A Nested Logit Model of Brand Choice Incorporating Variety-Seeking ...

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>\fe model Ihe effects of variety-seeking and marketing-mix variables on consumers' purchases of coffee using a nested logii model. V^ premise that on any ...

Marketing Letters 6:3 (1995): 199-210 © 199S Kluwer Academic I^iblishers, Manufactured in the Netherlands

A Nested Logit Model of Brand Choice Incorporating Variety-Seeking and Marketing-Mix Variables ASIM ANSARI University of British ColunAia KAPIL BAWA

McGill University AVIJIT GHOSH Stem School of Business. New K?/* University. 44 West 4th Street. 08-74, New Ybrk, NY 10012-1126 Ki^ words: Variety-seeking, marketing mix, nested logit, brand choice

Abstract >\fe model Ihe effects of variety-seeking and marketing-mix variables on consumers' purchases of coffee using a nested logii model. V^ premise that on any given purchase occasion, the utilities of brands other than the one purchased on the previous occasion may be correlated due to the consumer's tendency to seek variety or to avoid variety. This results in a two-level hierarchical model where choice on any purchase occasion is conditioned on the brand purchased on the immediately preceding occasion. Such a structure accounts for variety seeking and inertia tendencies of consumers and is consistent with a hierarchical decision process, where consimiers first decide whether or not to make a repeat purchase and then decide which brand size to purchase. The assumed hierarchical structure is shown to be consistent with observed coffee purchase behavior, and the model is shown to outperform a nonhierarchical logit model in predicting consumers' brand choices.

1. Introduction Considerable attention has been devoted to understanding the relative itnpacts of fectors that affect consumer choice among altemative brands of frequently purchased products and services (see Meyer and Kahn, 1991). One approach measures the impact of marketingmix variables such as price and promotion on brand choice, typically using a multinomial logit modeling framework (e.g., Guadagni and Little, 1993). A second approach examines the impact of consumers' variety seeking and inertia tendencies on switching and repeat purchasing (e.g., Givon, 1984). Givon (1984), for example, used a Markov model framework to measure variety seeking and inertia. Kahn, Kalwani, and Morrison (1986) incorporate the effect of past behavior on brand choice and Bawa (1990) etamined how brand preference is affected by repeat purehasing. Early models of variety seeking did not incorporate marketing-mix effects, while logit-based brand-choice models have not examined the impact of variety seeking. One exception is the work of Carpenter and Lehmann (1985), who developed an aggregate brand-switching model that included marketing-mix elements. Some recent studies of variety seeking have incorporated the impact of price on variety seeking (Kahn and Raju, 1991; Papatla and Krisbnamurthi, 1992).

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ASIM ANSARI, KAPIL BAWA, AND AVIJIT GHOSH

We present a hierarchical model of brand choice that incorporates the effects of point-ofpurcbase tnarketing-mix variables as well as variety seeking. Tbe model allows for a twostage decision process where the brand switching decision is distinguished from tbe brandchoice decision. We make this distinction because (1) the decision to switch brands mi^ occur before the decision to buy a specific brand, and (2) the factors affecting the brand switching decision may be different from the fectors influencing brand choice. For example, a consumer m ^ decide to switch brands because of boredom from purchasing the same brand repeatedly, while the actual brand choice may be influenced by prices and promotions at the point of purchase. Thus consumers may go through a sequential decisionmaking process in wbich the brand-choice decision is conditional on tbe decision to either repeat or switch from the brand last purchased. Our fundamental premise is that the presence of variety seeking or inertial tendencies affects how a consumer views the altematives in the choice set. If the consumer is seeking variety, brands not purchased on tbe previous occasons will appear to be more attractive because of satiation with the previously purchased brand. On tbe other band, those same brands will be less attractive to a routinized or inertia-prone consumer. This suggests a partitioning of the choice set based on the last brand purchased, thus allowing the utilities of brands within each partition to be correlated with each. Tbis leads to a hierarchical representation of the choice process where tbe consumer first decides whether to repurchase the last brand or to switch and tben decides which brand size to purchase. We model this process using a nested logit structure, which allows us to test the appropriateness of the hierarchical structure and the effects of the explanatory variables on brand switching and brand choice. An altemative approach might be to use a multinomial logit model that includes marketing mix variables and a last-brand-purchased dummy variable as predictors of brand choice. Such a model would be similar to the joint logit modei discussed by Ben-Akiva and Lerman (1985). However, a particular advantage of tbe nested logit approach is that it takes into account both observed and unobserved components of brand utility in modeling correlations across brands. That is, the nested logit model allows brand utilities witbin a partition to be correlated because of the observed characteristic shared by all brands within the partition (in tbis case, whether they were purchased on the last occasion) and because of unobserved characteristics, if any, shared by brands within tbe partition. In addition, the nested logit models allows a hierarchical representation of the consumer decision process. These represent significant advantages of the nested logit framework fbr modeling marketing mix and variety seeking effects on brand choice. Our approach differs from earlier applications of the nested logit model (e.g., Gaudagni and Little, 1987, Bucklin and Gupta, 1992) in three principal respects. First, we explicitly model tbe impact of inertia and variety seeking on choice. Prior studies using the nested logit bave focused on the impact of marketing variables such as price and promotion on choice but have not considered variety seeking. Second, we distinguish between the brandswitching decision and the brand-choice decision, which allows us to examine tbe determinants of each decision separately. The brand-switehing decision is modeled as a function of the consumer's long-term propensity to switch brands, as well as the more shortterm effect of recent brand choices. The brand-choice decision, on the other hand, is modeled as a function of in-store marketing variables (such as prices and promotions). In-store

