incorporating Context effects into a Choice model

RobeRt P. RoodeRkeRk, HaRald J. van HeeRde, and tammo H.a. biJmolt* the behavioral literature provides ample evidence that consumer preferences are partly driven by the context provided by the set of alternatives. three important context effects are the compromise, attraction, and similarity effects. because these context effects affect choices in a systematic and predictable way, it should be possible to incorporate them in a choice model. However, the literature does not offer such a choice model. this study fills this gap by proposing a discrete-choice model that decomposes a product’s utility into a contextfree partworth utility and a context-dependent component capturing all three context effects. model estimation results on choice-based conjoint data involving digital cameras provide convincing statistical evidence for context effects. the estimated context effects are consistent with the predictions from the behavioral literature, and accounting for context effects leads to better predictions both in and out of sample. to illustrate the benefit from incorporating context effects in a choice model, the authors discuss how firms could utilize the context sensitivity of consumers to design more profitable product lines. Keywords: context effects, behavioral decision making, choice models, hierarchical bayes, product line design

incorporating Context effects into a Choice model

There is substantial evidence that people make decisions that deviate strikingly and systematically from the predictions of the standard random utility model (RUM) (McFadden 2001). The evidence is especially apparent in the large body of literature documenting context effects. Context

effects mean that consumer choices are partly driven by the context provided by the set of alternatives (Chakravarti and Lynch 1983; Payne 1982; Prelec, Wernerfelt, and Zettelmeyer 1997; Ratneshwar, Shocker, and Stewart 1987). Context effects are in line with the view on decision making that utilities are constructed in a specific choice context rather than recalled (Bettman, Luce, and Payne 1998; Payne, Bettman, and Johnson 1992). The marketing and psychology literature provides robust evidence for the presence of three important context effects: the compromise effect (Simonson 1989), the attraction effect (Huber, Payne, and Puto 1982; Huber and Puto 1983), and the similarity effect (Tversky 1972).1 Compromise effects refer to the phenomena that an item has a disproportionally large choice share when it is the compromise option in a choice set. The attraction effect refers to the finding that

*Robert P. Rooderkerk is Assistant Professor of Marketing and CentER fellow, Tilburg School of Economics and Management, Tilburg University (e-mail: [email protected]). Harald J. van Heerde is Professor of Marketing, Waikato Management School, University of Waikato, New Zealand, and Extramural Fellow at CentER, Tilburg University (e-mail: [email protected]). Tammo H.A. Bijmolt is Professor of Marketing Research, Department of Marketing, Faculty of Economics and Business, University of Groningen (e-mail: [email protected]). The authors thank Eric Bradlow, Marnik Dekimpe, Ran Kivetz, and Els Gijsbrechts for valuable comments that improved earlier drafts of this article. They also thank seminar participants at the 2005 Marketing Science Conference, Catholic University of Leuven, University of Groningen, Tilburg University, Free University of Amsterdam, Erasmus University Rotterdam, 2nd Annual Conference on Collaborative & Multidisciplinary Research, Yale School of Management, Wageningen University, and Massachusetts Institute of Technology. Robert Rooderkerk and Harald van Heerde gratefully acknowledge the Netherlands Organization for Scientific Research (NWO) for research support. Russell Winer served as associate editor for this article.

© 2011, American Marketing Association ISSN: 0022-2437 (print), 1547-7193 (electronic)

1Several other context effects have been proposed, such as polarization, enhancement, and detraction (Tversky and Simonson 1993). They are beyond the scope of this article because there are few to no empirical studies that identify their presence. Our models could be extended to capture some of these effects, as we outline in the “Discussion” session.

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Journal of Marketing Research Vol. XLVIII (August 2011), 767–780

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JouRnal of maRketing ReseaRCH, august 2011

an item increases the favorable perceptions of a similar, but superior item. The similarity effect describes the finding that an item is hurt more by similar items than by dissimilar items, and it implies preferences for products that “stand out.” Swait et al. (2002) refer to a Lucas-like “context critique” (Lucas 1976), stating that choice models that ignore the context may provide biased predictions because policy actions may affect the context, which in turn may influence the choice process. Rather than perceiving context effects as a threat to commonly used choice models, we believe that the systematic and significant appearance of context effects provides an opportunity to account for these effects in models predicting choice behavior. With such models, firms could increase their understanding of consumer decision making—for example, to design more profitable product lines. Several studies have called for the construction of an empirical choice model that accounts for multiple context effects across a wide range of choice situations (Dhar, Menon, and Maach 2004; Huber and Puto 1983; Kivetz, Netzer, and Srinivasan 2004a, b). While the literature provides models that capture one context effect at a time (Kamakura and Srivastava 1984; Kivetz, Netzer, and Srinivasan 2004a; Tversky 1972), it lacks empirical discretechoice models that accommodate multiple context effects. The contribution of our study is that we propose and empirically test a choice model that captures compromise, attraction, and similarity effects. We advocate a componential probit model, in which we separate the partworth utility from the utility derived from the context. Our componential approach provides insight into the strength and significance of each context effect separately while allowing them to be present simultaneously. We organize the remainder of this article as follows: In the next section, we review three important context effects and discuss their consequences for consumer choices. Next, we review the literature on modeling the compromise, attraction, and similarity effects, and we present a unifying choice model that accounts for these three context effects. The subsequent section describes model results for conjoint data on choices made from sets of digital cameras. We empirically show that accounting for context effects significantly increases our ability to predict choice behavior both in and out of sample. In addition, we show that each of the context effects has a significant effect in the expected direction, even when accounting for unobserved heterogeneity. Then, we illustrate how context effects can be used to construct more profitable product lines. We conclude with a discussion of our findings, the limitations of our research, and opportunities for further research. RATIONAL CHOICE AND CONTEXT EFFECTS The theory of rational choice assumes that the relative preference between two options does not depend on the presence of other options (Tversky and Simonson 1993). In other words, rational choices satisfy the independence of irrelevant alternatives (IIA) assumption (Luce 1959). Rational choice theory further implies regularity, which states that the choice share of an option cannot be increased by enlarging the choice set. Another common assumption in choice theory is the betweenness inequality (Tversky and

