The Influence of Task Complexity on Consumer Choice: A Latent

The Influence of Task Complexity on Consumer Choice: A Latent Class Model of Decision Strategy Switching JOFFRE SWAIT WIKTOR ADAMOWICZ* The literature indicating that person-, context-, and task-specific factors cause consumers to utilize different decision strategies has generally failed to affect the specification of choice models used by practitioners and academics alike, who still tend to assume an utility maximizing, omniscient, indefatigable consumer. This article (1) introduces decision strategy selection, within a maintained compensatory framework, into aggregate choice models via latent classes, which arise because of task complexity; (2) it demonstrates that within an experimental choice task, the model reflects changing aggregate preferences as choice complexity changes and as the task progresses. The import of these findings for current practice, model interpretation, and future research needs is examined.

T

he judgment and decision-making (JDM) literature has devoted considerable attention to identifying and characterizing the strategies used by human beings and organizations to make decisions (Bettman, Johnson, and Payne 1991; Payne, Bettman, and Johnson 1993). Some researchers have concerned themselves with formulating descriptive and mathematical models of different decision strategies (for conjunctive and disjunctive decision rules, see Dawes [1964]; for satisficing, see Simon [1955]; for eliminationby-aspects, see Tversky [1972]); another stream of the JDM literature has concerned itself with finding evidence of the utilization of compensatory and noncompensatory decision strategies as task complexity and context change (Ball 1997; Payne et al. 1993; Russo and Dosher 1983). While this literature has established that people utilize multiple choice strategies depending on a number of factors (product, occasion, information presentation format, time pressure, alternative similarity, etc.), there has been little linkage of these findings to the literature on multiattribute, multialternative experimental choice tasks (Louviere and

Woodworth 1983). Choice experiments, while taking on many different forms, commonly present respondents with the task of choosing one alternative among multiple product profiles, each described in terms of a generally common attribute set. In addition, respondents are usually presented with multiple decision scenarios in a short time span. Traditionally, these data are modeled through specifications such as the Multinomial Logit (MNL), Nested MNL, and Probit models. The models in general use are almost exclusively compensatory and single decision rule in nature (with some notable exceptions, including Andrews and Srinivasan 1995; Roberts and Lattin 1991; Swait 2001; Swait and Ben-Akiva 1987a, 1987b). In this article we build on the established knowledge that decision strategies can change because of context and propose a modeling framework that allows for decision strategy and/or preference structure changes. We construct a model that can use choice data, as typically collected in commercial and academic applications, and that accounts for the types of decision strategy changes that have been found using eye-tracking, verbal protocols, or other laboratory techniques. The proposed framework allows factors like task complexity to affect inferences about preferences, with the goal of improving the modeling of experimental or revealed preference choice data. We also propose and employ a new summary measure of task complexity, based on the information theoretic concept of entropy. Rather than using verbal protocols (Bettman 1970) or eyetracking techniques (Russo and Dosher 1983), or registering information search patterns (Ball 1997) to develop measures of how individuals respond to complexity and other task

*Joffre Swait is a partner of Advanis, 12 West University Avenue, #205, Gainesville, FL 32601 ([email protected]), and an associated faculty member of the Department of Marketing, Warrington College of Business, University of Florida. Wiktor Adamowicz is Professor, Department of Rural Economy, University of Alberta, Edmonton, Alberta T6G 2H1, Canada ([email protected]). Send correspondence to Joffre Swait. The authors acknowledge the essential contributions of the editor, associate editor, and reviewers to the improvement of the research. The first author acknowledges the financial support of Advanis. The data used in this study originate from an independent research effort by Joffre Swait and Doug Olsen (University of Alberta).

135 䉷 2001 by JOURNAL OF CONSUMER RESEARCH, Inc. ● Vol. 28 ● June 2001 All rights reserved. 0093-5301/2002/2801-0009$03.00

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context factors, a particular latent class choice model is used to infer likely decision-making approaches across a sample of respondents in a given choice experiment, as a function of complexity and cumulative cognitive burden. For a particular application it is shown that complexity, cumulative cognitive burden, and task order significantly affect preference patterns, and, further, that these patterns appear to be changes in decision-making strategy and/or preference structures in response to changes in context or task demands. The hypothesis of no change in preference structure in response to changes in complexity is clearly rejected in the data utilized. Furthermore, the resulting preference patterns support the notion of a movement toward a simplified choice heuristic as complexity increases, which is consonant with the view of the consumer as a cognitive miser. Our models are still of compensatory form; thus, we cannot unambiguously state that we have captured the full range of decision strategies that could be employed, even at the aggregate level. However, changes in parameters in a compensatory model can approximate noncompensatory decision-making modes; such parameter changes in response to increases in complexity are observed in our data, supporting the notion of simplified decision making as difficulty increases and the task sequence evolves. Summary measures have not been available to reflect the impact of complexity on choice behavior, which may be one of the reasons choice models have not been extended in this direction. Thus, besides the modeling framework proposed, the other main innovation of this article is the development of a metric of complexity for use in choice models and in the general study of choice behavior, a metric that is based on entropy, an information theoretic measure. It is demonstrated that consumers respond to levels of complexity as measured by this metric. In the following sections, we review the literature on decision strategy selection, especially as it pertains to task complexity and cognitive burden in choice experiments; we propose a measure of task complexity based on information theory and develop an ordered latent class econometric model of choice behavior that allows decision strategy changes as a function of task complexity, cognitive burden, and task order; we then apply this model to choice data from a choice experiment involving frozen concentrate orange juice and review findings from this application; and finally, we discuss the implications of our approach and empirical findings for academic research and commercial practice.

STRATEGY SELECTION FOR MULTIATTRIBUTE DECISIONS Past Work in Decision Strategy Identification The usual explanation for the use of heuristics, or “nonoptimal” strategies, is the existence of a trade-off between decision cost and outcome benefit. (Here nonoptimality is defined with respect to a decision maker who utilizes full information, as is commonly assumed in the economics framework.) The large literature summarized by Payne et

