail survey. The survey obtained three types of information: (1) firm characteristics, used to segment results a posteriori; (2) RP data, in the form of most recent (proportional) carrier choice (eight carriers were available in the city at the time), and an indication of which carriers were actively considered to enable specification of firm-specific choice sets and associated attributes of carriers considered; and (3) SP choice data, elicited via 16 binary choice scenarios given to each respondent. (The reader is referred to Swait et al., 1994 for further information concerning this study.) The SP choice experiment was designed by treating the attributes of both choices as a collective set (i.e., a 8;4;2), and using an orthogonal main effects design to create 80 pairs of attribute descriptions (choice sets). The 80 paired profiles were blocked into five sets of 16 choice sets each, using an extra five-level factor. Thus, each respondent supplied 16 binary choice observations. 4.2. Modelling results Building on utility function (1), we assume that the deterministic utility of source k is given by »I "aI#bIXI , where the a’s are brand-specific constants GO G GO and other quantities as previously defined, k"RP, SP. Our objective is to combine both data sources to estimate a common taste vector, which given the above specification, requires us to test whether b0."b1."b. Note, however,

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that associated with the utility function are corresponding error terms; the scale (i.e. variance) of the utilities in each source may impact acceptance or rejection of the hypothesis of taste homogeneity across sources. Thus, we examine different possible assumptions about the structure of the scale differences within and between data sources, and their impact on the data combination process. Table 1 presents several models, which we discuss in order. Model 1 is an RP Multinomial Logit (MNL) model with homoscedastic error variances (i.e., we assume that j0."1,∀i,q.), arguably the standard model for such a data source. GO Most attribute coefficients are statistically significant and correctly signed, which is somewhat unusual because non-significance and counter-intuitive signs often occur with RP data. Note, however, that two parameters which, respectively, relate to ‘better’ levels of delivery speed and shipment tracing have incorrect negative signs (i.e. b and b ). We comment on this below.   Model 2 is a parametrised heteroscedastic MNL model (PHMNL) for the RP data, which relaxes the homoscedasticity restriction by allowing scale factors for three carriers (A, D and E). Lack of variability in RP attribute levels and sparse choice frequencies discourage identification of scale factors for the other carriers. Thus, the scales of alternatives B, C, F, G and H are set to unity for identification purposes. (NB: the scale of at least one alternative must be fixed to permit identification of the other scale factors.) Using previously introduced notation, in this second model we specify that j0."exp (tZ ), ∀q, (7) GO GO where Z is basically a vector of brand constants and t the vector of coefficients GO in Table 1 (see ‘scale function parameters’). The scale of carrier A relative to B, C, F, G and H is exp(!1.0134)+0.36, which corresponds to a variance of about 12.7 for an assumed Gumbel error variate. Carrier D has an error variance of 3.2, which is about 4 times smaller than that of A. The estimated error variances of the utility of carriers A and D not only differ from one another, but also are significantly larger than for the base group of carriers. On the other hand, carrier E has an estimated relative scale factor (variance) of about 1.26 (1.04), which is approximately equal to that of the base group. The hypothesis that the error variances in the RP data are equal across alternatives is tested by a likelihood ratio test. Comparing Models 1 and 2 in Table 1, the calculated chi-squared statistic is 71.8 (3 degrees of freedom), which is significant at the 95% confidence level. Hence, we conclude that the RP data source exhibits strong evidence of heteroscedastic error structure. Model 3 is the ‘standard’ homoscedastic MNL model for the SP data source (i.e., j1."1, ∀ i, q). It should be noted that almost all parameters are statistically GO significant (due to the controlled design), and all have the right sign. Model 4 is a PHMNL model for the SP data, which reveals that estimated variances for all alternatives are statistically equal (i.e. the elements of t are essentially zero); hence, the SP data seem to satisfy variance homogeneity. In turn, this suggests