Simonson 1993): Adding an extreme option (e.g., a toplevel camera) hurts a middle-level option (midrange camera) more than the other extreme option (a basic camera). Context effects refer to the phenomenon that consumer choice behavior is influenced by the composition of the choice set in a manner apparently inconsistent with the theory of rational choice (Prelec, Wernerfelt, and Zettelmeyer 1997). Several context effects have been reported over the past decades. We discuss three important ones, which are illustrated in Figure 1. The choice options in Figure 1 vary on two attributes, and the consumer preferences are increasing in both attributes. Compromise Effect The compromise effect (Simonson 1989) is the phenomenon that an alternative obtains a relatively large choice share when it is a compromise or middle option in the choice set. To formalize this statement, we define P(x; S) as the probability of a consumer choosing option x from the set of options S. Suppose the extreme option C would be added to the set {A, B} in Figure 1, Panel A, and option A becomes the compromise option. The compromise effect predicts that A’s relative choice share compared with the other extreme option B increases—that is, P(A;{A, B, C})/[P(A;{A, B, C}) + P(B;{A, B, C})] > P(A;{A, B}). Compromise effects violate the IIA assumption, because adding C changes the preference of A relative to B. Moreover, compromise effects also violate the betweenness inequality, which would predict that adding C to {A, B} should decrease (rather than increase) the relative choice share for A. In an extreme case, adding C leads to an increase in absolute choice share of option A: P(A;{A, B, C}) > P(A;{A, B}). Thus, compromise effects can also lead to violations of the regularity principle. Attraction Effect The attraction effect (Huber, Payne, and Puto 1982; Huber and Puto 1983) refers to the phenomenon that an item increases the favorable perceptions of similar, but superior, items in the choice set. An asymmetrically dominated item is dominated by one alternative in the choice set but not by others. Adding such a decoy alternative has been found to shift share to the item dominating it.2 In Figure 1, Panel B, option C is asymmetrically dominated by A but not by B. The attraction effect predicts that adding C increases the relative choice share of option A compared with option B: P(A;{A, B, C})/[P(A;{A, B, C}) + P(B;{A, B, C})] > P(A;{A, B}). The attraction effect leads to an IIA assumption violation. That is, the attraction effect implies that the addition of a similar, but inferior, option increases the relative choice share of the option to which it is similar. If adding an asymmetrically dominated option C increases the absolute choice share of option A, P(A;{A, B, C}) > P(A;{A, B}), regularity is violated as well (Huber, Payne, and Puto 1982; Huber and Puto 1983; Simonson 1989). 2Huber and Puto (1983) extend the attraction effect to include decoys that are not dominated but reflect a relatively worse trade-off on the attributes in the choice set. In this study, we focus on asymmetrically dominated decoys only.

incorporating Context effects into a Choice model Similarity Effect Another well-documented context effect is the similarity, or substitution, effect, which is the phenomenon that an item hurts similar alternatives more than dissimilar items (Tversky 1972). Suppose in Figure 1, Panel C, that option C figure 1 illustRation of Context effeCts A: Compromise Effect

Attribute 2

$" C"

Attribute 1

The compromise option A obtains more share than expected based on its attributes. B: Attraction Effect

Attribute 2

is added to a choice set initially containing only A and B. Because C is more similar to B than to A, the similarity effect predicts that B loses more share to C than A loses to C. In other words, we expect the relative choice share of option B compared with option A to be lower in the set containing options A, B, and C than in the set just containing A and B: P(B;{A, B, C})/[P(A;{A, B, C}) + P(B;{A, B, C})] < P(B;{A, B}). The similarity effect leads to choices that are inconsistent with the IIA assumption: Adding a similar option decreases the relative choice share of the option to which it is more similar. Huber, Payne, and Puto (1982) find that a higher relative similarity between target and decoy increases the strength of the attraction effect. In other words, they provide evidence for an interaction between the attraction and similarity effect. Our model accommodates this interaction. MODELING CONTEXT EFFECTS: LITERATURE REVIEW

a" #"

!"" b

a C

b Attribute 1

The addition of C improves the preference for A relative to B. C: Similarity Effect

Attribute 2

769

a

C b Attribute 1

C steals more share from B than from A. Notes: Each of the context effects prescribes that the relative share of alternative A compared with B increases after the introduction of a third alternative C.

Standard RUMs, such as the multinomial logit and multinomial probit (MNP) models (as well as nested-logit and nested-probit), do not explicitly account for context effects. Table 1 shows studies that have explicitly modeled context effects. Tversky (1972) shows that the IIA assumption was overly restrictive for describing choice patterns. This led him to formulate the elimination-by-aspects (EBA) model. The EBA process consists of sequentially choosing an aspect and removing products that do not possess this aspect until only one alternative remains. The EBA model accounts for similarity effects because products with many shared aspects will steal more share from one another than more dissimilar products. Kamakura and Srivastava (1984) also model similarity effects but do so using similarity-based error correlations in an MNP model. Tversky and Simonson (1993) present an analytical (nonempirical) model that has a relative advantage component, representing attraction and compromise effects. A specific form of their model would have to be chosen in an empirical study. Kivetz, Netzer, and Srinivasan (2004a) introduce context-dependent choice models designed to capture the compromise effect. Kivetz, Netzer, and Srinivasan also mention that some of their models can theoretically account for the attraction effect. Sharpe, Staelin, and Huber (2008) simplify Kivetz, Netzer, and Srinivasan’s model to an additive rather than multiplicative model. Orhun (2009) presents an analytical (nonempirical) choice model that accounts for choice set–dependent preferences. Orhun shows how her model could capture the attraction and compromise effect under the assumption of loss aversion with respect to a reference point. While significant progress has been made toward models capturing context effects, the literature lacks empirical discrete-choice models that accommodate the compromise, attraction, and similarity effects simultaneously. However, context effects do not appear in isolation but rather in combination, as Huber, Payne, and Puto (1982) illustrate with respect to the attraction and similarity effect. In this study, we develop a model that considers choices as the net outcome of the simultaneous presence of multiple context effects.

770

JouRnal of maRketing ReseaRCH, august 2011 table 1 emPiRiCal models aCCounting foR Context effeCts

Model

Authors

RUM Elimination by aspects MNP with distance-dependent covariances Componential context Context-dependent multinomial logit Comparative valuations model Extended contextual RUM

Compromise

Thurstone (1927), Marschak (1960) Tversky (1972) Kamakura and Srivastava (1984) Tversky and Simonson (1993)a Kivetz, Netzer, and Srinivasan (2004a)b Orhun (2009)c Current studyd

aThis study presents a conceptual (nonempirical) model for the attraction and compromise effects. bThis study argues that some of the models could be extended to capture attraction effects. cThis study presents an analytical (nonempirical) model accounting for choice set–dependent preferences.

