Two-stage discrete choice models for scanner panel data: An assessment of process and assumptions

Discrete choice models such as the multinomial logit assume that consumers choose from the full set of alternatives available to them. However, because (i) consumers may not be able to recall or recognize available brands, (ii) consumers may not have the cognitive capacity or mental energy to process information pertaining to all available brands, or (iii) careful consideration of all available brands might be suboptimal from an economic standpoint given the cost of information search, consumers tend to make choices from a relatively small subset of the available brands. This study assesses the process assumptions of existing two-stage models for scanner panel data and their consistency with the actual processes believed to be used by consumers in forming choice sets. After reviewing what is known from two-stage models in scanner data applications, we highlight issues in need of research. Ó 1998 Elsevier Science B.V. All rights reserved. Keywords: Choice sets; Choice models; Buyer behavior 1. Introduction Over the last 15 years, more than a dozen twostage choice models have been described in the marketing, management, econometric, geography, and transportation engineering literatures. These models have been developed in order to relax certain restrictive assumptions inherent in Lucebased discrete choice models such as multinomial logit, namely the IIA assumption relating to the similarity of available brands and the assumption that all consumers choose from the same universal set of brands available in the marketplace when making a choice. Compared to single-stage discrete choice models (which are reviewed by Manrai, 1995), two-stage models may better represent the underlying process which consumers are believed to use in selecting a brand from a set of competing brands (Gensch, 1987; Shocker et al., 1991). Typically, in the ®rst stage of a two-stage choice model, the consumer is assumed to form a set of brands from which the ®nal choice will be made, which is known as the choice set (Shocker et al., European Journal of Operational Research 111 (1998) 193±215 * Corresponding author. Fax: +1-302-831-4196; e-mail: [email protected] 0377-2217/98/$19.00 Ó 1998 Elsevier Science B.V. All rights reserved. PII S 0 3 7 7 2 2 1 7 ( 9 8 ) 0 0 1 4 5 3 1991). Forming this set may involve (i) building the set ``from scratch'' by recalling or recognizing brands that are capable of meeting the current need, (ii) reducing the full set of available brands by screening brands that are not desirable or capable of meeting the need, or (iii) some combination of these two processes. In the second stage of a two-stage choice model, the consumer is typically assumed to make a choice from this smaller set of brands using a brand-based compensatory analysis, such as that of the standard multinomial logit choice model. Behaviorally, several explanations can be put forth to justify two-stage models of brand choice. First, in memory-based choice situations (such as the choice of a restaurant), consumers may not be able to recall all brands or options that are available to them (Hutchinson et al., 1994). Inability to recall all brands in the awareness set results in an actual choice set that is smaller than the universal set. Likewise, the consumer may be exposed to brand names in a supermarket and fail to recognize some set of them as appropriate for the need at hand, resulting in a reduced set of alternatives from which to make the ®nal choice. Brand primes such as advertisements, point-of-purchase displays, and store features may make a brand's recall more likely (Andrews and Srinivasan, 1995; Bronnenberg and Vanhonacker, 1996; Nedungadi, 1990). Second, given awareness of the relevant brands, consumers may lack the processing capacity or the mental energy to process all information pertinent to these brands. Researchers have suggested ``phased'' decision strategies as characteristic of decision making in contexts where the choice situation is overly complex (Payne, 1982; Shocker et al., 1991; Wright and Barbour, 1977). With phased decision strategies, the consumer is thought to ®rst screen alternatives using relatively simple criteria before making a more thorough analysis and choice from the reduced set of brands. Third, exhaustive search and information processing may not be optimal given the costs associated with these activities. The theory of the economics of information beginning with Stigler (1961) demonstrates that the optimal number of brands to be searched in a choice situation may be smaller than the number of available brands given nonzero search costs. Empirical