al. (1993) discusses how changes in decision makers’ environments affect how they make choices. This cost-benefit framework is formalized in Shugan’s (1980) analysis, which demonstrates the theoretical basis for strategy selection as a compromise between making the right decision and reducing the effort needed to reach a decision. Shugan suggests that the costs of decision making to the individual are associated with his or her limited processing capability, the complexity of the choice, time pressure, and other factors. According to Bettman et al. (1991, p. 64), this research stream has demonstrated, via simulation and experimental work, that the cost-benefit viewpoint is able to explain contingent decision-making behavior. Few authors in the economics literature have discussed the limitations of an individual’s ability to process information and the implications of these limitations on choice behavior. Heiner (1983) argues that agents cannot grasp the full complexity of the situations they face and thus make decisions that appear suboptimal or employ decision strategies that are not utility maximizing. A more formal examination of the processing limitation argument is presented by de Palma, Myers, and Papageorgiou (1994), who model consumers with different abilities to choose; they assume that an individual with lower ability to choose will make more errors in comparisons of marginal utilities. Their main result of interest here is that heterogeneity in the ability to choose over a population of individuals produces widely different choices and apparent differences in choice strategies, even if in all other aspects the individuals are identical (including having the same tastes). Similar conclusions arise from the literature on bounded rationality (March 1978; Simon 1955). Alternatively, it has been suggested that individuals may attempt to avoid conflict when choices are complex, leading to simpler choice heuristics when attributes are negatively correlated. Keller and Staelin (1987) suggest that complexity may have an inverted U-shaped relationship with decision effectiveness: as the situation becomes more complex, individuals initially exert additional effort and become more effective, until a point is reached where their effectiveness begins to deteriorate. Findings by Olshavsky (1979), Payne (1976), Payne, Bettman, and Johnson (1988), and Simonson and Tversky (1992) indicate that the context and complexity of the decision—as given by the number of alternatives, number of attributes, correlation between attributes, time pressure, and various other factors—significantly influence decision strategy selection. A related hypothesis, proposed by Dhar (1997a, 1997b), suggests that consumers will choose the strategy to defer choice (avoid choosing or choosing the status quo) when the choice environment becomes more complex. Similarly, Tversky and Shafir (1992) show that when the choice environment is made complex, some individuals opt to delay choice, seek new alternatives, or even revert to a default (or status quo) option. Russo and Dosher (1983) approached the identification of strategy selection differently, concentrating on observing the strategies rather than modeling their effect on behavior.

INFLUENCE OF TASK COMPLEXITY ON CHOICE

For decisions involving choice between two alternatives, described by multiple attributes, they utilized a combination of eye-tracking and prompted verbal protocols to characterize information processing strategies. They identified two classes of processing: holistic (processing alternatives first) and dimensional (processing attributes first), and they find in their data a slight predominance of the latter. They also found that subjects adopted two simplification procedures: dimensional reduction (DR; ignoring attributes deemed of small importance) and majority of confirming dimensions (MCD; ignoring magnitudes and giving directional, but equal, importance to all attributes). While these processing strategies (with or without simplifications) have different effort and accuracy implications, note that from the point of view of traditional compensatory choice models they are indistinguishable since the information is assumed combined for all attributes to achieve an alternative-specific measure of object utility. In line with Russo and Dosher’s (1983) research, the present research is capable of indicating whether simplification strategies, arising in response to increasing complexity, result in dimensional reduction or consideration of all attributes. Ball (1997) examines the ability of single-step transition indices to discriminate between different decision strategies used by subjects in information processing experiments. He finds strong support for his contention that multistep indices are needed to adequately identify strategies. From the perspective of the present article, Ball’s research is noteworthy because he utilizes cluster analysis of transition information to characterize decision strategies. He warns, however, that because of the nature of cluster analytic methods, “the results of such cluster analyses . . . can not be supported statistically” (Ball 1997, p. 203). Bockenholt and Hynan (1994), in contrast, utilize a latent class model to cluster transition patterns. They apply the model to information acquisition data gathered in a trinary choice situation, each alternative described by three attributes. They argue that the latent classes are needed as a parsimonious representation of individual differences among subjects. Because their approach is model-based, they are able to determine the statistical significance of the clusters they find in their data, in contrast to Ball (1997). Bockenholt and Hynan (1994) differ from what we do in that (1) they concentrate directly on the information acquisition strategy itself, whereas we seek to infer strategy and/ or taste changes from the choices made; and (2) their specific model form is, therefore, quite different from the one proposed herein. Recently, econometric modeling efforts have been aimed at handling the repeated measures issue in choice experiments (see Revelt and Train 1998). The focus of this line of work is to model the effect of context change (from the perspective of the statistical treatment of repeated choice measures) on taste parameter inferences. The current article differs from these efforts because it aims at capturing, through modeling, the impact of underlying decision strat-

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egy changes made by respondents during the course of a choice task.

Strategy Selection, Task Complexity, and Cognitive Burden in Choice Experiments We propose, then, to take a model-based route to allow for and identify preference structure changes during choice experiments involving repeated choices among multiple alternatives described by multiple attributes. We hypothesize, based on the considerable literature in strategy selection, that preference structures may change throughout a set of tasks. More specifically, we hypothesize that (1) decision complexity and (2) cumulative cognitive burden will contribute to the strategy selection process. The basic reasoning behind these hypotheses is that a common sequence of events for a respondent in a choice task may be something like this: (1) learning about the task and the effort necessary to accomplish it by trying out different strategies for some number of replications, followed by (2) the application of the learned behavior during another number of replications. Finally (3), fatigue or boredom sets in, leading to the use of simplified strategies. Note how this reasonable sequence conflicts with the usual full information, compensatory-behavior-throughout-the-entire-task that is assumed in the traditional model forms used to analyze choice data. But this is not simply a modeling issue: the very notion that complexity affects decision-making conflicts with the traditional notion of value maximization used in economics, in which individuals are assumed to be able to assign values to alternatives and choose the alternatives with the highest value, independent of context, learning, fatigue, and so on. To bridge this gap between received knowledge about contingent decision making and choice model specification and to incorporate in such models the impacts of complexity and cumulative cognitive burden on decision strategy selection, we propose an alternative modeling approach that is outlined below in further detail. First we describe how complexity and cognitive burden can be quantitatively represented, then we present the specific model form proposed.

Quantifying the Complexity and Cumulative Cognitive Burden of Multiple Choice Tasks. Our objective in this section is to present and justify the use of a specific mathematical representation of choice environment complexity. Our aim is to suggest a measure that reflects complexity and can be used to model the impact that changing complexity has on decision strategy selection. Some dimensions of such a measure have already been discussed above (the number of attributes, the number of alternatives, and negative correlation of attributes, etc.). We should note, however, that each of these quantities is a component of complexity rather than an overall or summary measure. Distance between alternatives in attribute space, which is related to the correlation structure of the attributes, is a candidate for capturing the degree of overall complexity involved in a choice context. Suppose we wish to examine choice sets with three alternatives {A, B, C}, described by