Attraction

✓a ✓ ✓c ✓

Similarity

✓a ✓b ✓c ✓

✓ ✓

✓

Orhun’s (2009) appendix shows how this model

could theoretically account for the attraction and compromise effects. dOur study also accounts for the interaction between the attraction and the similarity effect.

A UNIFYING MODEL OF CONTEXT EFFECTS

Q

Vhi =

(2 )

Modeling Objectives

Lq

∑ ∑β

hql x iql ,

q = 1l = 2

Our objective is that the context-dependent model nests a heterogeneous RUM, such that it reduces to this model in the absence of context effects. This objective takes Tversky’s (1972) EBA approach out of consideration. An additional objective is to model the influence of context effects in the structural part of utility because it allows for standard parameter significance tests for each context effect. Thus, we do not opt for a context-dependent error approach (Kamakura and Srivastava 1984). We model the impact of context effects as direct utility gains or losses, consistent with the assumption that items directly gain or lose attractiveness as a result of the context of the choice set. Following Tversky and Simonson (1993), we split an item’s total utility into its partworth utility and a context-dependent (dis)utility. The context-dependent component is the sum of three context terms, accounting for the utility gain or loss due to the compromise, attraction, and similarity effects. Thus, we isolate the influence of the three context effects while allowing them to be present simultaneously. We do not claim that our componential approach is the only way of modeling context effects; it is the approach that meets our objectives best.

where COMSi , ATTSi , and SIMSi are the respective compromise, attraction, and similarity gain or loss of item i in choice set S. An important feature of the model is that it allows for SIM separate statistical tests of bCOM , bATT to examine h h , and bh the presence of each context effect. Note that the model SIM reduces to a heterogeneous RUM if bCOM , bATT h h , and b h are all equal to zero. Note also that we allow for response parameter heterogeneity (index h) in both the context-free and context-dependent parts of the utility function. Primary demand effects are taken into consideration through the inclusion of a “no-choice” option (Kohli and Sukumar 1990; McBride and Zufryden 1988), and its utility is described by the following equation:

Model Specification

(4 )

We formulate the utility participant h attaches to item i in choice set (= context) S as zShi. Equation 1 splits the deterministic part of utility into a partworth utility (Vhi) and a context-dependent part (VCShi):

We allow for a nonzero no-choice utility because setting it to zero leads to biased parameter estimates (Haaijer, Kamakura, and Wedel 2001).

(1)

zShi

=

V hi { partworth utility

+

VCShi { context-depend dent utility

+

ε Shi ,

with h = 1, …, H and i = 1, …, NS, where H denotes the number of participants, NS represents the number of options in choice set S, and eShi is the random error term. Consistent with the extant context effect literature (e.g., Huber, Payne, and Puto 1982; Huber and Puto 1983; Kivetz, Netzer, and Srinivasan 2004a; Simonson 1989; Tversky 1972), we assume that every item in set S can be described along Q metric attributes. To allow for a flexible utility structure, we model the partworth component using level dummies:

where xiql is a dummy variable taking on the value 1 if item i has Level l of attribute q and 0 if otherwise. Note that the first level of every attribute is set to 0 for identification purposes. The contextual component is a linear combination of three variables: the utility gains or losses due to respectively the compromise, attraction, and similarity effect: (3)

S VCShi = βCOM COMSi + β hATT ATTiS + β SIM h h SIM i ,

zSh 0 = β h 0 + ε Sh 0 .

Context Variables We operationalize our context variables by quantifying the relative positions of items in attribute space. To this end, we define the distance measure, the preference vector, and the positioning vector. Because the attributes are metric, we define the distance between two items, A and B, in a choice set, dAB, as their Euclidean distance in attribute space (i.e., the length of the vector between them). We use a preference vector for a choice set S (Tversky, Sattah, and Slovic 1988; Wedell 1991), which starts at the point in attribute space that represents the minimum values of all attributes in set S and ends at the point in attribute space that represents the maximum values of all attributes in set S. In notation,


) (

)

where xkq indicates the value of item k on attribute q and S vpreference is the preference vector in choice set S. Next, we define the positioning vector vSpositioning for choice set S as the vector orthogonal to the preference vector (Tversky, Sattah, and Slovic 1988; Wedell 1991)3:

figure 3 visual illustRations of tHe Context vaRiables in diffeRent CHoiCe sets s = {a, b, C} A: Compromise Effect max xk2

(

(5 ) vSpreference =  max xk1 − min xk1 ... max x kQ − min x kQ  , k ∈S k∈S k ∈S  k∈S 

771

C

vSpreference ⊥ vSpreference . Attribute 2 xs m2

Figure 2 illustrates the two vectors for an example choice set S consisting of three items, A, B, and C. Equation 5 ensures that the preference vector (and hence the positioning vector) is endogenous to the choice set because this vector itself is also affected by the choice context. Figure 3 illustrates the context variables, which we define next. Compromise. The compromise variable is based on compromise option M in a set S. Its attributes are the middle values of the attribute ranges as defined by the options in the choice set:

M

B

min xk1

min xkq + max x kq k ∈S

2

The compromise option can be a real or, as in Figure 3, Panel A, a virtual choice option. The shorter the distance from item i to the compromise option M (dSiM), the more item i benefits from being (close to) a compromise option. 3Tversky, Sattah, and Slovic (1988) and Wedell (1991) use the label “indifference curve respectively equi-preference contour” to indicate what we refer to as the “positioning vector.”

figure 2 PRefeRenCe and Positioning veCtoR in CHoiCe set s = {a, b, C}

max xk1

d SAC, preference A

C

vSpreference

B

min xk1

max xk1 Attribute 1 S S S S S ATTA = –dAC, preference, ATTB = 0, ATTC = –dAC, preference C: Similarity Effect max xk2

A

d SAC, positionin g

C

min xk2

Attribute 2

C

vSpreference

A

Attribute 2

max xk2

xs m1 Attribute 1 S S = –dAM COMA

B: Attraction Effect

, q = 1, ..., Q. Attribute 2 max xk2

k∈S

min xk2

xSMq =

(7)

d SAM

A

min xk2

(6 )

vSpositioning

vSpreference

vSpositioning

B

min xk2

B min xk1

max xk1

min xk1 Attribute 1

Notes: vSpreference is the preference vector in set S, and vSpositioning is the positioning vector orthogonal to it. The orientation of the positioning vector (to northwest as drawn or to southeast) is immaterial.

max xk1 Attribute 1 S S S SIMA = min –dAj, positioning = –dAC, positioning j ŒS

S Notes: dAM is the distance between Item A and the virtual middle option S S M in set S; vpreference is the preference vector in set S, and vpositioning is the S S positioning vector orthogonal to it; and dAC, preference and dAC, positioning are

the distances between the projections of Items A and C on the preference and positioning vector, respectively.