Utility function (Taste) parameters Alternative-specific (Carrier) constants RP: Carrier A B C D E F G H SP: Carrier A B C D E F G H Attribute coefficients b (Price Linear)  b (Price Quadratic)  b (RP: Delivery Speed 1) 

Parameter

(5.9) (1.9) (1.5) (1.7) (2.8) (0.1) (1.7)

4.5262 0.6303 0.6150 0.8129 0.8546 0.3033 0.8836 -0-

(3.8) (1.7) (1.6) (1.8) (3.2) (0.8) (2.4)

Model 2 (RP) Alternative-specific variances (t-stats in parentheses)

0.8196 0.1894 0.6371 0.7245 0.4274 0.4484 0.3095 -0-

(4.6) (1.1) (3.8) (4.2) (2.4) (3.1) (1.8)

Model 3 (SP) Homogenous variances (t-stats in parentheses)

0.7512 0.1378 0.6084 0.5893 0.3764 0.4440 0.3839 -0-

(3.2) (0.8) (2.6) (2.5) (1.9) (2.4) (1.5)

Model 4 (SP) Alternative-specific variances (t-stats in parentheses)

!0.0509 (!11.4) !0.0743 (!10.4) !0.0551 (!19.6) !0.0531 (!5.4) 0.0095 (3.5) 0.0124 (3.2) 0.0019 (0.6) 0.0027 (0.9) !0.0982 (!0.9) !0.0088 (!0.1)

1.7303 0.6545 0.5310 0.5176 0.8667 0.0373 0.6058 -0-

Model 1 (RP) Homogenous variances (t-stats in parentheses)

Table 1 Parametrised heteroscedastic MNL model estimation example

(5.0) (1.5) (0.9) (1.9) (2.0) (0.1) (1.2)

(4.8) (1.9) (4.2) (4.3) (2.8) (3.5) (2.5)

0.8415 0.3317 0.8030 0.7366 0.5888 0.5656 0.4136 -03.4672 0.5388 0.4063 0.7777 0.5274 0.2656 0.6058 -0-

(3.8) (1.7) (1.2) (1.8) (1.9) (0.7) (1.7)

(4.2) (1.6) (3.1) (2.9) (2.4) (3.0) (1.7)

Model 6 (RP#SP) Variances between data sources and in parentheses)

1.0677 0.2390 0.9385 0.8713 0.6477 0.6628 0.5199 -04.1653 0.6904 0.6835 0.6811 0.9477 0.2610 0.8179 -0-

(3.8) (2.0) (1.9) (1.4) (3.1) (0.7) (2.2)

(4.0) (1.0) (3.1) (2.7) (2.4) (2.8) (1.4)

Model 7 (RP#SP) Variances between data sources and alternatives (t-stats in parentheses)

!0.0434 (!12.7) !0.0619 (!10.2) !0.0794 (!11.7) 0.0051 (2.8) 0.0075 (2.9) 0.0088 (2.9) 0.2647 (5.3) 0.3835 (4.8) !0.0876 (!0.6)

0.6879 0.2632 0.5424 0.6017 0.3838 0.4042 0.3282 -01.4338 0.4799 0.2938 0.5586 0.5804 0.0242 0.4131 -0-

Model 5 (RP#SP) Variances only between data in parentheses)

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0.2818 (3.3) !0.0025 (0.0) !0.3423 (!5.4) !0.2041 (!2.1) 0.0453 (0.7) 0.0544 (0.6) 0.0298 (0.3) 0.4208 (6.3)

!1.0134 (!5.2) -0-0!0.3341 (!2.4) 0.2316 (1.8) -0-0-0-

!1376.7 0.2484 21

0.2778 (4.5) !0.0439 (!0.6) !0.3023 (!5.8) !0.2545 (!3.3)

0.1437 (2.7)

0.1918 (2.4) 0.0894 (1.2) 0.2123 (4.6)