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K-vectors of attributes xA, xB, and xC. Distance measures can generally be constructed as sums of distance norms (e.g., absolute value distance or Euclidean distance) for vectors xi and xj , i, j 苸 {A, B, C}. While such measures would reflect the distance between alternatives in attribute space, they may not capture the number of alternatives in the measure of complexity. A serious deficiency of such measures is that they require that all attributes be commensurable, a constraint that usually cannot be met in practice. An even greater difficulty with these measures is that interproduct distance in attribute space alone will not be useful in assessing how complex the choice task is because one needs information on preferences in order to construct a meaningful measure of complexity. To make a quick digression, the terms “complexity” and “difficulty” are often used in the literature but are not always defined precisely. In this article we use the term “complexity” to refer to our measure of the complexity of the choice situation. If there are a large number of alternatives, there are many attributes, and many of the alternatives are similar in a utility sense, then this is a more complex situation than one with fewer attributes, fewer alternatives, and more dominant alternatives. If a consumer is attempting to maximize utility then a complex task will make the choice difficult. Of course, if a consumer is responding using some other scheme (e.g., expenditure minimization), then the task may be quite simple. Thus, our notion of complexity is a multidimensional assessment of the choice context, summarized in the measure to be presented below. In order to obtain a more complete and formally defined measure of complexity, we turn to information theory to provide a measure of information content or uncertainty inherent in a decision context. Information theory refers to an approach taken to characterize or quantify the amount of information contained in an experiment or phenomenon (Shannon 1948; Soofi 1994). Given a set of outcomes, or alternatives, in our context, {xj , j p 1, . . . , J}, that are described by a probability distribution p(x), the entropy (or uncertainty) of the choice situation is defined as

冘 J

H(X) p H(px ) p ⫺

p(xj ) log p(xj ) ≥ 0.

(1)

jp1

In a case with J alternatives in a choice set, entropy reaches its maximum of ln J if all alternatives are equally likely. Thus, if the number of alternatives increases, maximum entropy also increases. It can also be shown that the entropy function for a given J is everywhere greater than or equal to the entropy function for any 2 ≤ J ! J. Thus, the number of alternatives in the choice set directly affects the level of complexity, making this measure a useful mechanism for testing hypotheses regarding the impact of the number of alternatives on different components of the choice process (e.g., decision rule, choice set composition, tastes, variance). Entropy is minimized if there is one dominant alternative in the choice set: if one alternative has a probability of one,

and the others therefore have probabilities of zero, entropy achieves its minimum value of zero. The number of attributes and the degree of attribute correlation also impact entropy since these elements will affect the probabilities p(x). Similarly, to the extent that attribute correlations translate into preference correlations through tastes and error structure, choice probabilities will change and cause changes in entropy. However, as we have noted before, attribute correlations per se are not of great interest; only to the extent that preference (dis)similarities are generated should complexity be impacted, and so it is with entropy. An additional aspect associated with the use of entropy as a measure of task complexity is the fact that cumulative entropy can be used to assess the impact of the cumulative complexity of multiple choice tasks (i.e., cumulative cognitive burden). Cumulative entropy provides a measure of the amount of uncertainty faced by individuals as they make sequences of choices. It can be shown that the entropy of a joint probability distribution that is probabilistically independent is the sum of the entropies of the marginal distributions. Hence, use of cumulative entropy as a measure of cumulative impact of complexity is akin to assuming independence between choice scenarios. We address this property further in the article’s concluding section. Our measure of task complexity and cumulative cognitive burden is incorporated into a latent class discrete choice econometric model along with other factors that are hypothesized to affect preference structure and/or strategy selection. We give details on the model and the incorporation of the complexity factor to identify strategy selection in the following section.

Justification and Formulation of Proposed Model. The model we construct is one in which various strategies, represented by different parameter vectors for the utility component, are allowed to be present in the choice data in a logically ordered fashion. These strategies are systematically related to factors hypothesized to influence strategy selection, namely, complexity, cumulative complexity, and task order. The rationale for including complexity and cumulative complexity was presented above. Task order is included to assess the influence on preference structures of the repeated nature of choice questions, independent of cumulative complexity. Responses such as fatigue, for example, could arise simply from answering a large number of choice questions, or from increasing cumulative complexity. Thus, the model simultaneously estimates groups of taste weights (interpreted as potential decision strategies suggested by associated preference structures) and the weights on factors influencing which group the respondent is most likely to fall into at a certain point in the choice sequence. More formally, suppose that a respondent will be in one of S latent (i.e., unknown to the analyst) decision states during a choice task. Thus, in one task an individual might be in one state (say, s), while in the next choice task, either because of the complexity of that task or the cumulative


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effort expended up to that point, the same person might be in another state (say, s⬘). Each state has associated with it a taste parameter vector bs , s p 1, . . . , S , which is the basis for the individual’s evaluation of the attractiveness of product offerings in the current choice set. If, in a particular state s, bs contains all zero elements corresponding to attribute values and nonzero elements corresponding to brand intercepts, one might surmise that the state corresponds to a purely brand-based decision strategy (since attributes are being ignored); by contrast, if both brand and attribute coefficients are nonzero, one might cogently argue that a decision strategy that is used in that state employs more of the available information and is more akin to full information processing. These interpretations are similar to those made by Russo and Dosher (1983), who identify the MCD and DR decision strategies in their work. These compensatory strategies can be characterized by special configurations of the taste vectors. One might also be able to discern compensatory behavior, relative to strategies that appear to use less information, though in a model that is by definition compensatory this will be difficult to support conclusively. Nevertheless, in such a situation one can still argue that the individual is likely to be using more of the information on attributes while making a choice. Thus, it is logical to interpret the configuration of the taste vector in latent state s as directly reflective of the decision process used by individuals when in that state. The literature has noted before the capacity of compensatory models to mimic noncompensatory processes through functional form nonlinearity and parameter vectors (e.g., Johnson and Meyer 1984; Johnson, Meyer, and Ghose 1989; Swait 2001). However, it behooves us to recognize that factors besides decision strategy selection (e.g., context, fatigue, and variety-seeking) may also affect parameter vectors. Conditional on being in state s, we assume that the utility r UiFs of the ith product offering in replication r is given by r r UiFs p bs X ir ⫹ ␧iFs ,

(2)

where X ir is the vector of product attributes and context r characteristics and ␧iFs is an error term. (For clarity, we suppress throughout the subscript for the individual respondent.) If it is assumed that the joint distribution of the error terms, conditional on the decision state, is independent and identically distributed Gumbel with unit scale factor across alternatives, replications, and respondents, then the conditional choice probability of choosing alternative i is the familiar MNL model:

Z 冘 exp (b X ),

PiFsr p exp (bs X ir )

j苸C r

s

r j

(3)

where C r is the set of alternatives from among which choice is exercised in the rth replication. An observer is unable unambiguously to classify a randomly selected individual from the population into a par-

ticular decision state s for a particular replication r. Instead, the existence of a certain latent stochastic cost-benefit strategy selection factor Y r, defined as follows, is postulated: Y r p a1 H r ⫹ a 2 (H r ) 2 ⫹ a 3w r ⫹ a 4 (w r ) 2

冘

(4)