772


Therefore, we base the compromise variable of an item i in set S, COMSi on the negative of the distance between that item and the compromise option:

items as the distance between the two items on the positioning vector. This leads to the following specification for the interaction variable:

COMSi = –dSiM.

(11) ATT × SIM Si = S S  d ij, preference d ij, positioning if item i dominates item j in set S.   S if item i is dominated by item j in  –d dS  ij, preference ij, positioning set S.  if item i is neither dominating nor 0  dominated in set S.

(8)

The higher (i.e., the less negative) the compromise variable, the more option i becomes a compromise, which adds utility according to the compromise effect. Thus, we expect the effect of COMSi on utility in Equation 3 to be positive: bCOM > 0. h Attraction. According to the attraction effect, an item that asymmetrically dominates another item gains share disproportionally, whereas the dominated item loses share disproportionally. We use the preference vector to understand how items dominate other items because this vector shows in which direction attribute values become more desirable. As Figure 3, Panel B, shows, we project each item onto the preference vector. The distance between items i and j on the preference vector (dSij, preference) is the basis for the attraction variable. The dominating item’s utility should increases in this distance (be proportional to +dSij, preference), whereas the dominated item’s utility should decrease in this distance (be proportional to –dSij, preference). For nondominating and nondominated items, the attraction variable is zero. Thus, the attraction variable for item i in set S is as follows:  dSij, preference   – dS  ij, preference (9 ) ATTiS =   0 

if item i dominates item j in set S. if item i is dominated by item j in set S. if item i is neither dominating nor dominated in set S.

The more positive (negative) the attraction variable, the more (less) attractive option i becomes. Thus, we expect the effect of ATTSi on utility in Equation 3 to be positive: bATT h > 0. Similarity. The similarity effect implies that an item loses share when it becomes more similar to another item. To operationalize the similarity variable, we observe the distance between two items measured along the positioning vector (Figure 3, Panel C). This operationalization enables us to measure similarity independent of the attraction variable, capitalizing on the orthogonality of the positioning vector to the preference vector. An item’s utility should increase in the distance to the closest item on the positioning vector because it means the item becomes more dissimilar. Therefore, the similarity variable becomes the following: (10)

SIMSi = min dSij, positioning . j ∈S /{ i}

The higher the similarity variable, the more dissimilar option i becomes, which adds utility according to the similarity effect. Thus, we expect the effect of on utility in Equation 3 to be positive: bSIM > 0. h Interaction between attraction and similarity effect. Huber, Payne, and Puto (1982) find that those decoys that had the strongest similarity to the target had the strongest positive effect on the target. To test for this interplay between attraction and similarity effect, we formulate their interaction: the product of the attraction gain (loss) of a dominating (dominated) item and the dissimilarity between the target and decoy. In line with our specification for the similarity variable, we define the dissimilarity between two

For dominating items, the interaction is zero if it is perfectly similar to the dominated item (because dSij, positioning = 0). When the dominating item becomes more dissimilar from the dominated item, the interaction term ATT ¥ SIMSi becomes positive, which is expected to weaken the attrac¥ SIM tion effect, and thus bATT < 0. h Normalization. To ensure that the context variables are comparable across choice sets, we normalize them before including them in the model. Within each choice set, we divide each variable for a main context effect by the relevant maximum distance for that context effect. The interaction between attraction and similarity is the product of the two corresponding normalized variables. The normalization also ensures that the context variables are measured on a relative scale rather than an absolute scale. The Web Appendix (http://www.marketingpower.com/jmraug11) provides all operationalization details. Final model components. We embed our contextual utility formulation in an independent MNP model by assuming i.i.d. N(0, 1) errors and that any participant h picks the option with the highest utility from a given choice set S: (12)

ε Sh 0 , ε Shi i.i.d. ~ N(0, 1) ∀i = 1, ..., N S ,

(13)

yShi = 1 if zShi > zShj

∀j ≠ i, j = 0, ..., NS ,

where yShi = 1 indicates that participant h has chosen option i from set S. The reason we assume independent errors is that we prefer to model the influence of the context, including the similarity effect, directly through the structural part of utility rather than through error correlations. We define the participant-specific parameters to be i.i.d. according to a normal population distribution, bh i.i.d. ~ N(b, Vb), where Vb is a full matrix. EMPIRICAL APPLICATION Data Description Participants. To calibrate the model, we ran a choicebased conjoint experiment. One hundred fifty-four undergraduate students participated in return for a monetary compensation of $7. Stimuli. We used hypothetical digital cameras in the experiment. Pretests indicated that, in addition to price, picture quality (measured in number of megapixels) and optical zoom (measured in the number of times an object can be magnified while retaining the same resolution) were the most important attributes for respondents. These attributes were also emphasized most in print advertisements around the time of data collection (September 2004). Participants

incorporating Context effects into a Choice model were told that all choice options had the same price and that the only differences were the picture quality and optical zoom. Both attributes contained five equidistant levels. Picture quality ranged from two to six megapixels, and optical zoom ranged from 2¥ to 10¥. The attribute ranges and levels were representative for the market values at the time of data collection. In each of the choice sets discussed in the following subsections, participants could pick either a camera or the no-choice option. Procedure and design. We manually constructed all feasible choice sets that were free of overall dominating or dominated options, because such options are unlikely to appear in reality. However, we allowed for choice sets with asymmetrically dominating items. This resulted in 700 feasible sets. Next, we ran the widely used %ChoiceEff macro in SAS (Huber and Zwerina 1996; Kuhfeld 2005; Kuhfeld, Tobias, and Garrat 1994) to find an efficient set of 30 choice sets among the 700 feasible sets. Of the 30 sets, 8 contained a dominating–dominated pair.4 Each participant made choices from 15 choice sets, representing the estimation sample. These 15 choice sets were obtained by randomly blocking the 30 choice sets into 10 overlapping groups of 15 choice sets. The order of the choice sets and of the profiles within each choice set were randomized. Next, participants made choices from six additional holdout choice sets. In addition to a no-choice option, these choice sets contained three (2 sets), four (2 sets), and five (2 sets) digital cameras. These holdout choice sets, ten for each choice set size, were generated using the same procedure that was used to construct the estimation choice sets. For each choice set size, the choice sets were randomly blocked into five nonoverlapping groups of two holdout choice sets. Again, participants were randomly assigned to one of these groups. The experiment was administered on personal computers in a behavioral research lab using the software package Authorware 6 (Macromedia 2001). Figure 4 illustrates one of the choice sets. 4Whereas 600 of the 700 feasible sets contained a dominating–dominated pair, the %ChoiceEff macro only selected 8 of 30 choice sets with such pairs. If anything, this reduced proportion of such pairs stacks the odds against finding a significant attraction effect.