-0-0-0-0-0-0-0-0-

!1412.6 0.2288 18

!810.2 0.3556 18

-0-0-0-0-0-0-0-0-

(9.6) (4.5) (2.1) (4.0)

(4.7) (3.8) (1.8) (2.8)

!809.3 0.3563 25

0.0733 (0.3) 0.1486 (0.6) 0.0340 (0.1) 0.1390 (0.6) 0.0715 (0.2) !0.0080 (0.0) !0.1073 (!0.4) -0-

0.4325 0.1964 0.1018 0.1661

0.1941 (3.4)

0.1886 (4.2) 0.4478 0.1995 0.1009 0.1827

0.4032 (3.4) 0.3555 (3.4) !0.0975 (!1.2) !0.2074 (!2.5)

0.4362 (5.7) 0.3747 (5.1) !0.1066 (!1.4) !0.2280 (!4.5)

Note: Grey cells denote structurally non-identifiable parameters within specific data source.

b (SP: Delivery Speed 1)  b (Delivery Speed 2)  b (Delivery Speed 3)  b (Pickup Time)  b (RP: Shipment Tracing)  b (SP: Shipment Tracing)  b (RP: European Coverage)  b (SP: European Coverage)  b (Refund Policy)  b (Payment Terms)  b (On Time Reliability)  Scale function parameters (t) SP (1): RP (0) RP: Carrier A B C D E F G H SP: Carrier A B C D E F G H Goodness-of-fit Log Lik. @ conv. McFadden’s o C Parameters !2230.0 0.2781 36

!0.1182 (!0.6) !0.8265 (!4.9) -0-0!0.2940 (!2.1) 0.1481 (1.1) -0-0-00.2025 (0.9) 0.0914 (0.4) !0.0092 (0.0) 0.1330 (0.5) 0.0012 (0.0) 0.0489 (0.2) 0.0529 (0.2) -0-

0.2825 (3.3) -0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0!2256.0 0.2697 26

0.3835 0.3261 (5.4) !0.0932 (!1.5) !0.2425 (!5.4) 0.0796 (1.6) 0.0796 0.3275 (7.7) 0.3275 0.1966 (4.1) 0.0826 (1.7) 0.2583 (6.0)

0.2647 0.2839 (6.7) !0.1003 (!2.2) !0.1906 (!6.1) 0.0677 (2.2) 0.0677 0.2892 (9.3) 0.2892 0.1593 (4.9) 0.0505 (1.6) 0.1619 (5.8)

!2192.5 0.2903 39

!0.3776 (!2.0) !0.9917 (!5.5) -0-0!0.3941 (!2.9) 0.0724 (0.6) -0-0-00.1040 (0.5) 0.1165 (0.5) 0.0071 (0.0) 0.0927 (0.4) 0.0252 (0.1) !0.0108 (!0.1) !0.1178 (!0.5) -0-

0.6401 (5.3) 0.3981 (5.4) !0.0421 (!0.6) !0.3303 (!5.8) !0.2311 (!2.4) 0.2630 (3.4) 0.6543 (7.7) 0.0449 (0.7) 0.2277 (3.9) 0.1368 (2.2) 0.3260 (6.5)

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that unobserved characteristics do not induce different levels of variance in the SP data, in contrast to actual market choice data. As noted before, all parameter signs are correct in the SP data, but two parameters (b and b ) have opposite   signs in the RP data. Of particular concern is that b is statistically significant  and incorrectly signed in the RP model. We now use standard practice to combine both data sources by pooling them under the hypothesis of equal taste parameters but unequal variances between data sources (e.g. Morikawa, 1989; Ben-Akiva and Morikawa, 1991; Hensher and Bradley, 1993; Bradley and Daly, 1994), and ignoring heteroscedastcity within data source. As noted earlier, if this hypothesis holds, a graph of one parameter vector against the second should exhibit a positive, proportional relationship, the slope of which should equal the ratio of variances between the data sources. Fig. 2 graphs Model 1 (RP, constant variance) against Model 3 (SP, constant variance), and reveals that the expected relationship holds for all coefficients except b and b (these have different signs in the two data sets), in   addition to b (this parameter seems of greater relative importance in the SP  than in the RP model). Fig. 2 is insufficient to test the hypothesis of taste equality but data source variance inequality (see Swait and Louviere, 1993). Model 5 in Table 1 tests this standard hypothesis on the pooled RP and SP choice data. The relative scale ratio between the SP and RP data sources is about exp(0.2825), or 1.33, which differs significantly from one at the 95% significance level, and implies that under the maintained hypothesis the variance of the SP was less than that of the RP data. More precisely, the average SP variance is 75% (+1/1.33) of the