R

⫹ a 5 H rw r ⫹

rp1

a 5⫹r Z rr ⫹ n r,

where a’s are parameters, H r is the entropy of the rth choice set seen by a respondent, w r is the cumulative entropy en countered by the respondent up to the rth replication, Z rr r identifies the task number (or order), and n is an error term with zero mean and distribution to be specified. The vari ables Z rr equal one for Gr ≤ r and equal zero otherwise, for r p 1, . . . , R. Cumulative entropy w r is defined as

{冘 0

wr p

for r p 1 .

r⫺1

r p1

(5)

H r for r p 2, . . . , R

Through Equation 4, it is assumed that as the cumulative cognitive burden and the complexity of the current task increase, the latent selection factor Y r also increases. In addition, we include an interaction term between current entropy and cumulative entropy to permit a nonlinear response in the factor as fatigue sets in: as cumulative cognitive burden increases, sensitivity to current complexity level may increase. We should note that in this model implementation, it is assumed that once observable linkages among replications are accounted for through task order (see Eq. 4), each task is independent of all others, which is to say, the errors n r have no unobserved correlation arising between replications. We must now relate the factor Y r to the decision state entered by the individual at replication r. Define a latent state indicator I r, which takes on values in the set {1, . . . , S}. It is related to Y r as follows: 1 2 r I p _ S

{

Y r ≤ t1 t1 ≤ Y r ≤ t2 , _ tS⫺1 ≤ Y r

(6)

where the ts , s p 1, . . . , S ⫺ 1, are cutoff parameters to be estimated that define the ranges of Yr that lead to classification into each latent decision state. Only S ⫺ 1 cutoff parameters are needed to construct S states. Note that Equation 6 imposes an ordinal relationship among the latent decision states: membership in higher order strategies implies higher values of Y r, and vice versa. Each range on the latent factor, as defined by the cutoffs, corresponds to a different decision strategy, as interpreted from the configuration of relative attribute importances contained in the associated taste vectors bs , s p 1, . . . , S. In other


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words, Y r is an index presumed increasing in complexity, cumulative complexity, and task order, and it is based on the notion that each of these elements increases cognitive burden and influences the propensity to change strategies. As Y r increases, individuals are placed into different categories in terms of their strategy or set of taste weights. See Greene (1990, p. 705) for the rationale and a graphic description of ordered latent variable models. Since Y r is a random variable, we must assume some distribution law to describe v r so that the probabilities Wsr p Pr (I r p s), s p 1, . . . , S may be calculated. For purposes of this model development, it is assumed that nr is independently logistic distributed across individuals and decision states, so that the cumulative density function is G(n r ) p [1 ⫹ exp (⫺n r )]⫺1, ⫺ ⬁ ! n r ! ⬁.

(7)

Therefore,

fication conditions common to choice models also apply: for example, constants can only be estimated for (J ⫺ 1) of J brands in the conditional choice model. The reader is referred to Ben-Akiva and Lerman (1985) for further details on identification conditions for choice models. Before proceeding to the case study, we first present the operationalization of the entropy measure.

Empirical Calculation of Entropy and Cumulative Entropy. A measure of the probability of selection of the alternatives is required to operationalize entropy as a complexity measure (see Eq. 1). Here, an a priori estimate of the measure is constructed that will sufficiently characterize the choice context to allow discrimination among decision strategies. A measure of probability of choice can be obtained from an MNL model with the following form: p˜ ir(X) p

Wsr p Pr (I r p s)

p

(10)

j苸C

G(t1 ⫺ Y¯ r ) sp1 G(t2 ⫺ Y¯ r ) ⫺ G(t1 ⫺ Y¯ r ) s p 2 , _ _ r ¯ 1 ⫺ G(tS⫺1 ⫺ Y ) spS

{

(8)

where Y¯ r p En (Y r ); see Equation 4. Thus, each respondent on each task has some probability of falling into any of the S decision states. The elements in Y r will directly affect the probability of being in any of the S states. We can now express the unconditional probability that a consumer will choose alternative i 苸 C r as

冘 S

Pi r p

exp (qX ir ) 冘 r exp (qXjr ) ,

PiFsr Wsr.

(9)

sp1

Equation 9 shows that the probability of choosing alternative i depends on the probability of choosing alternative i when using strategy s, times the probability of being in (latent) strategy class s, summed over all S strategy classes. The structural model proposed above is termed the ordered logistic latent class MNL choice model. This model has been previously used by Swait and Sweeney (2000) to study the impact of value perception on consumers’ retail outlet choice behavior. Gopinath and Ben-Akiva (1995) also use an ordered latent segment model (though not an MNL model for the conditional choice); their application context is transport mode choice and models the implicit ordering among consumers resulting from their value of time. Swait (1994) develops a similar model to this but does not permit ordered segments. These models are examples of Dayton and Macready’s (1988) use of concomitant variables to identify latent segment membership. Certain parameter identification conditions apply to the model above. Only (S ⫺ 2) of the cutoff parameters, ts , s p 1, . . . , S ⫺ 1, are actually identifiable, so one of them must be arbitrarily fixed (say, t1 { 0). Other identi-

where q is a vector of unknown attribute weights, and other quantities are as previously defined. Thus, obtaining an approximate choice probability reduces to specifying the weight vector q. Several approaches could be taken to specify q in the absence of knowledge of the true parameters: (1) if there is no prior knowledge of relative attribute importance, one could give equal weight to all attributes; (2) the analyst might venture to specify q on the basis of his or her experience with similar choice problems, perhaps with the support of economic theory, where possible; (3) one could “borrow” estimates from another study considered similar to the one being conducted; or (4) one might conduct an initial data collection effort to estimate q and use this estimate in the second stage of data collection. These options roughly span the spectrum of the analyst’s willingness to inject exogenous information into the estimation of the choice probabilities. In the empirical work reported below, we have specified a simplified choice model (Eq. 10) in which the principal effects of attributes are given the sign expected by theory or the analyst’s experience (e.g., high price is worse than low price, high quality is more attractive than low quality), and in which equal weight is assigned to all attributes, which is essentially the MCD heuristic (Russo and Dosher 1983). We term this estimate of q a flat prior since weights are equal. We were inspired to take this approach by Dawes (1979) and Dawes and Corrigan (1974), who show that using equal weights in the General Linear model applied to predicting numerical standardized responses from numerical standardized predictors yields results that compare quite favorably with the use of optimal weights (see Table 1 in Dawes 1979). Thus, the level of uncertainty about a choice set is described using a measure of alternative similarity, where similarity is based on an attractiveness metric calculated using a set of equal prior weights. The resulting approximate entropy measure is, therefore,


˜rp⫺ H

冘

p˜ ir(X r ) ln [p˜ ir(X r )],

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(11)

i苸Cn

where p˜ ir(X r ) is given by (Eq. 10) using equal, but appropriately signed, weights. Based on this entropy approximation, we also define our proxy for cumulative cognitive burden, namely, cumulative entropy: w˜ r p