figure 4 examPle of a CHoiCe set PResented to tHe PaRtiCiPants

Which of these digital cameras would you choose? Double click on the item you wish to choose, double click on “None” if none of these options is satisfactory. Option 1

Option 2

Picture quality: 4 megapixel optical zoom: 8¥


Option 3

Option 4


i would not purchase any of these.

773 Estimation We estimated three models: Model 1: The heterogeneous RUM without any context variables: ¥ SIM bCOM = bATT = bSIM = bATT = 0; h h h h Model 2: The contextual RUM with all context variables except the interaction between the attraction and similarity ¥ SIM effect: bATT = 0; and h Model 3: The extended contextual RUM with all context variables including the interaction between the attraction and similarity effect.

Both the contextual RUM and the extended contextual RUM allow for taste heterogeneity. Thus, the heterogeneous RUM is nested in both. We estimate the models with Gibbs sampling, as outlined in the Web Appendix (http://www. marketingpower.com/jmraug11). We determined in-sample fit of the models by calculating the deviance information criterion (DIC; Spiegelhalter et al. 2002), which balances model fit and complexity (lower DIC is better). In addition, we established both in-sample and out-of-sample fit by computing the log-marginal density (LMD; larger is better) and hit rate (larger is better). The hit rate is defined as the fraction of times in which the choice option with the highest predicted probability corresponds to the chosen option. Results Table 2 contains the fit statistics for all three models. For seven of eight in- and out-of sample fit statistics, the extended contextual RUM (Model 3) with the interaction between attraction and similarity dominates both the contextual RUM without this interaction (Model 2) and the heterogeneous RUM without any context effects (Model 1). For only one statistic (hit rate for holdout sample for choice set of size 4), Model 3 does not dominate. Thus, it is important to account not only for the main effects of the three context variables but also for the interaction between attraction and similarity (Huber, Payne, and Puto 1982). The relatively mild drop in hit rates when moving from three to four and five items set is noteworthy. Choices from four- and five-item sets took longer than those from three-item sets, as reflected by (unreported) choice latencies, but apparently the commonality in the design of the sets evoked consistent behavior across choice set sizes. Table 3 shows the posterior intervals for the hyperparameters for the three models. In all models, the partworth component of the item utilities displays a concave utility structure with decreasing returns to scale for both attributes. It is interesting to note that for both attributes, the shape of the partworth utility function is similar across the contextfree versus contextual models. We note that the median hypermean partworth for 10¥ optical zoom is slightly lower than that of 8¥ optical zoom. This suggests a violation of monotone preferences, though it is not significant as the posterior parameter interval of the difference between 8¥ and 10¥ does not exclude 0.5 5We also estimated counterparts of Models 1–3 that enforced monotone preferences at the individual level on both picture quality and optical zoom. These models fit worse than the unrestricted models (log-Bayes factors > 160 in favor of the unrestricted models). More details on these models and their estimation appear in the Web Appendix at http://www.marketingpower. com/jmraug11).

774

JouRnal of maRketing ReseaRCH, august 2011 table 2 summaRY of desCRiPtive and PRediCtive fit Three Items In Sample

Model Model 1: Heterogeneous RUM model without context effects Model 2: Contextual RUM model with context main effects Model 3: Extended contextual RUM model with context effects plus attraction ¥ similarity interaction

Four Items

Five Items

Out of Sample

Out of Sample

Out of Sample

LMD

Hit Rate

DIC

LMD

Hit Rate

LMD

Hit Rate

LMD

Hit Rate

–1375

.813

2886

–283

.695

–332

.692

–334

.682

–1376

.802

2849

–270

.701

–327

.679

–324

.653

–1359

.814

2844

–267

.714

–305

.662

–319

.692

Notes: LMD = log-marginal density (Newton and Raftery 1994). Hit rate is the percentage of times that the option with highest mean posterior predicted probability was selected across all 500 posterior draws. DIC = deviance information criterion (Spiegelhalter et al. 2002). We calculated the hit probabilities required for the computation of the log-marginal density using the Geweke-Hajivassiliou-Keane simulator from Geweke (1991), Hajivassiliou and McFadden (1990), and Keane (1990, 1994). Boldface figures represent the best values across the three models.

table 3 PosteRioR PaRameteR estimates foR tHe HYPeR mean Model 1: Heterogeneous RUM Symbol Partworths b0 b12 b12 b12 b12 b12 b12 b12 b12 Context Variables bCOM bATT bSIM bATT ¥ SIM

Model 2: Contextual RUM

Model 3: Extended Contextual RUM

Variable

Expected Sign

2.5%

50%

97.5%

2.5%

50%

97.5%

2.5%

50%

97.5%

No choice 3 megapixel 4 megapixel 5 megapixel 6 megapixel 4¥ optical zoom 6¥ optical zoom 8¥ optical zoom 10¥ optical zoom

N.A. + + + + + + + +

5.761 .741 3.107 4.869 5.481 2.173 3.731 4.193 4.092

6.138 1.017 3.291 5.009 5.684 2.489 4.052 4.604 4.524

6.538 1.258 3.465 5.173 5.909 2.782 4.418 4.980 4.903

5.379 1.062 3.261 4.671 4.961 2.038 3.260 3.739 3.211

5.976 1.243 3.490 4.932 5.277 2.274 3.595 4.071 3.555

6.604 1.423 3.755 5.233 5.627 2.522 3.940 4.426 3.922

4.966 .895 2.955 4.409 4.807 1.777 3.077 3.335 3.169

5.353 1.143 3.128 4.572 4.997 2.122 3.477 3.730 3.629

5.772 1.408 3.299 4.711 5.200 2.432 3.824 4.094 4.037

Compromise Attraction Similarity Attraction ¥ similarity

+ + + –

.062 1.079 .114

.181 1.278 .383

.336 1.506 .593

.358 .979 .230 –3.771

.480 1.115 .369 –3.458

.575 1.278 .560 –3.117

Notes: The posterior intervals, not including zero, are in bold. For identification, we set the levels 2 megapixels and 2¥ optical zoom to 0. N.A. = not applicable.