Fig. 2. Plot of MNL attribute coefficients (Models 1 and 3).

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average RP variance. The chi-squared statistic for the hypothesis of taste equality and data source variance inequality contrasts Model 5 to Models 1 and 3, and equals 66.4 ("!2[!1412.6!810.2!(!2256.0)]) with 10 degrees of freedom; hence, the standard pooling hypothesis is rejected at the 95% confidence level. Fig. 2 suggests that the rejection is due in part to parameter sign reversals. However, our prior analysis also suggests that variance differences between alternatives also may be responsible. The latter conjecture is supported by Model 6 (Table 1), which allows alternative-specific scale effects within data sources. Compared to Models 2 and 4, which both allow within-data source alternative-specific variance differences, the chi-squared statistic for Model 6 is 88.0 with 10 degrees of freedom. This again suggests that the two data sources cannot be combined, even if we allow within-data source heteroscedasticity. In fact, allowing alternative-specific heteroscedasticity makes it more difficult to retain taste homogeneity between data sources. Swait and Adamowicz (1997) reported a similar result. They parametrised variance as a function of complexity, and found that incorporating the impact of choice context on variance made the combination of their RP and SP data less plausible. Yet, accounting for heteroscedasticity within data sources made the between-data source variance differences disappear! That is, the between-data source variance difference in Model 5 is eliminated by improved specification of the variance heteroscedasticity within-data source, particularly for the RP data. Thus far, our results suggest that for these data sources, combination is not a statistically sound option even if we account for within-data source heteroscedasticity. Another logical possibility is to test whether it is possible to combine the data sources if we allow for differences between data sources in parameters b , b and b . We previously noted that the estimate of b is negative     and significant in the RP data, but (correctly) positive and significant in the SP data. Parameter b exhibits the same sign reversal between data sets, but is not  significant in the RP data source. The last apparent difference hinted at in Fig. 2 is the greater relative importance of b in the SP data compared to the RP data.  Model 7 allows a separate estimate in each data source for these three parameters, which improves the log likelihood from !2230.0 to !2192.5 (Table 1). The removal of the equality restriction on these three parameters results in a chi-squared statistic of 13.0 with 7 degrees of freedom, compared to the critical value of 23.4 at the 95% confidence level. Our conclusion, therefore, is that the hypothesis of taste parameter equality holds across the two data sources, except for the three source-specific parameters (b , b and b ), as long as within-source    heteroscedasticity and between-source variance differences are accounted for. Note that in this final model (1) the SP data source does not exhibit scale factors significantly different from one, indicating that the IID assumption seems warranted within that data source; (2) the RP data, however, exhibit strong heteroscedasticity via alternatives A and D, which have scale estimates of 0.37