evidence has supported the theory to some extent (e.g., Andrews, 1992). Roberts and Lattin (1991) and Hauser and Wernerfelt (1990) have formulated cost-bene®t models to describe the formation of the consumer's choice set, and Andrews and Srinivasan (1995) developed an extension of the Roberts and Lattin model which is intended for use with scanner panel data. Perhaps because the research in this area has emerged from di€erent disciplines, there has previously been no complete conceptual comparison of available two-stage choice models. Given the rapid proliferation of two-stage models in recent years, the goal of this paper is to take inventory of the available models to determine how they are di€erent conceptually, what process assumptions are being made by the models, and what work remains to be done in the area. It is not our intention to review all literature on choice simpli®cation and choice sets ± only two-stage models of choice which may be applied to scanner panel data. See Roberts and Lattin (1997) for a review of other recent choice set research. Section 2 describes various criteria on which two-stage discrete choice models di€er and presents an overview of existing models. Section 3 examines the processes, assumptions, and mathematical forms of these models in some detail. Section 4 presents evidence on the explanatory power and forecasting performance of existing two-stage models. Finally, Section 5 provides conclusions and outlines some directions for future research. 2. Criteria for assessing two-stage discrete choice models Manski (1977) provides a general expression for computing the choice probabilities for two-stage models. When consumer n makes a choice from among a set S ˆ f1; 2; . . . ; i; . . . ;mg of feasible brands on some choice occasion t, the probability that the consumer will choose some brand i is computed as 194 A.K. Manrai, R.L. Andrews / European Journal of Operational Research 111 (1998) 193±215 P …i j S; b; c;X n t ; Zn† ˆ X 2mÿ1 jˆ1 P …Cj j c;X n t ; Zn†P …i j Cj; b;X n t ; Zn†; …1† where Cj is one of the 2m ÿ 1 nonempty subsets of S; c and b are vectors of parameters re ̄ecting the e€ectiveness of explanatory variables at the two stages of the model; X n t is a matrix containing the attributes of all brands in set S, as experienced by consumer n at choice occasion t; and Zn is a matrix containing consumer n's characteristics, which are assumed to be time invariant. Thus, the ®rst stage of a two-stage model is concerned with how the consumer generates the reduced choice set, and this is captured in the ®rst component on the righthand side of Eq. (1). The second stage, represented by the second component on the right-hand side of Eq. (1), describes how the consumer makes a choice from this set. The two sets of parameters c and b describe the e€ectiveness of explanatory variables in choice set formation and choice, respectively. In Eq. (1), it is not necessary that all variables contained in the matrices X n t and Z n be involved in both stages of the two-stage model; variables determining choice set composition and choice may overlap partially, completely, or not at all. The simulation study by Andrews and Manrai (1998) found no adverse consequences from including the same variables as determinants of both consideration and choice. Eq. (1) is a two-stage model in its most general form. When the universal set is large, Eq. (1) is not a feasible choice set model since the number of possible choice sets …2m ÿ 1† is so large as to become computationally burdensome. Hence, most two-stage brand choice models are special cases of Eq. (1). Though existing models consistently assume that the consumer makes the second-stage choice from the restricted choice set using a compensatory, brand-based evaluation strategy, they posit a variety of speci®cations for the choice set formation component P Cj j c;X n t ; Zn ÿ : Choice set generation can be (i) memory-based or stimulusbased, (ii) naive or based on consumer and/or product characteristics, (iii) attribute-based or brand-based, (iv) static or dynamic, and (v) deterministic or probabilistic. 