Overall, given the superior in- and out-of-sample fit (for choice sets of size 3) and high face validity, we pick the extended contextual RUM (Model 3) with the interaction between attraction and similarity as our focal model. The posterior parameter intervals of all context variables have the expected sign and exclude zero. That is, participants value a choice option more when it (1) is closer to the compromise option (bCOM = .480), (2) dominates another option (bATT = 1.115), and (3) is less similar to any of the other items (bSIM = .369). In addition, the parameter corresponding to the attraction ¥ similarity interaction is negative, as we expected (bATT ¥ SIM = −3.458). Thus, participants value attraction more when the target is more similar to the decoy. Inspection of Individual-Level Context Parameters Table 4 summarizes the individual-level posterior parameter intervals corresponding to the four context parameters in the extended contextual RUM (Model 3). The table classifies the 95% posterior parameter intervals of each participant into four categories according to whether (1) the posterior median has the right sign as hypothesized and (2) the posterior interval excludes zero.

Table 4 reveals that the context parameter estimates are well behaved at the individual level. The vast majority of participants have correct significant signs for compromise effects (71.4%), attraction effects (87.0%), and the interaction effect between attraction and similarity (92.2%). The main effect of similarity is correct and significant for 42.9% of the participants. There are only a few participants (7.1%) with a significant incorrect sign for the similarity effect, and this is 0% for the other context effects. In summary, the results illustrate that accounting for context effects in a discretechoice model increases the model’s descriptive and predictive ability substantially. In addition, the contextual choice models display good face validity. Next, we discuss some robustness checks. Robustness Checks Heterogeneity versus context effects. Hutchinson, Kamakura, and Lynch (2000) offer unobserved heterogeneity as an alternative explanation for context effects. They show that choice behavior attributed to context effects may result from aggregating different consumer segments that do not exhibit these effects when considered separately. The


775 table 4

summaRY of individual-level PosteRioR Context PaRameteR estimates foR tHe extended Contextual Rum (model 3) WitH similaRitY-attRaCtion inteRaCtion (in % of PaRtiCiPants)

Correct sign, 95% posterior interval excludes 0 Correct sign, 95% posterior interval includes 0 Wrong sign, 95% posterior interval includes 0 Wrong sign, 95% posterior interval excludes 0 Total

Compromise

Attraction

Similarity

Attraction × Similarity

71.4% 20.8% 7.1% .6% 100.00%

87.0% 13.0% .0% .0% 100.00%

42.9% 30.5% 19.5% 7.1% 100.0%

92.2% 7.1% .6% .0% 100.0%

Notes: A correct sign refers to a posterior median with the hypothesized sign: positive for similarity, attraction, and compromise; negative for similarity ¥ attraction.

(14)

vpreference(h) = [1 wh],

where we set the weight for the first dimension equal to 1 for model identification, and the weight for the second dimension wh is larger than 0 for every participant h = 1, ...,

figure 5 illustRation HoW tHe extended Contextual Rum (model 3) aCCounts foR tHe similaRitY effeCt beYond tHe HeteRogeneous Rum (model 1) A: Replacing Item C1 with C2

A

8

Optical Zoom

authors suggest that the only way to distinguish individual differences in preferences from individual-level departures from IIA is to use repeated choices for multiple respondents. Our choice model is based on such choice data. We employ hierarchical Bayes techniques to allow for unobserved parameter heterogeneity. Importantly, even while controlling for heterogeneity, context effects are significant at the individual level. This is consistent with the idea that non-IIA behavior is displayed at the individual level and that it cannot be resolved by allowing for individual-level parameters. However, the similarity effect deserves further attention. Our benchmark model, the heterogeneous RUM (Model 1), already produces a within-subject similarity effect due to partworth correlations across posterior draws. This could also result in an aggregate-level similarity effect, meaning that more similar items compete more heavily for choice share. Figure 5 illustrates that our extended contextual RUM (Model 3) predicts a similarity effect beyond that of the heterogeneous RUM (Model 1). The choice set initially consists of Items A, B, and C1, but next, we replace C1 with C2. In an IIA model, the relative share of A versus B is predicted to remain unchanged. The similarity effect, however, predicts that the relative share of Item A versus B increases when we replace C1 with C2 because C2 is less (more) similar to A (B) than C1. If the extended contextual model (Model 3) accounts for a similarity effect beyond that arising from mere heterogeneity, the increase in relative share of A versus B should be larger under Model 3 than under Model 1. Indeed, the increase in relative share when we replace C1 with C2 is considerably larger under the context model (2.0) than under the heterogeneous RUM (1.6). Thus, the similarity effect captured by Model 3 holds beyond the effect of taste heterogeneity in Model 1. Note that, by construction, the other context effects (compromise and attraction) do not play a role in Figure 5. Context effects in utility versus attribute space. Our context variables are based on the preference and positioning vectors. In turn, these vectors are determined by the attribute ranges implied by the choice set. Instead of defining the context effects in attribute space, we could define them in utility space. That is, we could estimate the importance attached to the attributes in the preference vector. To this end, we respecify and reestimate the preference vector as follows:

C1

6

C2

4

B

2

3

4

5 Megapixel

6

B: Relative Share of Item A Versus Item B PModel(A; Set)/[PModel(A; Set) + PModel(B; Set)] Model

Set S1 = {A, B, C1} S2 = {A, B, C2} Ratio

Heterogeneous RUM (M1)

Extended Contextual RUM (M3)

39.6% 61.7% 1.6

28.0% 55.4% 2.0

H (extension to more dimensions is straightforward). In addition, we have estimated a version of the model in which the preference vector was allowed to vary across participants and within a participant across choice sets, depending on the attribute ranges: (15)

  max x k 2 − min x k 2   k ∈S k ∈S  , vSpreference (h) = 1 w*h    max x k1 − min x k1      k ∈S k ∈S 

where w*h > 0 for every participant h = 1, ..., H. The Gibbs samplers for these alternative preference vectors appear in the Web Appendix (http://www.marketingpower.