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and 0.67, respectively, in contrast to a scale of 1.0 for most of the other alternatives; and (3) that the SP data source has a scale of about 0.69, compared to a scale of 1.0 for the RP data, indicating that on average the former’s variance is greater than the latter’s. This last result is expected since, by construction, the SP data source has more variability in attributes than is found in the RP data. By combining the two data sources via Model 7, we are able to utilise the well-behaved SP design matrix to correct sign and collinearity problems in the RP data. Because of the SP data, we are also able to obtain more robust parameter estimates that are valid over wider attribute ranges than found in the RP data. The availability of the RP data, on the other hand, contributes a ‘real-world flavour’ to the joint model by establishing alternative-specific constants that reflect population characteristics. To predict to actual market conditions, we can utilize the following subset of Model 7 parameters: RP alternative-specific constants, all jointly estimated attribute parameters, and the RP scale function parameters. In addition, a judgment call must be made by the analyst concerning the source-specific attribute parameters. In our opinion, given the counterintuitive and/or non-significant RP results for the three parameters in questions, we recommend adopting the SP estimates for (b , b and   b ).  This simple example of combining two data sources illustrates the fact that many issues must be considered in data combination, and demonstrates that such exercises should first seek to establish the best-possible specification (involving both taste and covariance parameters) within each data source. Failing to do so may result in unwitting retention of the taste homogeneity and variance difference hypothesis. Ultimately, the better the specification within each particular data set, the stronger and more generalisable will be the results obtained if data combination is actually possible. On the other hand, it must also be said that the better the specification for a data set, the less likely data combination will be due to capitalisation on chance and overfitting to sourcespecific nuances; sufficiently large sample sizes will then make retention of the null hypothesis of taste invariance less probable.

5. Summary and conclusion Discrete choice models estimated from mixtures of data sources provide exciting opportunities for research into the demand for new products and services, as well as extending the attribute space of existing products and services to domains not currently available. This paper reviewed several new techniques

 Note that to apply the estimates shown in Table 1 for these three SP parameters, they must be divided by the corresponding scale factor from the SP data set.

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being developed in marketing, resource economics and transportation to analyse, model and combine sources of preference data, and illustrated the insights possible from several generalisations of extant discrete choice models which explicitly allow for error heteroscedasticity. Recognition that multiple data sources (e.g., RP and SP data) can be used to estimate choice models within the well-developed random utility theory framework provides opportunities for new research into ways to take both scale and taste into account, and capture complex behavioural constructs such as latent segments, random taste variation and choice dynamics, as well as extend utility spaces well beyond the domains of today’s actual markets. As well, there are significant opportunities to enrich and extend choice models by paying more and closer attention to processes that lead to different scale factors, which in turn may impact many elements of choice processes and models of those processes in complex ways. Behavioural differences in both the mean and variance of the distribution of consumer choices have both theoretical and practical implications. Theoretically, the models we discussed extend our ability to represent complex behavioural processes, and suggest future research into antecedents of variance differences, as well as more traditional research on differences in means. To our knowledge, the suggestion that the behaviour of variance components can be specified in ways consistent with random utility theory is new. In fact, this paper demonstrated that placing structure on variance components is not only possible, but practical. Moreover, our empirical illustration suggested significant gains in behavioural insights over more traditional models that focus largely on differences in means. As discussed and demonstrated in the empirical example in this paper, variance differences have important practical implications for marketing (and other) policy. For example, differences in tastes may be less common than previously thought, but even if segments are relatively taste homogeneous, they may exhibit different variances in preferences. The latter situation has considerable practical implications for marketing policy because it suggests that resources should be devoted to understanding antecedents of variance and developing strategies to overcome and/or reduce same, rather than concentrating on serving what seem to be different taste segments. In fact, strategies based on differences in means may be wrong for populations who display variance differences, because the optimal strategy may be variance reduction. Theory and empirical evidence provided in this paper suggests that research directed towards models that better capture differences in variances, as well as understanding sources of variance differences and their role in choice, should be interesting and fruitful. We individually and collectively are engaged in research programs consistent with these suggestions. For example, Louviere and Swait (1996) demonstrated that accounting for differences in variance often accounts for most of the differences in taste parameters in a number of new and published