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A NESTED LOGIT MODEL OF BRAND CHOICE

variables can also affect the propensity to switch through an inclusive value. Thus our model examines the relative effects of a consumer's long-term propensity for inertia or variety seeking, of short-term variety seeking caused 1^ recent purchases, and of point-of-purchase marketing variables on brand choice. Examining these three types of effects in conjunction provides a comprehensive picture of the brand-choice process. A third point of departure is that in our model the nesting structure depends on the immediate purchase history and can vary from one purchase occasion to another. A choice altemative may be in one nest on one purchase occasion and in another nest on the next occasion, depending on whether the consumer purchases that brand. For example, as shown in Figure I, if a consumer purchased Maxwell House coffee on the (r — l)th purchase occasion, then on the (/)th purchase occasion, all Maxwell House brand sizes would be in the repeat nest (they will be candidates for a repeat purchase), while all other brands would be in the switch nest (they will be candidates for a brand switch). If, on the other hand, the consumer had purchased Folger's on the (t - l)th occasion, the repeat nest on the next purchase occasion would include all Folger's brand-size combinations, and all other brands (including Maxwell House) would be in the switch nest. Thus the nesting structure and the number and identity of brand sizes in each nest on any given purchase occasion depend on the brand purchased on the previous occasion. Such a nesting scheme captures state dependence t^ modeling the consumer decision process as conditional on past purchases and induces a structuring of the choice set that is both consumer specific and occasion specific. The rest of the paper is organized as follows. In Section 2, we discuss the nesting scheme of our model in greater detail and describe the variables in the different levels of the model. Section 3 describes the data and sampling procedures we employ. In Section 4, we discuss the parameter estimates and assess the predictive validity of the model on calibration and holdout samples. Finally, in Section 5, we present the conclusions and discuss the limitations of our study. Previous Purchase = MH 32

Repeat

MH 32

MH 16

Switch

F 16 F 13

Figure I. The hierarchical decision structure.

Other

Brand-sizes

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2. Model 2.}. Nesting structure The nested logit model accounts for the structural relationships arising due to shared observable and unobservable features among different product alternatives by specifying a hierarchical partitioning of the choice set on any choice occasion. In this application, we assume that choice alternatives are partitioned based on the brand name last purchased. In the first decision stage, the consumer decides whether to repurchase the last brand or to switch to another brand. Thus the upper level of our model has two nests—a repeat nest and a switch nest. If the repeat nest is chosen, then the choice alternatives available at the lower level consist of the different sizes and varieties of the last brand. If the switch nest is chosen at the upper level, the alternatives consist of the different sizes and varieties of all other brands in the choice set. Given this nesting structure, we make the usual assumptions to arrive at the nested logit specification. The utility of each consumer for each altemative can be decomposed as f/ju, = Kij -f- K(, + cjt, + f y, where (1) K^, and K;, are the deterministic components of the consumer's utility function specific to the upper and lower levels respectively, (2) c^ is the random component of utility attributable to the upper level k and is distributed such that maxif^CiPkit 's double exponential with scale parameter X^, and (3) cy, is the random component associated with the Wth alternative and is assumed to be i.i.d. double exponential with scale parameter X/. In addition, Ci^ and e^, are assumed to be independent of each other. Given these assumptions, the probability of choosing the ife/th altemative is then decomposed as (suppressing the / subscript for convenience)/7(^, /) = p{l\k)p{k), where (1) i j X , )

