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Article Excerpt
Greedoid languages provide a basis to infer best-fitting noncompensatory decision rules from full-rank conjoint data or partial-rank data such as consider-then-rank, consider-only, or choice data. Potential decision rules include elimination by aspects, acceptance by aspects, lexicographic by features, and a mixed-rule lexicographic by aspects (LBA) that nests the other rules. We provide a dynamic program that makes estimation practical for a moderately large numbers of aspects.
We test greedoid methods with applications to SmartPhones (339 respondents, both full-rank and considerthen-rank data) and computers (201 respondents from Lenk et al. 1996). We compare LBA to two compensatory benchmarks: hierarchical Bayes ranked logit (HBRL) and LINMAP. For each benchmark, we consider an unconstrained model and a model constrained so that aspects are truly compensatory. For both data sets, LBA predicts (new task) holdouts at least as well as compensatory methods for the majority of the respondents. LBA's relative predictive ability increases (ranks and choices) if the task is full rank rather than consider then rank. LBA's relative predictive ability does not change if (1) we allow respondents to presort profiles, or (2) we increase the number of profiles in a consider-then-rank task from 16 to 32. We examine trade-offs between effort and accuracy for the type of task and the number of profiles.
Key words: lexicography; noncompensatory decision rules; choice heuristics; optimization methods in marketing; conjoint analysis; product development; consideration sets
History: This paper was received January 25, 2005, and was with the authors 5 months for 2 revisions; processed by Eric Bradlow.
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1. Noncompensatory Decision Processes
We explore new methods to study heuristic decision processes. These methods use "greedoid languages" and dynamic programming to solve combinatorial computational problems significantly more efficiently than as reported in the extant literature. We demonstrate how the methods can be used to identify the heuristic decision processes that best describe observed consideration and/or choice. Because the methods work with either rank-order data or consider-then-rank data, we are able to examine empirically how well each data-collection format predicts choice. A consider-then-rank task might be more enjoyable and less effortful for respondents (e.g., Malhotra 1986, Oppewal et al. 1994, Srinivasan and Park 1997) and, hence, might mean shorter questionnaires (less cost) and might encourage more respondents to complete the task (fewer nonresponse issues).
Noncompensatory decision processes are important both academically and managerially. Academically, there is ample evidence in the psychology, consumer behavior, and marketing science literatures that consumers simplify consideration and/or choice with a heuristic process. (1) Such processes are identified using a variety of methodologies ranging from verbal process tracing to information display mechanisms (e.g., Mouselab), and researchers have studied how consumers adapt and/or construct decision processes based on the characteristics of the decision environment (see Payne et al. 1993 for a review). Greedoid methods attempt to infer such processes from less intrusive observations where respondents are asked either to rank profiles, provide partial profile orders, or indicate whether or not they will consider a profile. These methods are, thus, complementary to existing methods.
Consider Figure 1 from a SmartPhone Web site (2) that encourages consumers to select SmartPhones for further consideration based on features such as carrier, brand, size, and price. Consumers can choose to keep or eliminate levels of these features to form a consideration set. If consumers use a heuristic, noncompensatory process and we can identify the features that drive the process, then the Web site designer knows which features to use, the product designer knows which features to include in the product line, and the advertising manager knows which features to emphasize.
[FIGURE 1 OMITTED]
Typically, compensatory conjoint analysis methods are used in these situations to identify the features with the largest partworths. Such methods are computationally tractable and often provide excellent paramorphic approximations of consumer consideration and/or choice processes. However, if consumers are not making compensatory trade-offs among features but, rather, are using noncompensatory heuristics, a method to identify those heuristics might be appealing. Heretofore, analyzing rank, partial rank, or consideration data to infer noncompensatory processes has not been computationally feasible for moderately sized problems because the number of potential noncompensatory descriptions grows as n! where n is the number of distinct feature levels (aspects). (3) We provide an algorithm that can identify the best-fitting heuristic in seconds (rather than days). We illustrate the algorithm on two data sets and with experiments that vary the consumers' decision environment. Some of these experimental manipulations are designed to replicate existing findings; some experimental manipulations are new.
The paper proceeds as follows. First, we briefly review the literature on heuristic processes and provide examples. Next, we describe the respondents' tasks. We present greedoid-based methods and discuss the traditional methods to which they are compared. We test the methods empirically in a 2 x 2 experiment in which 339 respondents choose from 32 SmartPhones chosen from a fractional factorial [4.sup.3][2.sup.4] design. We examine the impact of the number of profiles, the respondents' tasks, and sorting on the relative predictability of noncompensatory models. For comparison, we reanalyze classic data in which 201 respondents rated 16 computers chosen from a fractional factorial [2.sup.13] design. Finally, we close by illustrating how greedoid analysis provides managerial insight.
2. Brief Review of Noncompensatory Decision Processes
We consider decision processes in which products are represented by their features and consumers decide which product to purchase or consume. While the process by which consumers encode products into features can be complex and important (Einhorn and Hogarth 1981), that topic is beyond the scope of this paper. Our scope includes situations in which such encoding is feasible and reasonably descriptive of consumer decision processes. For practical applications, we might use voice-of-the-customer methods to identify a representative set of features (e.g., Griffin and Hauser 1993, Zaltman 1997). When a feature is binary, it is called an aspect (e.g., Tversky 1972). Multilevel features can be considered collections of aspects that are related (Verizon versus Cingular versus Nextel versus Sprint for SmartPhone service providers). A profile is the aspect description of a product.