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empirical preference and choice results. Some context effects which have produced large model differences in consumer decision-making research largely disappear if context differences in variances are taken into account. Hence, conclusions about the effects of context on means should be revisited in light of variance effects. de Palma et al. (1994) and Swait and Adamowicz (1997) studied decision task and decision environment complexity, and showed that variance has a convex relationship with decision context complexity. Brazell and Louviere (1997) reported two studies of different order and task length conditions, which showed that virtually all differences in choice model parameters were due to variance differences, and that variance (i.e. reliability) decreased up to about 40 pairs of choices, then rapidly increased until respondents saw the survey’s end, at which time variance rapidly decreased again. The above represent only a few examples of many new research avenues suggested by the theory and empirical results reviewed in this paper. Together they offer a compelling case that econometricians and marketing researchers can learn from one another to the mutual enrichment of both fields.

References Adamowicz, W., Louviere, J., Williams, M., 1994. Combining stated and revealed preference methods for valuing environmental amenities. Journal of Environmental Economics and Management 26, 271—292. Adamowicz, W., Swait, J., Boxall, P., Louviere, J., Williams, M., 1996. Perceptions versus objective measures of environmental quality in combined revealed and stated preference models of environmental valuation. Journal of Environmental Economics and Management 32, 65—84. Allenby, G., Ginter, J., 1995. The effects of in-store displays and feature advertising on consideration sets. International Journal of Research in Marketing 12, 67—80. Anderson, D.A., Wiley, J.B., 1992. Efficient choice set designs for estimating availability cross-effects models. Marketing Letters 3 (4), 357—370. Anderson, S., de Palma, A., Thisse, J., 1992. Discrete Choice Theory of Product Differentiation. MIT Press, Cambridge. Ben-Akiva, M., Lerman, S., 1985. Discrete Choice Analysis: Theory and Application to Predict Travel Demand. MIT Press, Cambridge. Ben-Akiva, M., Morikawa, T., 1991. Estimation of travel demand models from multiple data sources. In: Koshi, M. (Ed.), Transportation and Traffic Theory, Proceedings of the 11th ISTTT. Elsevier, Amsterdam, pp. 461—476. Bhat, C.R., 1995. A heteroscedastic extreme value model of intercity travel mode choice. Transportation Research 29B (6), 471—483. Bhat, C.R., 1996. An endogenous segmentation mode choice model with an application to intercity travel. Transportation Science 31, 34—48. Bradley, M., Daly, A., 1994. Use of the logit scaling approach to test rank-order and fatigue effects in stated preference data. Transportation 21 (2), 167—184. Brazell, J., Louviere, J., 1997. Respondents’ help, learning and fatigue. INFORMS Marketing Science Conference. University of California at Berkeley, Berkeley, CA. Bunch, D., 1991. Estimability in the multinomial probit model. Transporation Research 25B (1), 1—12.