figure 6 illustRation of HoW tHe extended Contextual Rum (model 3) aCCounts foR tHe ComPRomise effeCt on tHe no-CHoiCe sHaRe A: Replacing Item C1 with C2

A

10 Optical Zoom

com/jmraug11). Inspection of the posterior parameter intervals of wh and w*h shows that they are wide, indicating overfitting. In the case of the heterogeneous, set-invariant preference vector, the posterior interval vpreference(h) included [1 1] for every participant. Moreover, in case of the heterogeneous, set-varying preference vector, the posterior parameter intervals always included our current operationalization as specified in Equation 5 (w*h = 1). Therefore, we opt for the more parsimonious current operationalization. Attraction losses and gains. It is conceivable that the attraction effect is mainly due to a share loss for the dominated item and less to a share gain for the dominating item. To test for this asymmetry, we extended the current model (Model 3) with separate attraction gains and losses in both the main effect (Equation 9) and the interaction with the similarity effect (Equation 11). In-sample model fit is comparable to the current model (log-Bayes factor 1 in favor of the current model) but worse out of sample (log-Bayes factors of 24, 18, and 39 for, respectively, three, four, and five items in favor of the current model). Thus, we believe there is not enough statistical evidence for the extended model. Still, the face validity of the model is noteworthy. Both the posterior parameter intervals of the attraction gain and the attraction loss variable exclude zero and lie in the positive domain, as hypothesized. Note that the posterior median of the loss/gain ratio is 2.00. The finding that losses hurt about twice as much as gains satisfy is echoed in many studies (Hastie and Dawes 2001, p. 216). The compromise parameter remains positive and significant, while the posterior interval of the similarity parameter now includes zero. While the interaction between attraction losses and similarity is insignificant, the interaction is significant and negative (as expected) for attraction gains. Thus, the degree to which losses hurt is independent of the similarity to the dominating item, whereas attraction gains are felt more when the dominated item is more similar. No-choice and context effects. In our model, the utility of the no-choice option is not directly affected by the choice context. However, research in psychology suggests that context effects have an impact on the no-choice option as well. In particular, Dhar (1997b) shows that people pick the no-choice option when the choice task is considered too difficult. Other research has shown that a choice task is considered easier in the presence of a dominating alternative (i.e., under the influence of the attraction effect) (Dhar 1997a; Hedgcock and Rao 2009; Tversky and Shafir 1992). In addition, by extending a forced-choice set of alternatives with a no-choice option, Dhar and Simonson (2003) show that the no-choice option competes most heavily with the compromise option. They argue that choosing the no-choice or the compromise option are both mechanisms that help consumers resolve difficult choices. This implies that the presence of a compromise option could decrease the utility of the no-choice option. Our model indirectly accounts for the context effects on the no-choice option. That is, context effects affect the utilities of the choice options, which may increase or decrease their attractiveness compared with the no-choice option. Figure 6 illustrates this indirect effect for the compromise effect. Initially, the choice set has Items A, B, and C1, and next, C1 is replaced with C2. Item C2 represents a stronger compromise option (i.e., closer distance to the middle


8 6

C2

4

C1 B

2

2

3

4 5 Megapixel

6

B: No-Choice Share 55

54.8 54.8

52.8 52.8

Extended Contextual (M3)3) extended contextual RumRUM (model Heterogeneous RumRUM (model Heterogeneous (M1)1)

50 No-Choice Share (in %)

776

45 30 35 30 25.7 25.7

25 21.7 21.7 20 S1 = {A, B, C1}

S2 = {A, B, C2} Set

option) than item C1. Consequently, when C1 is replaced with C2, the compromise effect becomes stronger, and thus, the no-choice share should shrink beyond the expected decrease because C2 is a more attractive item than C1. Indeed, Figure 6 shows that decrease in the no-choice share is larger under the extended contextual RUM (Model 3; from 54.8% to 21.7%) compared with the heterogeneous RUM (Model 1; from 52.8% to 25.7%). This illustrates how the extended contextual model (Model 3) accounts for the indirect effect of context on no choice. To explore whether there are also direct effects, we included no-choice context variables as direct drivers of the

incorporating Context effects into a Choice model no-choice utility. The no-choice context variables were formulated as the maximum compromise, similarity, and attraction value of the items: (16)

NC_COMS = max COMSj , NC_ATTS = max ATTjS , j ∈S

NC_SIMS =

NC_COMS,

NC_ATTS,

j ∈S

max SIM Sj , j ∈S

NC_SIMS

where and represent the no-choice values for the compromise, attraction, and similarity effects, respectively. Using these variables, we extend the no-choice utility in Equation 4 to the following: (17)

777 the optimal solution. (For more details and the exact mathematical formulation of the product line design problem, we refer to the Web Appendix at http://www.marketingpower. com/jmraug11.) Figure 7 summarizes the resulting optimal product lines visually. The 13 candidate cameras are indicated by small figure 7 designing moRe PRofitable PRoduCt lines: boosting a taRget item (t) tHRougH Context effeCts A: Optimal Product Lines: Heterogeneous RUM (Model 1)

_ COM zSh 0 = β h 0 + β NC NC _ COMS + h

Expected Profit = 153.1

C _ SIM _ ATT NC _ SIMS + εSh 0 . β NC NC _ ATTS + β N h h

PRODUCT LINE DESIGN IN THE PRESENCE OF CONTEXT EFFECTS Context effects can be used in product line design to boost more profitable items through the choice context. To illustrate this potential, we optimized a three-item product line under both the heterogeneous RUM (Model 1) and the extended contextual RUM (Model 3). The chosen objective is profit maximization in a single-seller case (for product line optimization under competition, see Moorthy 1988; Vandenbosch and Weinberg N 1995). We considered 13 digital cameras that represent a trade-off between picture quality and optical zoom. These cameras form a substantial subset of the cameras encountered in the experiment. We assumed all profit margins to be 1, except that of the hypothetical target item T (5 megapixels, 6¥ optical zoom). For the target item, we assume a slightly higher margin of 1.1. From the feasible set of 13 digital cameras, it is possible to construct 286 possible three-item product lines. This relatively small number enables complete enumeration to find

A1

Optical Zoom

10

1.5%

B1

8

33.4%

T

6

58.6%

4

2

No-choice share = 6.4%

2

3

No-cho

4 5 Megapixel

6

B: Optimal Product Lines: Extended Contextual RUM (Model 3)