Noncompensatory Processes
In a compensatory process, high levels on some aspects compensate for low levels on other aspects. In a noncompensatory process, high levels on some aspects cannot compensate for low levels on other aspects. One well-known noncompensatory process is a lexicographic process: Consumers evaluate profiles first by one feature, then another, until a judgment or choice is made (Fishburn 1974, Nakamura 2002). For example, consider an illustrative example in which consumers rank SmartPhones that differ on the features of brand and operating system. As illustrated by the first row of Figure 2, a consumer might rank first on the feature of brand, putting first all BlackBerry SmartPhones, then Nokias, Samsungs, and, last, Sony Ericssons, then rank on the feature of operating system (within brand) by putting all Microsoft-based SmartPhones before PalmOS-based SmartPhones. We call this process lexicographic by features (LBF).
[FIGURE 2 OMITTED]
Other heuristics are possible. A consumer might rank SmartPhones by aspects, say, by first accepting BlackBerry SmartPhones, then Microsoft-based SmartPhones, Nokias, and, finally, Samsungs until all SmartPhones are ranked (second row of Figure 2). (Whenever there is a tie, the consumer moves to the next aspect in the lexicographic order.) For ease of reference, we call such processes acceptance by aspects (ABA). ABA is related to Tversky's elimination-by-aspects process (EBA) in which consumers successively eliminate aspects (third row of Figure 2). Tversky defines EBA as a random process in which the probability that an aspect is chosen is proportional to its measure. In this paper, we follow Johnson et al. (1989), Montgomery and Svenson (1976), Payne et al. (1988), and Thorngate (1980), and use EBA to refer to a deterministic process in which an aspect order is given. Finally, consumers may mix acceptance and elimination criteria. We call such a mixed process lexicographic by aspects (LBA). Because ABA, EBA, and LBF are special cases of LBA, we focus on LBA.
When a feature has more than two aspects, eliminating an aspect (Sony Ericsson) is the same as accepting its complement (BlackBerry U Nokia U Samsung), but EBA is not equivalent to an ABA process of accepting BlackBerry, then Nokia, then Samsung. The ABA process orders BlackBerry-Nokia-Samsung, while the EBA process does not. However, for two-level aspects, there exists an equivalent EBA process for every ABA process. Figure 3 illustrates this equivalency for SmartPhones that differ on three binary aspects (brand, operating system, and carrier).
[FIGURE 3 OMITTED]
ABA, EBA, LBA, and LBF define orderings and hence can be used to explain either full or partial rankings, including respondent tasks such as rank all profiles, choose a single profile, or indicate which profiles are worth further consideration. Finally, the processes can be modified to include constraints within features such as "lower prices are always preferred to higher prices."
Compensatory Processes
Many authors represent a compensatory process as an arithmetic rule in which each aspect receives a weight and consumers sum the weights associated with the aspects in a profile to form "utility." Consumers then choose the product with the highest "utility." However, not all sets of aspect partworths imply a compensatory process. If the aspect partworths follow an appropriate geometric sequence (e.g., [2.sup.1-n] for the nth aspect), then an additive model produces a lexicographic process in which no set of lower ranked aspects can compensate for the lack of a higher ranked aspect (Jedidi et al. 1996, Kohli and Jedidi 2004, Olshavsky and Acito 1980). Thus, we reserve the word "compensatory" for additive models that are truly compensatory, e.g., when the partworths are constrained so that the presence of other aspects can compensate for the lack of an important aspect.
Constructive Processes
Research suggests that consumer decision processes are contingent on many context effects including the range of aspects, correlation among aspects, base-rate information, reference points, the size of the choice set, the relevance of the decision, and the difficulty of comparison (see review in Payne et al. 1993). To the extent that data collection approximates the essential characteristics of real choice environments, greedoid methods provide insight into how context affects respondents' tendency to use noncompensatory decision rules. Our empirical experiments illustrate this context-dependent variation.
Existing Methods to Infer Noncompensatory Processes
Many measurement examples in the marketing science literature are consistent with noncompensatory decision processes. For example, both Srinivasan and Wyner's (1988) Casemap and Johnson's (1991) adaptive conjoint analysis (ACA) include steps in which respondents are asked to eliminate unacceptable levels. Because this task is often difficult for respondents (Green et al. 1988, Klein 1988), other researchers have attempted to infer the elimination process in a single estimation step (DeSarbo et al. 1996, Gilbride and Allenby 2004, Gensch 1987, Gensch and Soofi 1995, Jedidi and Kohli 2005, Jedidi et al. 1996, Kim 2004, Roberts and Lattin 1991, Swait 2001). For example, Gilbride and Allenby (2004, p. 399) use hierarchical Bayes methods to analyze choice-based conjoint data to infer screening rules for cameras. They estimate that 58% of the respondents screen on a single feature, 33% on two features, 2% on three features, and 8% use fully compensatory processes.
In psychology, Broder (2000) analyzes choices among two profiles described by...
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