and

where VI is given by (l/X^Jln E/^Q exp(K,X;). V^'X/ is the logarithm of the denominator of p{l\k) and is termed the inclusive value (McFadden 1981). It represents the deterministic component of the maximum utility of the alternatives in nest k and is a scalar measure of the expected worth of the subset of altematives within nest k (Ben-Akiva and Lerman, 1985). The parameters, X/ and X^, cannot be estimated separately, but their ratio, X^/X/, can be estimated as the coefficient of the inclusive value of nest k. The deterministic components of utility, V^ and V/, are assumed to be linear functions of explanatory variables described in the following section. As equation (2) indicates, the brand-switch decision at the upper level is a function not only of the explanatory variables affecting K^ but also of the inclusive value Vl_. This allows us to capture any effects of brand-level price and promotion variables (at the lower level of the model) on the decision

A NESTED LOGIT MODEL OF BRAND CHOICE

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to switch brands (at the upper level). Such effects might occur, for example, if there is a particularly attractive promotional offer for a brand in the switch nest, and this increases the likelihood of the consumer switching brands to take advantage of the offer. The model accommodates such behavior and in this respect provides a reasonable representation of brand-switching behavior.

2.2. Explanatory Variables 2.2.1. Brand-switching model. The upper-level utility Vj, is modeled as a function of the consumer's variety-seeking or variety-avoiding tendencies. Two types of variety-seeking effects are considered: a short-term propensity to seek or avoid variety that depends on the consumer's recent consumption history and a long-term propensity that is independent of the recent consumption history. The short-term effect of variety seeking has been exanuned in several studies that consider purchase event feedback (e.g., Givon, 1984; Kahn, Kalwani, and Morrison, 1986; Bawa, 1990). We measure each consumers propensity for variety in terms of the overall proportion of repeat purchases or switches made by the consumer in the past. K^ is therefore a linear function of three fectors: RLength: The number of consecutive purchases of the last brand—that is, the run length of the last brand up to the last purchase occasion. This variable reflects the recent consumption history and thus captures the impact of short-term inertia or variety seeking. We expect that for variety-seeking consumers there would be a positive correlation between RLength and the probability of switching. The correlation would be negative, on the other hand, for variety-avoiding (inertial) consumers. The greater the RLength the less likely they are to switch brands. To capture this differential response at the aggregate level, we code this variable differently for the two nests. RLength is coded positive for all altematives belonging to the switch nest and is coded negative for the choice altematives in the repeat nest.' The coefficient of RLength thus reflects the average amount of variety seeking in the sample: a positive coefficient implies variety seeking, while a negative coefficient implies inertia. PRepetU: Proportion of the household's purchases in an initial period (not used for model calibration) that were repeat purchases. This variable measures the consumer's long-term propensity to repeat purchase brands. Households with high values of PRepeat are hypothesized to be less likely to switch on any occasion. For estimation purposes, we code PRepeat as positive for the switch nest and negative for the altematives in the repeat nest. Indizl: The inclusive value for the nest, which is a mesure of the overall attractiveness of the nest, detennined from the lower-level model. The coefficient for IncVal must lie between zero and one if the hierarchical stnicture is appropriately specified. 2.2.2. Brand-choice model. We model the choice among brand sizes at the lower level as a function of the following variables:

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Price: Feature: Deal: Display: Prefer:

Price in cents per ounce, 1 if the brand size was featured in the store, 0 otherwise. Store coupon amount in cents for the brand size, 1 if brand size was specially displayed, 0 otherwise. A brand size's share of the household's purchases over an initial period, which measures the household's overall preference for the brand size, Psize: 1 if last purchase was the same size, irrespective of brand, 0 otherwise. Brand-size constants: A set of binary variables representing the unique characteristics of the brand sizes not captured by the above variables.^