D. Hensher et al. / Journal of Econometrics 89 (1999) 197–221

219

Bunch, D., Louviere, J., Anderson, D., 1996. A comparison of experimental design strategies for choice-based conjoint analysis with generic-attribute multinomial logit models. Unpublished working paper, UC Davis Graduate School of Management, May. Carson, R., Louviere, J., Anderson, D., Arabie, P., Bunch, D., Hensher, D., Johnson, R., Kuhfeld, W., Steinberg, D., Swait, J., Timmermans, H., Wiley, J., 1994. Experimental analysis of choice. Marketing Letters 5 (4), 351—368. Daganzo, C., 1980. Multinomial Probit. Academic Press, New York. Daly, A., 1987. Estimating ‘tree’ logit models. Transportation Research B 21B, 251—267. de Palma, A., Myers, G.M., Papageorgiou, Y.Y., 1994. Rational choice under an imperfect ability to choose. American Economic Review 84, 419—440. Englin, J., Cameron, T.A., 1996. Augmenting travel cost models with contingent behavior data. Environmental and Resource Economics 7, 133—147. Green, P., Srinivasan, V., 1978. Conjoint analysis in consumer research: Issues and outlook. Journal of Consumer Research 1, 61—68. Green, P., Srinivasan, V., 1990. Conjoint analysis in marketing research: New developments and directions. Journal of Marketing 54 (4), 3—19. Green, P., Wind, Y., 1971. Multiattribute Decisions in Marketing: A Measurement Approach. Dryden Press, Hinsdale, IL. Greene, W., 1996. Heteroskedastic extreme value model for discrete choice. Working paper, New York University. Hanemann, M., Kanninen, B., 1997. The statistical analysis of discrete-response CV data. In: Bateman, I.J., Willis, K.G. (Eds.), Valuing Environmental Preferences: Theory and Practice of the Contingent Valuation Method in the US, EC and Developing Countries. Oxford University Press, Oxford. Hausman, J., Wise, D., 1978. AFDC participation: measured variables or unobserved characteristics, permanent or transitory. Working paper, Department of Economics, MIT, Cambridge, MA. Hensher, D.A., Louviere, J., 1983. Identifying individual preferences for alternative international air fares: An application of functional measurement theory. Journal of Transport Economics and Policy XVII (2), 225—245. Hensher, D., Johnson, L., 1981. Applied Discrete Choice Modelling. Croom Helm, London. Hensher, D.A., 1994. Stated preference analysis of travel choices: The state of the practice. Transportation 21, 107—133. Hensher, D.A., (in press). Extending valuation to controlled value functions and non-uniform scaling with generalised unobserved variances. In: Ga¨rling, T., Laitila, T., Westin, K., (Eds.), Theoretical Foundations of Travel Choice Modeling. Pergamon, Oxford. Hensher, D.A., (1998). Establishing a fare elasticity regime for urban passenger transport. Journal of Transport Economics and Policy 32 (2) 221—246. Hensher, D.A., Barnard, P.O., 1990. The orthogonality issue in stated choice designs. In: Fischer, M., Nijkamp, P., Papageorgiou, Y. (Eds.), Spatial Choices and Processes. North-Holland, Amsterdam, pp. 265—278. Hensher, D.A., Bradley, M., 1993. Using stated response data to enrich revealed preference discrete choice models. Marketing Letters 4 (2), 39—152. Huber, J., Zwerina, K., 1996. The importance of utility balance in efficient choice set designs. Journal of Marketing Research 33, 307—317. Kahneman, D., Tversky, A., 1979. Prospect theory: An analysis of decisions under risk. Econometrica 47, 263—291. Kahneman, D., Tversky, A., 1984. Choices, values and frames. American Psychologist 39, 341—350. Keane, M., 1995. Modelling heterogeneity and state dependence in consumer choice behavior. Working paper, Department of Economics, University of Minnesota. Keller, K.L., 1993. Conceptualizing, measuring and managing customer-based brand equity. Journal of Marketing 57 (1), 1—22.