2.1. Memory-based versus stimulus-based choice set formation Choice set formation is memory-based if the consumer retrieves the contents of the choice set from memory without any cues from the external environment and stimulus-based if the consumer forms the choice set when the universal set of options is physically present in the consumer's environment at the time of choice. Purely memorybased choice set formation may be more common in store-choice decisions (e.g., choosing a restaurant) than in brand-choice decisions (e.g., choosing a brand of orange juice), though some argue that consumers use memory-based choice even in the presence of the alternatives since information overload is common, and consumers are limited information processors (Alba et al., 1991). Choice set formation may also be purely memory-based when the consumer makes the brand choice decision prior to entering the store (Bucklin and Lattin, 1991). In memory-based choice situations, the consumer may generate the choice set by considering only brands which s/he has purchased before (e.g., Siddarth et al., 1995), only brands which are most preferred, or only brands whose advertising the consumer remembers at the time of purchase (Mitra, 1995). Since in-store marketing information would not be used in a memory-based context, modeling choice set formation may also be accomplished by assigning probabilities to some or all possible combinations of brands available to the consumer (a strategy used by Chiang et al., 1996). We refer to this modeling strategy as naive choice set formation since no information from the purchase environment in ̄uences the generation of the choice set. In stimulus-based choice situations, the consumer may generate the choice set using prices, promotions, store feature advertisements, shelf space allocation, or other point-of-purchase in ̄uences in the store environment. For example, one stimulus-based heuristic is to consider only brands that are on sale (e.g., Fader and McAlister, 1990). It is also possible that memory-based and stimulus-based factors may jointly a€ect choice set formation (Shocker et al., 1991). For example, A.K. Manrai, R.L. Andrews / European Journal of Operational Research 111 (1998) 193±215 195 Andrews and Srinivasan (1995), Bronnenberg and Vanhonacker (1996) and Siddarth et al. (1995) model choice set formation as a function of both previous purchases and marketing mix information in the purchase environment, which would be typical of a ``mixed'' choice set formation strategy. Perhaps the consumer's choice set consists of acceptable previously purchased brands prior to entering the store but is expanded to include brands with price promotions once the consumer enters the store environment (cf., the promotion expansion strategy described by Siddarth et al., 1995). 2.2. Naive versus theoretical choice set formation In the case of memory-based choice set formation, marketing mix information at the point of purchase does not a€ect choice set size and composition. When consumer and/or brand characteristics do not a€ect choice set formation (naive choice set formation), the ®rst-stage utility of a brand or a set of brands will be estimated directly as a free parameter. In this case, the set generation component becomes P Cj j c ÿ , which is free of conditioning variables. Choice sets formed on the basis of the consumer's purchase history (another memory-based choice set formation strategy) are also labeled as naive. Naive models may be more appropriate when (i) choice set formation is believed to be primarily memory-based, (ii) the researcher is unable to specify which variables in ̄uence membership in the choice set, or (iii) data on the desired variables are not available. Empirical results show that models with choice set generation components speci®ed as a function of marketing and/or consumer variables often have better out-of-sample forecasting performance than do naive models (e.g., Andrews and Manrai, 1995; Andrews and Srinivasan, 1995; Siddarth et al., 1995; Swait and Ben-Akiva, 1987). 2.3. Attribute-based versus brand-based choice set formation A two-stage choice model is called a brandbased model if the brands are evaluated holistically prior to inclusion in the choice set. For example, the consumer may be more likely to consider a brand if its salience exceeds some cuto€ level (e.g., Bronnenberg and Vanhonacker, 1996). Shocker et al. (1991) note that brand-based choice set formation is probably not supportable empirically since it implies that all brands in the universal set are screened for possible inclusion in the choice set. A model is attribute-based if the consumer processes information by attribute rather than by brand, screening out brands that contain (or do not contain) certain features or attributes. For example, a consumer may consider only brands which have yellow shelf tags indicating price reductions, without processing other brand and marketing mix information for the universal set of brands. While judgment processing is brand-based, choice processing tends to be attribute based (Alba et al., 1991; see also Bettman et al., 1991). Consumers seem to prefer to compare brands on each attribute sequentially and to integrate the results of these comparisons (a noncompensatory