{冘 0

for r p 1

r⫺1

r p1

˜ r for r p 2, . . . , R H

,

(12)

where r refers to replication index, R is the total number of ˜ r is the entropy replications seen by each respondent, and H of the rth replication (given by Eq. 11) seen by a respondent. Our use of the flat prior can be considered an approximation to the true level of information uncertainty since (1) we have neither constructed individual-specific priors nor (2) have we used the true parameter values (since these are unknown). However, it is important to note that we do not wish to make behavioral assumptions about the consumer, such as what are her true tastes. Rather, we are constructing an index that characterizes the task demands on the respondent. Thus, while more accurate information about the consumer might result in a more precise measure of the task demands or complexity the consumer faces, it may be that the benefit of such additional refinement is marginal. To support this contention, some limited testing of the relative performance of the flat prior versus an improved estimate of q has been conducted, and it shows that results are quite insensitive to improvements. Specifically, a flat prior was used to estimate taste parameters, which then became the estimate of q, and so forth, until convergence. It was found that iterative improvement of the prior estimate of q resulted in very small improvements in goodness-of-fit: 0.1–0.2 percent log likelihood improvements. Thus, on the basis of this limited experience, the flat prior is adopted in the empirical work reported below. Nonetheless, it is recognized that using such a simple flat prior may not always be effective. The choice experiment examined here and the attributes used may be relatively easy to characterize with a flat prior. In cases with other goods the flat prior may not be a good characterization. As an additional investigation of the appropriateness of the entropy measure being proposed here to summarize task complexity, its consistency with the findings by Dhar (1997a, 1997b) was verified. Dhar found that increasing complexity results in increasing choice of the status quo or nonchoice alternative. In analyzing five different choice experiment data sets (two recreational site choice data sets, one consumer loan product choice data set, one land use planning data set, and the data series employed here), all of which included a nonchoice alternative, the average entropy level in choice environments in which the defer choice (or status quo) option was chosen was higher than the average entropy level in which other choices were made. For ex-

ample, in the data set employed in this study, the average entropy level when the nonchoice alternative was chosen was 0.814, while the averages when the other three alternatives were chosen were 0.709, 0.679, and 0.609.

Summary A conceptual and modeling framework within which to detect and characterize the adoption of different preference structures by subjects in experimental choice tasks has been developed above. The proposed approach attempts to graft previous work in the JDM literature with a structural econometric model to identify a posteriori classes of decision strategies utilized by a group of respondents at different replications in an experimental choice task. The method utilizes a latent class model that associates decision strategy states with unique taste parameter vectors, the estimated values of which can then be examined to characterize the decision strategies approximately. The basis for classifying an individual subject into a decision state at a certain stage of a sequence of choice scenarios is a function defined in terms of current decision task complexity, cumulative cognitive burden, and task order. Complexity is represented in the model through an empirical entropy measure, which is then summed up to capture cumulative complexity.

EMPIRICAL EVIDENCE OF MULTIPLE DECISION STRATEGY SELECTION In this section, we discuss the estimation of an ordered logistic latent class MNL choice model. The data originate from a choice experiment about frozen concentrate orange juice. We firsr describe the data utilized, followed by model estimation results. The more substantial part of this section interprets the results from the perspective of strategy selection.

Data Collection The variables manipulated in this experiment to describe the orange juice alternatives available to respondents are (1) brand (McCain’s, Old South, Minute Maid, and Generic), (2) grade (A vs. C), (3) sweetness (sweetened vs. unsweetened), (4) package size (unit vs. package of four), and (5) price per unit ($1.30 vs. $1.60/unit). A one-half fractional factorial design was used to create 32 orange juice profiles that permit the independent estimation of all main effects and two-way interactions. These profiles were presented with two other orange juice profiles. The first of these was created by randomly assigning profiles created by the foldover of the original design described above. The second was a fixed alternative, described as generic, grade C, sweetened orange juice, sold by the unit at $1.00. It should be noted that none of the levels of attributes are out of the ordinary and would be found in typical purchase situations faced by respondents. Furthermore, the fixed alternative used in all of the sets is a commonly seen promotion in area supermarkets. To complete the choice set, a nonpurchase alternative was added. Thus, the total size of each choice set


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was four alternatives, three of which are described by four attributes. The blocks of 16 choice sets presented to respondents had total cognitive loads of comparable magnitudes at all points during the course of the entire exercise for each respondent, though some tasks were somewhat more demanding than others. Individuals were recruited by telephone after being randomly selected from the telephone book; prospective respondents were provided with a general description of the study (i.e., that they would be required to fill out a short survey about frozen concentrated orange juice) and were then asked how frequently they went grocery shopping for a major grocery purchase. Only those people who went grocery shopping two or more times per month were given the option to participate. Two incentives were given to take part in the study: first, $2.00 was offered to the respondent if they agreed to do the survey, and second, $2.00 was given to a charity of the respondent’s choice. Those people agreeing to participate were randomly assigned to one of the 16 choice set blocks described above. The final sample has 280 respondents. Each individual provided responses for 16 choice scenarios; we observed 4,464 choice decisions, somewhat less than the potential of 4,480 (280 # 16), because of a few missing choices. This large number of choices is interesting for model development because the highly nonlinear latent class model requires much data to be numerically (and, therefore, statistically) stable. These choices are assumed to be statistically independent once the observable information about task and task order effects is included, which is to say, no unobserved dependence between the error terms of the latent cost-benefit factor or between the error terms of different choice tasks is permitted.

Estimation Method and Results The estimation procedure is made somewhat more complex than usual by the fact that the optimal number of decision states (S) must be determined simultaneously with the taste and cutoff parameters. Traditionally, this is done by varying S until an appropriate criterion, such as a sample likelihood, is optimized. For a given value of S, the log likelihood of the sample is given by

冘冘冘 R

L(b, tFS) p

n

rp1 i苸C r

dinr ln (Pinr ),

(13)

where dinr equals one if individual n chose alternative i in replication r and equals zero otherwise; Pinr is given by Equation 9; and all other quantities as previously defined. Log likelihood function (Eq. 13) assumes that the R p 16 choices observed from each respondent are independent. Fundamentally, this results from the operationalization of our assumption that all dependence between the choices made by the same individual is captured in the cumulative cognitive burden variable defined by (Eq. 5). This is an assumption, to be sure, but it is intrinsic to the research objective: if different individuals can occupy different de-