Expected Profit = 161.4

10

Optical Zoom

A larger maximum compromise value indicates a stronger presence for a compromise option, which should negatively affect the no-choice utility. Thus, according to Dhar and < 0. A stronger attracSimonson (2003), we expect bNC_COM h tion effect should make choosing easier and thus reduce the no-choice utility (Dhar 1997a, b). Consequently, we expect bNC_ATT < 0 If one of the items is clearly dissimilar, this will h reduce the perceived choice difficulty and, as a consequence, lower the no-choice share. Therefore, we hypothesize that bNC_SIM < 0. h We augmented the extended contextual RUM (Model 3) with the no-choice context variables and estimated it. However, this augmented model could not outperform the current model without the no-choice context variables (in sample: log-Bayes factor 21; out of sample: log-Bayes factors of 13, 49, and 51 for three, four, and five items, respectively, in favor of the current model). In addition, the corresponding posterior parameter intervals either included 0 or had low face validity. Apparently, in our empirical application, accounting for the indirect effect of the context on the no-choice option suffices, and there is no need to account for a direct effect. Using alternative specifications for Equation 16 (averages instead of maxima), or culling respondents with either very high or very low no-choice shares, does not alter this conclusion.

A2

8

0.0%

T 6

92.5%

B2

4

2

3.1%

No-choice share = 4.4%

2

3

4 5 Megapixel

6

Notes: All items have a profit margin of 1 except for the target item T (5 megapixels, 6¥), which has a margin of 1.1. The numbers next to the depicted items represent the expected choice shares under the extended contextual RUM (Model 3). In case of an included item, the size of the circle represents the expected choice share.

778


circles. The included cameras under both models are indicated by a letter and accompanied by the expected choice share under the extended contextual RUM (Model 3). Accounting for context effects leads to a (significant) expected profit increase of 5.4%. The difference in composition of both product lines is noteworthy. The context-free product line consists of items on the top diagonal, consistent with the notion of offering attractive cameras that cater to heterogeneous tastes. We expect the target item to achieve a share of 58.6%. Under the context model, the optimal product line looks very different. Only the target item lies on the top diagonal, and it dominates Item B2 in the direction of the preference vector. As a result, the similarity between the target and decoy B2 is very high, and the attraction value of the target item T is maximal. The positioning of A2 makes the target item closest to the compromise option of all alternatives. In summary, the product line is composed in such a way that the target item benefits from similarity and attraction effect and their interaction and from the compromise effect. Consequently, the target item obtains a very high share (92.5%), which is the basis for the profit increase compared with the context-free product line. DISCUSSION Conclusion Our article extends the literature on context effects by demonstrating that context effects do not necessarily need to lead to a rejection of commonly used choice models but can be added as extra components to these models. As such, we have developed an empirical discrete-choice model accounting for the influence of context effects. Our model extends the standard MNP model by decomposing a product’s utility into a partworth utility and a context-dependent component capturing the compromise, attraction, and similarity effects. We have developed context variables that account for the utility gains or losses due to these three important context effects. Our componential approach provides insight into the strength of each context effect individually while allowing them to be present simultaneously. We also allow for an interaction between the attraction and similarity effect, anticipating that a more similar decoy provides a bigger boost in share of the target than a dissimilar decoy (Huber, Payne, and Puto 1982). Thus, our model extends current efforts of modeling at most one context effect at a time by considering multiple context effects simultaneously. We estimated our model on repeated choices made from sets of three digital cameras varying on two attributes in a behavioral lab. We find that the contextual models (with and without the attraction ¥ similarity interaction) significantly enhance both descriptive and predictive fit compared with the heterogeneous RUM. Our results indicate that even after accounting for heterogeneity and for nonlinear attribute effects, accommodating context effects leads to significant improvements in predictive ability. Moreover, the face validity of the contextual choice models is good, even at the individual level. Using the estimated model, we illustrate that firms can use context effects to construct more profitable product lines. The underlying idea is to use context effects to give more profitable items a boost in choice share.

Limitations and Further Research In this section, we describe some limitations and possible extensions of our study. The first limitation of our study is that the context-dependent part of our model assumes that the attributes are metric and that consumers’ preferences are increasing monotonically in each attribute. This is consistent with the extant literature on context effects (e.g., Huber, Payne, and Puto 1982; Huber and Puto 1983; Kivetz, Netzer, and Srinivasan 2004a; Simonson 1989; Tversky 1972). However, it prohibits us from including nominal attributes, such as brand, in the contextual part of the model. Before we can relax the “metric monotonicity” assumption, additional lab experiments are required to show the occurrence of context effects for nonmetric attributes such as brand names. Recently, there has been some evidence of context effects along the brand dimension in the context of multitier private label strategies (Geyskens, Gielens, and Gijsbrechts 2010). We envision that optimal scaling techniques could be used to map a nominal attribute on a latent metric dimension (e.g., Wedel et al. 1998), facilitating the use of our context variables. Another possibility is to replace the brand with metric scores that measure the brand positioning on relevant dimensions, such as reliability, quality, or familiarity. We have restricted the number of attributes to two in the empirical application, though we specified the model in a general way for Q attributes. Our decision to limit ourselves to two attributes is motivated by the desire to stay close to the empirical literature on context effects. Those studies typically resort to three-item choice sets defined on two attributes when studying context effects (Kivetz, Netzer, and Srinivasan 2004a). In addition, even analytical studies (e.g., Orhun 2009) regularly limit themselves to two attributes. Still, further research could investigate the extent to which context effects influence choice behavior when products are defined on more than two dimensions. This study compares our contextual choice models with the standard independent MNP model. Further research could compare our contextual models with a wider range of benchmark models such as a MNP model with correlated errors. Although this model does account for similarity effects, it is unclear how it would accommodate compromise effects and attraction effects. In addition, varying choice sets considerably complicates the estimation of MNP models with full error-covariance matrices (e.g., see Zeithammer and Lenk 2006). Previous research has identified other context effects, such as enhancement and detraction (Tversky and Simonson 1993). Our model could be adapted to account for such effects. By including the (degree of) dominance with respect to the middle option as an additional context variable, we can account for enhancement and detraction effects with only one additional parameter. The literature has noted various moderators of the strength of context effects, including stimulus meaningfulness and familiarity with the product category (Ratneshwar, Shocker, and Stewart 1987), category knowledge and information mode (Sen 1998), time pressure (Dhar, Nowlis, and Sherman 2000), and private self-awareness (Goukens, Dewitte, and Warlop 2009). It would be interesting to include these moderators as drivers of the context effect heterogeneity observed in our study.

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