strategy) rather than to integrate all information about each brand into a single overall evaluation and then choose the alternative with the best overall evaluation (a compensatory strategy). Of course, consumers are more likely to process information by brand when the number of alternatives is small (e.g., once the choice set has been formed) than when there are many alternatives (Bettman et al., 1991). As reviewed in Gensch (1987), most protocol-based research on two-stage decision strategies has demonstrated that the initial screening takes place using a noncompensatory attribute screening process to reduce the universal set of brands down to a ®nal choice set. Once the smaller choice set has been generated, a compensatory, brand-based strategy is typically used to evaluate the remaining brands. Roberts and Lattin (1991) point out that ``though the consumer behavior literature argues for noncompensatory screening processes on theoretical grounds, a substantial literature suggests that under a wide range of situations, compensatory models provide a reasonably accurate approximation to noncompensatory processes'' (p. 431). Fader and McAlister (1990) conclude that attrib196 A.K. Manrai, R.L. Andrews / European Journal of Operational Research 111 (1998) 193±215 ute-based noncompensatory processes such as Elimination By Aspects (EBA) (Tversky, 1972) could be better representations of actual consumer decision processes, even if they do not ®t the data better than their compensatory counterparts. The relative explanatory power and predictive ability of attribute-based and brand-based two-stage models remains an unresolved empirical question. However, the simulation study by Andrews and Manrai (1998) shows that at least one two-stage model with brand-based screening is not very capable of mimicking the noncompensatory, attribute-based screening strategies believed to be used to form choice sets. Parameter bias and poor forecasting accuracy resulted when models with brand-based screening were ®t to data with choice sets generated by an attribute-based screening. The type of information processing model (brand-based or attribute-based) dictates how the choice set generation component P Cj j c;X n t ; Zn ÿ is speci®ed in Eq. (1). Brand-based models ®rst compute the probability that any given brand will enter the choice set. In contrast, attribute-based models assign probabilities to sets of brands containing certain attributes or features. These models assign probabilities to brands only in the special case of choice sets containing single brands. Regardless of the strategy used to form the choice set, a compensatory brand-based evaluation is typically assumed for the task of making a choice from the choice set. 2.4. Static versus dynamic choice set formation Choice set formation is static if the set of brands from which the consumer makes a choice does not change over choice occasions. A static model results from Eq. (1) when (i) only consumer characteristics Zn (which typically do not change over choice occasions) determine choice set composition, (ii) only brand characteristics X n which do not change in the short run (e.g., the sugar content of a cereal) determine choice set composition, (iii) choice set probabilities which are constant across consumers and purchase occasions are estimated for all possible choice sets, or (iv) choice set probabilities varying across consumers but not purchase occasions are estimated for all possible choice sets. Choice set formation is considered to be dynamic if it allows for the possibility that the composition of the choice set may vary over choice occasions. A dynamic model results if such variables as price, television and store feature advertising, and past purchases a€ect choice set formation (Shocker et al., 1991). Dynamic models of choice set formation typically assume that there is heterogeneity in choice set composition across purchase occasions but not across consumers. That is, all consumers are assumed to update their choice sets using the same strategy (say, consider only previously purchased brands), even though the composition of the choice set obviously does vary across consumers. In contrast, the static model by Chiang et al. (1996) assumes that choice sets are heterogeneous across consumers but constant across purchase occasions. As yet, no model has described choice sets which are heterogeneous across consumers and which also evolve over time in di€erent ways for di€erent consumers. Dynamic two-stage models should perform better than static models when (i) the store environment (e.g., displays, store features, or prices) frequently changes across purchase occasions, (ii) store environment variables are important determinants of brand consideration and choice, and (iii) brand loyalty, size loyalty, or loyalty to other attributes is an important determinant of consumer purchasing behavior (as in memory-based choice situations). We suspect that all three of these conditions hold in most situations, and consequently, that dynamic two-stage models would perform better than static two-stage models. The studies by Mitra (1995) and Siddarth et al. (1995) provide evidence in support of this assertion. 