cision states at the same replication because they have faced different sequences of prior choices, then a structural model of dependence must be formulated that allows this. We have done so, implementing the dependence via the structure imposed by the latent cost-benefit factor (Eq. 4) and cumulative complexity (Eq. 5). Other forms of dependence among choices of an individual could be included in the model, such as state dependence, habit formation, variety-seeking, serial correlation, and so on. We have not done these things, but we do note here that incorporation of certain of these would change neither our basic approach nor its dependence on exogenous information (in particular, complexity, cumulative complexity, and order) for class membership identification. This latter point about identification is an important one since most applications of latent class models in marketing have depended on repeated measures to support class membership identification. This is not the only way classes can be identified, however: we use the concomitant variables approach of Dayton and Macready (1988) to enable latent class identification. Those authors state, “Situations with inadequate degrees of freedom for fitting a latent class model based on grouping of cases can often be analyzed using a concomitant-variable model” (Dayton and Macready 1988, p. 174). We refer the reader to Dayton and Macready (1988), Swait (1994), and Swait and Sweeney (2000) for examples of the use of independent exogenous information to aid in latent class identification (details on identification in the model we employ, including a set of simulation results, are available from the first author on request). Maximum likelihood estimation theory requires continuity in the parameter space, so maximization of Equation 13 does not apply to the discrete parameter S. Several alternative measures have been suggested in the literature, but we shall utilize both the Akaike Information Criterion (AIC) and the Bayes Information Criterion (BIC) as the bases for selection of S. Multiple measures are often used to guide selection of S since there is neither irrefutable theory nor unanimous researcher agreement on the basis for selection. The AIC is calculated as [⫺2(L S ⫹ KS )], where LS is the log likelihood at convergence in Equation 13 and KS is the number of free parameters, for a model with S latent segments. The BIC is similarly defined but considers sample size in addition to the number of parameters: [⫺2L S ⫹ KS # ln (N)]. The model with smallest AIC and/or BIC is selected. Using these criteria, model selection is affected by goodness-of-fit and parsimony. Below are the empirically determined values of the AIC and BIC measures for S p 1, 2, and 3 decision states: S 1 2 3

AIC 10,261.9 9,771.1 9,763.8

BIC 10,389.96 10,174.54 10,301.76

In this case, the BIC measure is minimized with two latent states while the AIC measure is still decreasing for three states. However, the AIC measure is only slightly smaller


for three states than for two states. On the basis of these results, we select two segments as our best estimate of S. The corresponding taste, latent cost-benefit factor, and cutoff parameter estimates are given in Table 1. To verify the robustness and optimality of this two-segment solution, we conducted a number of tests. First, we determined that the hessian of the log likelihood function, evaluated at the two-segment solution, is of full rank. Second, because the log likelihood function is not globally concave, we cannot guarantee that the solution reported in Table 1 is the global two-segment optimum. However, to increase our confidence that this is likely to be the case, we used 15 different randomly selected starting points; none of the solutions found were better than the one reported in Table 1. Third, five of the random starting points were created by perturbing the reported solution. All but one of these points converged to the reported solution, indicating that the reported solution is locally well-defined. Thus, we feel relatively confident that the reported solution is the global twosegment optimum. We addressed concerns regarding collinearity between the task order variable and cumulative entropy by reestimating the two-segment model without order effects; this latter model has a significantly lower likelihood value (⫺4,879 without order effects vs. ⫺4,822 with order effects), but the remainder of the parameters are very robust in terms of signs, significance, and magnitude. Therefore, we will discuss only the results of the full model including both order and entropy effects.

Discussion of Results The model presented above is a highly structured approach to assessing the implications of changes in complexity on consumer decision strategies. However, it is also fruitful to explore more descriptive approaches to assessing the relationship between complexity and choice. In part, this descriptive approach is useful in assessing our measure of complexity (entropy) as a characterization of complexity, but these other measures are also helpful in interpreting the results of the more structured model. As an assessment of the relationship between complexity and choice, note below the distribution of choices as a function of entropy:

Entropy range [0, .5) [.5, .7) [.7, .9) [.9, ⬁)

Percent choosing none 4.8 9.5 15.1 19.1

Percent choosing all other alternatives 95.2 90.5 84.9 80.9

Note that as entropy increases, more and more choices of none occur, whereas with the other alternatives the choices tend to occur with greater likelihood in the lower and middle ranges of entropy. This corresponds to the results of Dhar (1997a, 1997b) and others, who suggest that increasing com-

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plexity produces more nonchoice or adherence to the status quo. A similar result is observed from a simple MNL model with entropy entering as an interaction on all attributes. In order to assess the impact of complexity on brand, an MNL model was estimated with interaction effects between the attributes and the levels of complexity and cumulative complexity. Some of these results are presented graphically in Figure 1, which shows that average utilities of alternatives relative to the generic brand are all initially negative but rise as complexity increases. In Figure 1 the none alternative shows the most dramatic increase in utility, moving from being the most undesirable alternative to the most desirable at the upper end of the complexity range (supporting the discussion above regarding the increased likelihood of choosing none as complexity increases). The impact of increasing complexity appears to be not only an increase in choosing none but also a change toward brand orientation, which is a form of dimensional reduction. These results suggest that the entropy measure is functioning as a significant explanator of choice and is elucidating significant differences in attribute weights. Note that the majority of the interaction effects involving complexity, cumulative complexity, and brand were highly significant. (Detailed results are available from the first author on request.) While the results of MNL models with interactions are interesting, they are also somewhat difficult to interpret because of the large number of interactions terms and the number of possible combinations of parameters to assess. Therefore, we now turn to the discussion of the latent class model, which has two advantages over the simpler MNL model just described: it involves significantly fewer parameters, and, additionally, the structure in the latent cost-benefit strategy function allows a more direct assessment of the impact of complexity, cumulative complexity, and order on choice parameters. In the discussion below, we use the terms “strategy,” “decision state,” and “decision strategy” interchangeably. We also abbreviate decision state as DS and refer to the two decision strategies as DS 1 and DS 2. Referring to Table 1, we note that the linear and quadratic terms for the entropy measure, the cumulative entropy measure, and task order in the latent cost-benefit strategy selection function are all statistically significant, indicating that all these factors influence decision state assignment. While this supports the hypothesis that complexity, as characterized by entropy, systematically affects strategy selection, interpreting this expression is difficult without knowledge of the base levels of entropy and cumulative entropy. Figure 2 provides a graphic representation of the influence of task order and cumulative entropy (i.e., our proxy for cumulative cognitive burden) on the likelihood of being in the two DSs, assuming all tasks faced by the respondent have the same entropy value of 1.0. (Note that the maximum entropy for the data in question is ln4 ≈ 1.386, so the unit entropy represents a relatively complex choice situation.) The order and cumulative entropy effects must be viewed