220

D. Hensher et al. / Journal of Econometrics 89 (1999) 197–221

Krantz, D.H., Tversky, A., 1971. conjoint-measurement analysis of composition rules in psychology. Psychological Review 78, 151—169. Krantz, D.H., Luce, R.D., Suppes, P., Tversky, A., 1971. Foundations of Measurement. Academic Press, New York. Lancaster, K., 1966. A new Approach to consumer theory. Journal of political Economy 74, 132—157. Louviere, J.J., 1995. Relating stated preference measures and models to choices in real markets: Calibration of CV responses. In: Bjornstad, D.J., Kahn, J.R. (Eds.), The Contingent Valuation of Environmental Resources. Edward Elgar, Brookfield, pp. 167—188. Louviere, J.J., 1974. Predicting the evaluation of real stimulus objects from an abstract evaluation of their attributes: The case of trout streams. Journal of Applied Psychology 59 (5), 572—577. Louviere, J.J., 1988a. Analyzing Decision Making: Metric Conjoint Analysis. Sage Publications, Newbury Park, CA. Louviere, J.J., 1988b. Conjoint analysis modelling of stated preferences: A review of theory, methods, recent developments and external validity. Journal of Transport Economics and Policy 20, 93—119. Louviere, J.J., 1994. Conjoint analysis. In: Bagozzi, R. (Ed.), Advanced Methods of Marketing Research. Blackwell Publishers, Cambridge, MA, pp. 223—259. Louviere, J.J., Hensher, D.A., 1983. Using discrete choice models with experimental design data to forecast consumer demand for a unique cultural event. Journal of Consumer Research 10 (3), 348—361. Louviere, J.J., Swait, J., 1996. Searching for regularities in choice processes, or the little constant that could. Working paper, Department of Marketing, Faculty of Economics, University of Sydney, August 1996. Louviere, J.J., Woodworth, G., 1983. Design and analysis of simulated consumer choice or allocation experiments: An approach based on aggregate data. Journal of Marketing Research 20, 350—367. Louviere, J.J., Fox, M., Moore, W., 1993. Cross-task validity comparisons of stated preference choice models. Marketing Letters 4 (3), 205—213. Luce, R.D., 1959. Individual Choice Behavior: A Theoretical Analysis. Wiley, New York. Lynch, J., 1985. Uniqueness issues in the decompositional modeling of multiattribute overall evaluations. Journal of Marketing Research 22, 1—19. Machina, M.J., 1987. Choice under uncertainty: Problems solved and unsolved. Economic Perspectives 1 (1), 121—154. McFadden, D., 1974. Conditional logit analysis of qualitative choice behaviour. In: Zarembka, P. (Ed.), Frontiers in Econometrics. Academic Press, New York, pp. 105—142. McFadden, D., 1981. Econometric models of probabilistic choice. In: Manski, C., McFadden, D., (Eds.), Structural Analysis of Discrete Data with Econometric Applications. MIT Press, Cambridge, MA 198—272. McFadden, D., Tye, W., Train, K., 1977. An application of diagnostic tests for independence from irrelevant alternatives property of the multinomial logit model. Transportation Research Record 637, 39—46. Meyer, R., Levin, I., Louviere, J., 1984. Functional analysis of mode choice. Transportation Research Record 673, 1—7. Morikawa, T., 1989. Incorporating stated preference data in travel demand analysis. Ph.D. Dissertation, Department of Civil Engineering, MIT. Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T., 1986. Numerical Recipes. Cambridge University Press, Cambridge. Restle, F., 1961. Psychology of Judgment and Choice. Wiley, New York. Rushton, G., 1969. Analysis of spatial behaviour by revealed space preference. Annals of the Association of American Geographers 59, 391—400.

D. Hensher et al. / Journal of Econometrics 89 (1999) 197–221

221

Small, K., 1987. A discrete choice model for ordered alternatives. econometrica 55 (2), 409—424. Small, K., 1994. Approximate generalized extreme value models of discrete choice. Journal of Econometrics 62, 351—382. Swait, J., Adamowicz, W., 1997. The effect of choice environment and task demands on consumer behavior: Discriminating between contribution and confusion. Working paper, Department. of Rural Economy, University of Alberta, 39 pp. Swait, J., Louviere J., 1993. The role of the scale parameter in the estimation and use of multinomial logit models. Journal of Marketing Research 30, 305—314. Swait, J., Stacey, E.C., 1996. Consumer brand assessment and assessment confidence in models of longitudinal choice behavior. Presented at the 1996 INFORMS Marketing Science Conference, 7—10 March, Gainesville, FL. Swait, J., Erdem, T., Louviere, J., Dubelaar, C., 1993. The equalization price: A measure of consumer-perceived brand equity. International Journal of Research in Marketing 10, 23—45. Swait, J., Louviere, J., Williams, M., 1994. A sequential approach to exploiting the combined strengths of SP and RP data: Application to freight shipper choice. Transportation 21 (2), 135—152. Thurstone, L., 1927. A law of comparative judgment. Psychological Review 34, 273—286.