2.5. Deterministic versus probabilistic choice set formation If a model predicts with certainty the composition of the consumer's choice set, then the model is deterministic. A deterministic model may be appropriate, for example, when the researcher can A.K. Manrai, R.L. Andrews / European Journal of Operational Research 111 (1998) 193±215 197 observe that certain brands (e.g., regional brands) were not available to some consumers at the time of choice. Unless there is hard evidence that certain brands are not available to certain consumers, deterministic two-stage models do not lend themselves well to scanner data applications, at least when maximum likelihood estimation is used. This is because the log likelihood function for such models goes toward negative in®nity when the consumer makes the ``surprise'' choice of a brand that is not believed to be in the choice set. A deterministic model results from Eq. (1) when the occurrence probability of one set of brands (the ``true'' choice set) is one, and the occurrence probabilities of the remaining 2m ÿ 2 subsets of brands are all zero. Thus, P Cj j c;X n t ; Zn ÿ ˆ 1 if set j is the ``true'' choice set (however this is determined), and P Cj j c;X n t ; Zn ÿ ˆ 0 if not. The models by Gensch and Soo® (1995) and Roberts and Lattin (1991) are examples of deterministic two-stage models, and the nested logit model is an example of a deterministic, possibly multi-stage, hierarchical choice model (cf. Kamakura et al., 1996). A two-stage model is probabilistic when the composition of the consumer's choice set is not known with certainty, and nonzero occurrence probabilities are attached to two or more sets. All of the models we review in this study are probabilistic since deterministic models are not wellsuited to scanner panel data. Shocker et al. (1991) note that choice sets themselves are latent in the sense that they cannot be determined with certainty, especially with scanner panel data, so probabilistic models of choice set formation are probably more realistic. Table 1 describes recent two-stage models amenable to analysis with scanner panel data, broken down according to whether they are (i) memory-based or stimulus-based, (ii) attributebased or brand-based, and (iii) static or dynamic. All models in the table are probabilistic, and since the naive versus theoretical dimension is very highly correlated with the memory-based vs. stimulus-based dimension, we do not present this information. Other than the individual-level model by Fader and McAlister (1990), there exists no purely stimulus-based choice set formation model, most likely because the consumer's purchase history always seems to be an important predictor of choice set composition. In the next section, we review the models in Table 1 in some detail. 3. Two-stage brand choice models for scanner panel data Table 2 provides a more detailed description of those models for which choice set generation is strictly memory-based, while Table 3 describes Table 1 Two-stage discrete choice models for scanner panel data Model Memory-based or Stimulus-based? Attribute-based or Brand-based? Static or Dynamic? Bronnenberg and Vanhonacker (1996) Mixed Brand Dynamic Competing Destinations (Fotheringham, 1988) Mixed Brand Dynamic Consideration By Aspects (Andrews and Manrai, 1995) Mixed Attribute Dynamic DOGIT (Gaudry and Dagenais, 1979) Memory Brand Static Dynamic Bayes (Siddarth et al., 1995) Memory Brand Dynamic Dynamic Heuristic (Siddarth et al., 1995) Memory Brand Dynamic Free parameter model (Andrews and Manrai, 1995) Memory Attribute Static Heterogeneous Parameter and Choice Set model (Chiang et al., 1996) Memory Attribute Static Independent Availability Logit (Swait, 1984) Memory Brand Static Parameterized Independent Availability Logit (Andrews and Srinivasan, 1995) Mixed Brand Dynamic Parameterized Logit Captivity (Swait and Ben-Akiva, 1987) Mixed Brand Dynamic Promotion Expansion (Siddarth et al., 1995) Mixed Both Dynamic Static Bayes (Siddarth et al., 1995) Memory Brand Static Static Heuristic (Siddarth et al., 1995) Memory Brand Static 198 A.K. Manrai, R.L. Andrews / European Journal of Operational Research 111 (1998) 193±215