TABLE 1 ESTIMATION RESULTS FOR ORDERED LOGISTIC LATENT CLASS MULTINOMIAL LOGIT MODEL Parameter estimates (asymptotic t-statistics) Decision state 1 Utility functions: Brand constants: McCain’s Minute Maid Old South None Generic (base) McCain’s attributes: Grade (p 1 if A, p ⫺1 o.w.) Sweetness (p 1 if sweet, p ⫺1 o.w.) Package size (p 1 if four-pack, p ⫺1 o.w.) Price p (x ⫺ 1.45)/.15 Minute Maid attributes: Grade Sweetness Package size Price Old South attributes: Grade Sweetness Package size Price Generic attributes: Grade Sweetness Package size Price Latent cost-benefit strategy selection factor Y r: Entropy H r Entropy squared (H r )2 Cumulative entropy Wr Cumulative entropy squared (Wr )2 Hr # Wr Cumulative order (1) Cumulative order (2) Cumulative order (3) Cumulative order (4) Cumulative order (5) Cumulative order (6) Cumulative order (7) Cumulative order (8) Cumulative order (9) Cumulative order (10) Cumulative order (11) Cumulative order (12) Cumulative order (13) Cumulative order (14) Cumulative order (15) Cumulative order (16) Cutoff parameters: t1 Summary statistics: Log likelihood (random choice) Log likelihood at convergence r2 p 1 ⫺ LL(Conv)/LL(0) NOTE.—o.w. p otherwise. *p ≤ .05.

.504 (4.7)* .823 (7.6)* .387 (3.3)* ⫺19.32 (⫺.0) 0

Decision state 2

8.64 1.90 1.64 11.13

(.1) (.0) (.0) (.1) 0

MNL model

.678 .974 .587 .374 0

(8.1)* (11.3)* (6.6)* (5.2)*

.525 (7.3)* ⫺.72 (⫺10.1)*

1.332 (3.1)* ⫺1.256 (⫺4.5)*

.654 (11.8)* ⫺.78 (⫺14.2)*

⫺.289 (⫺3.9)* ⫺.149 (⫺2.0)*

⫺.343 (⫺1.5) ⫺1.363 (⫺3.8)*

⫺.209 (⫺3.7)* ⫺.284 (⫺5.1)*

.420 ⫺.351 ⫺.078 ⫺.368

(6.1)* (⫺5.0)* (⫺1.1) (⫺5.6)*

1.412 ⫺17.753 ⫺.584 ⫺1.222

(6.3)* (⫺.0) (⫺2.7)* (⫺5.1)*

.567 (11.1)* ⫺.66 (⫺13.4)* ⫺.145 (⫺2.6)* ⫺.450 (⫺8.8)*

.724 ⫺.493 .208 ⫺.245

(8.8)* (⫺5.6)* (2.6)* (⫺3.0)*

.794 ⫺8.273 ⫺.136 ⫺.806

(4.2)* (⫺.0) (⫺.8) (⫺4.2)*

.717 (11.8)* ⫺.77 (⫺13.3)* .112 (1.9) ⫺.369 (⫺6.5)*

.556 ⫺.861 .308 ⫺.414

(7.5)* (⫺11.9)* (4.0)* (⫺8.1)*

.684 ⫺13.294 ⫺.371 ⫺4.006

(2.9)* (⫺.0) (⫺1.5) (⫺.3)

.592 ⫺.948 ⫺.230 ⫺.480

5.174 (2.5)* ⫺2.671 (⫺1.6) 1.150 (2.3)* ⫺.061 (⫺2.0)* ⫺.072 (⫺.8) ⫺.587 (⫺.6) ⫺.312 (⫺.6) ⫺1.042 (⫺2.2)* ⫺.760 (⫺1.5) ⫺.760 (⫺2.0)* ⫺.278 (⫺.6) ⫺.370 (⫺.8) ⫺.503 (⫺1.1) ⫺2.94 (⫺6.48)* .267 (.7) .435 (.1) ⫺.244 (⫺.7) .009 (.0) .177 (.4) .548 (1.1) .678 (1.7) 0 ⫺6,188.4 ⫺4,822.5 .221

⫺6,188.4 ⫺5,110.9 .174

(10.5)* (⫺16.6)* (⫺3.9)* (⫺11.5)*

INFLUENCE OF TASK COMPLEXITY ON CHOICE FIGURE

1

UTILITY OF BRAND CONSTANTS BY ENTROPY LEVEL (MULTINOMIAL LOGIT MODEL)

together, of course, since both change simultaneously. The pattern that emerges is a high probability (about 0.92) of being in DS 1 until approximately the eighth task (of the 16 tasks each subject did). After this point there is an abrupt reduction in the probability of being in DS 1, and the probability of membership in DS 2, all else held constant, is higher throughout the remaining tasks. The latent classification function captures the likelihood of being in each segment and shows that segment membership is significantly associated with the degree of complexity, cumulative complexity, and task order faced by the individual. However, from these results little can be said about the behavioral responses to complexity that arise when moving from decision state to decision state. It is to this topic that we now turn. The taste parameter estimates in Table 1 for the two decision states show the differences in the structure of the two decision states. In DS 1 most taste parameters are significant. The brand specific constants are all quite similar in magnitude, indicating that there is relatively little brand discrimination. In DS 2, however, there appears to be strong discrimination between brands (ceteris paribus, McCain’s is highly preferred to the other two brands and the generic alternative), while some attributes (i.e., sweetness and package size) are not considered for most brands. The relatively large parameters on sweetness for three brands in DS 2 are likely to reflect noncompensatory preferences over this attribute. It appears that very few individuals chose sweetened juice, and thus sweetness appears as large negative coefficients in the model, but we should note that these are also characterized by lack of significance. The model, therefore,

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has specified unsweetened juice as very desirable, but limited variation results in the large standard error. Finally, DS 2 alternative-specific constants indicate a strong propensity to choose the none alternative (brand constants are smaller than the constant for none, which is large and positive): across the sample, the average probability of choosing none (within sample prediction) is nearly zero for DS 1, and nearly 0.60 for DS 2. In contrast, the constant for none in DS 1 is negative and large relative to the positive and significant constants for brands, indicating that nonchoice is not a preferred alternative in DS 1, all other things being equal. These two decision states appear to reflect individuals who are following a decision strategy that employs more attributes (DS 1) at a certain level of entropy and cumulative entropy, until later in the set of tasks when they begin to switch to the more brand-oriented, more inclined-to-opt-out (choose none) strategy (DS 2). In DS 2 respondents seem to focus on certain brand-attribute combinations, and then they base their decision entirely on this subset of attributes (or they choose to avoid choice). Thus, it would seem that the following summary characterization of these decision states, loosely based on Russo and Dosher’s (1983) nomenclature, is possible.

FIGURE

2

INFLUENCE OF ENTROPY ON DECISION STATE CLASSIFICATION PROBABILITIES BY TASK ORDER


146

Statistically significant information utilization Brand Grade Sweetness Package size Price

Decision state 1: “compensatory”/ complete attribute set employed

Decision state 2: Brandfocused dimensional reduction and/or opt-out

⻬⻬⻬⻬⻬

⻬⻬ X X ⻬

As task order increases, respondents move from the apparently rich, attribute-based strategy, to a simpler one. This was graphically portrayed in Figure 2, where, with entropy levels of 1.0 per task, respondents begin by employing more attributes in choosing but evolve to the brand/opt-out heuristic. Thus, it may be that the effort of using more attributes early in the sequence appears to make respondents switch to a strategy of using less attribute information in the later tasks. Also, it seems that respondents take on the challenge of the higher entropy early in the sequence by choosing the richer strategy (with increased probability), which is consonant with Keller and Staelin’s (1987) concept that individuals initially exert additional effort and become more effective, until a point is reached where their effectiveness begins to deteriorate. For comparison, Table 1 provides the results from a simple MNL model applied to the same data (i.e., a one-segment model). The signs of the attribute parameters in the MNL model are nearly always the same as those of the latent classes. However, the sizes and significance levels of these parameters are quite different. The MNL model parameters are all significant and appear to support what could be inferred as a strategy that employs all attribute and brand information. However, in DS 2 of the latent class model, many of the attribute parameters are not significant, suggesting that less information is being employed, at least not in a compensatory fashion. Furthermore, the brand effects are very different between the two models. As expected from a comparison of the goodness-of-fit of the MNL and latent segment models, the two-decision state model provides better predictions, particularly for the none option. The overall prediction success from the MNL model is 38.4 percent, while the prediction success from the latent class model is almost the same, at 41.7 percent. Furthermore, prediction success for alternatives 1, 2, and 3 is similar between the two models; however, the MNL model is only successful at predicting 24.6 percent of the none alternatives, while the latent class model correctly predicts 34.0 percent of the none choices. This result is supportive of Dhar’s (1997a, 1997b) findings that complex decision environments result in individuals deferring choice or choosing not to choose. The latent class model, because it incorporates complexity, can better predict such behavior than the simpler MNL model.

CONCLUSIONS AND FUTURE RESEARCH The fact that consumers appear to change their decisionmaking strategies in response to choice context, and particularly in response to choice environment complexity, has been well documented in the literature on human decision processing. However, these findings have not been incorporated into aggregate econometric models of choice behavior, nor have they been incorporated into the design or analysis of choice experiments. There are good reasons for this: (1) a consistent method for representing choice context and complexity within aggregate econometric models of choice has not been available; and (2) a method that allows aggregate econometric models to test for changes in decision-making strategy over ranges of task complexity (or other context factors) has not been developed. In this article we provide potential solutions to both of these issues. We employ entropy, which is simultaneously a function of number of alternatives, the number of attributes, the relationship (correlation) between the attribute vectors themselves, and the structure of preferences, as a measure of choice task complexity, and we employ cumulative entropy as a measure of cumulative cognitive burden, within an aggregate, latent class model of choice. (We also consider the effect of task order, which is found to have a separate and statistically significant effect to that of cumulative entropy.) Furthermore, we use these measures of complexity in a model that allows for changes in decision-making strategies over ranges of task complexity. This latent classification scheme provides the link between the choice environment and the potential for the selection of different processing strategies by the respondent. In the particular case we examined, decision makers appear to fall into two segments, depending significantly on the level of complexity of a particular choice task and on the amount of complexity already faced in previous tasks (or cumulative cognitive burden, as we have termed it), as well as on task order. The proposition that preference parameters depend on the degree of complexity is strongly supported. Furthermore, the empirical analysis suggests that a distinct, simpler processing strategy arises in cases with high levels of task complexity (or after significant expenditure of processing effort, through cumulative entropy) later in the task sequence. This simplified processing strategy appears to focus more on brand effects and less on attributes, and it includes an increased propensity to avoid choice. While our empirical analysis supports the notion that increasing complexity over a number of tasks generates changes in choice behavior toward strategies that employ less attribute and brand information, this may not always be the case, of course. However, models such as the one developed here are able to test the hypothesis that task complexity results in changes in processing strategy. Furthermore, these models can be used to simulate at what point decision-making strategies begin to change, and what the implications of increasing complexity are for the choice of specific alternatives. Such information will enable better understanding of how to present information to decision mak-


ers, and can also be used better to forecast the response of individuals to changes in complexity arising from the introduction of new goods or from changing attribute levels within actual markets. We would like to point out some of the limitations of our study. First, we have assumed that compensatory models are able adequately to capture noncompensatory behaviors and that different configurations of preference vectors in such models can be interpreted as evidence pointing to the presence of underlying heuristics. Future research can attempt to avoid the use of compensatory models; such efforts will be forced to choose which noncompensatory heuristics to employ, so significant challenges will have to be faced. Second, entropy, the summary measure of complexity we have proposed, reflects the impact of number of attributes only indirectly, via the structure of preferences. Future research might examine extensions to entropy to account for this effect more directly. Third, we have argued that the flat prior assumption (i.e., calculating an approximate entropy measure based on equal, but directionally appropriate, weights) yields an entropy measure that is sufficiently discriminatory to enable the detection of different decision strategies. We presented some evidence supporting this, but future research must explore this issue in more depth, since the existence of taste heterogeneity poses a difficulty for the approach we adopted in this article. Fourth, we have found that cumulative cognitive burden is an important driver of strategy switching. Cumulative complexity, given by Equation 5, assumes that all prior tasks are equally important. Future research should relax this assumption and investigate whether recent tasks are more influential than earlier tasks in determining the cumulative cognitive burden imposed on the respondent. Finally, we have assumed that the experimental choice tasks are independent (except for task order effects); incorporating the possibility of error correlation across tasks would be beneficial. One of the directions that this stream of research must take in the future is to investigate how the decision strategies used in choice tasks relate to those used by consumers in real markets. Experience with aggregate choice models has shown that well-designed choice tasks result in models that can predict well to real markets (see Louviere, Hensher, and Swait 2000, chap. 13). However, it is unclear what relationship exists between decision strategies adopted in hypothetical tasks (not to speak of variation in decision strategies during the course of a task!) and market decisions. We believe that because the model presented here takes into account context effects relating to complexity, it should be able to perform better in predictions of choices where these effects are significant. Thus, consumers opting not to choose, or ignoring some attributes and focusing on brand, as the market becomes more complex should be an expected result from our model. Further research with revealed preference data can help clarify if we are finding a survey effect (fatigue, boredom, etc.) or a real market effect. The degree to which dynamic elements of behavior (habits, variety seeking, etc.) interact with complexity are also useful avenues

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for research. Responses to complexity may include a move to more habitual choice or habit behavior, which may explain much of what appears to be a response to complexity in choice data. Also, an improved understanding of this matter will certainly aid in determining choice experiments that better reflect market decision making; this should lead to improved external validity of choice experiments. [Received February 1998. Revised October 2000. David Glen Mick served as editor, and Joel Huber served as associate editor for this article.]

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