3. Data Tb test the proposed model we use IRI scanner panel data on purchases of regular ground coffee in Pittsfield, Massachusetts. Ofthe two years of purchase data available. Year 1 data were used to measure FRepeat and Prefer since they reflected long-term characteristics ofthe household. In addition, we used the last brand switch in Year 1 for each household to initialize the run length variable (RLength) for the first purchase occasion in Year 2. The model was estimated using Year 2 data only. We identified the nine largest brand sizes in the market among our panelists and restricted our sample to households who purchased this set ofnine brand sizes at least 90 percent ofthe time. These nine brand sizes represented six brands, with three of the six brands having two different sizes represented. In addition, to be included in our sample, a bousehold had to have made at least five purchases in Year 2 so that a sufficient number of observations were avaiiabie for model calibration as well as predictive testing.^ A total of 360 households met our criteria. We partitioned the data set into three samples. Sample I consisted of observations over Weeks 1 to 43 for 301 randomly selected households. This sample was used for model calibration. Sample II consisted of purchases made during Weeks 44 to 51 by the households in Sample I. Sample in consisted ofdata on Weeks 1 to 51 for the remaining 59 households. Samples II and i n were used as holdout samples for predictive testing.

4. Results ^ estimated the parameters on Sample I, the calibration sample, using the sequential estimation procedure described in Ben-Akiva and Lerman (1985, pp. 296-297). This procedure provides consistent estimates, but they are not asymptotically efficient. We therefore corrected the standard errors for the upper-level model by employing the McFadden (1981) correction.

4J. Coefficients for the nested logit model Results of four versions of the nested logit model are shown in Tbble I. In each version, the parameter estimates and fit statistics are shewn separately for the upper and lower levels

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A NESTED LOGIT MODEL OF BRAND CHOICE

Table 1. Parameter estimates (T-ratios in parentheses). Logit Model

Nested-Logit Model Parameter Estimates for Lower-Level Model:

BS2 BS3 BS4 BS5 BS6 BS 7

I

BS8 BS9

Ml

M2

M3

M4

-0.6204 (-6.27) -1.1701 (-10.83) -1.0030 (-9.29) -1.4981 (-16.46) -2.1960 (-16.64) -2.2771 (-13.72) -2.9320 (-17.35) -3.1527 (-12.17)

-0.4854 (-4.67) -0.6104 (-5.09) -0.5417 (-t.63) -0.8072 (-7.84) -1.7832 (-12.64) -1.6849 (-9.68) -2.3090 (-12.97) -2.9062 (-11.13) 1.9745 (-12.42)

-0.9445 (-8.12) -0.4273 (-3.18) -2.0901 (-13.12) -0.8063 (-7.76) -1.2638 (-8.27) 3.0934 (10.18) -2.2637 (-11.77) -4.8477 (-16.91)

-0.4994 (-2.96) 1.1746 (6.58) -0.8451 (-3.89) -0.8776 (-3.99) -1.0482 (-4.64) 0.62089 (1.32) -0.4005 (-164) -2.1140 (-6.16)

Prefer Price

1.9959

(11.92) -0.9262 (-17.52)

Feature Display Deal Psize Pbrand

1

2.7067

(11.37) -0.2776 (-3.312) 2.3511 (7.812) 0.56269 (2.296) 1.1567 (3.870) 0.9057 7.766

1 1

LL (max)

-1932

LI

-0.2681 (-2.32) 1.1971 (9.48) -0.4984 (-3.16) -1.1377 (-6.76) -0.8951 (-5.18) 1.0916 (3.46) -0.2709 (-1.42) -1.1971 (-5.97) 2.6666 (17.35) -0.1630 (-3.133) 2.3942 (11 246) 0.7375 (4 423) 1.3259 (6.430) 0 8073 (9.05) 1 6341 (21.643)

-862

-1853

ftrameter Estimates for Upper-Level Model:

-0.0804 (-40.2) Incval 0.4751 (21.59) r Prepeat [1 -0.4029 (-4.24) Overall Goodness of Fit Statistic (Both Levels): LL (max) -3211 -3126 0.21 0.23 BIC i' -3253 -3172 Rlength

0.0858 (-42.9) 0 4857 (14.72) -0.4551 (-3.61)

-0.0878 (-35.23) 0.5516 (43.J9) -0.4519 (-5.H8) -2050 0.50 -2100

-0.1098 (-48.954) 0.8624

(177.07) -0.4124 (-8.014) -1603 060

-1665

-1732 0.64 -1790

20$

ASIM ANSARI. KAPIL BAWA, AND AVIJIT GHOSH

ofthe model. Model 1 (Ml) a simple mode! with only brand-size constants included at the lower level, provides a baseline for comparison. Additional explanatory variables were successively added to the lower level of this initial model. Model 2 (M2) includes the variable Prefer., in addition to the alternative specific constants. The variable Price is added in Model 3 {M3), and Model 4 (M4) includes the three point-of-purchase promotion variables and the size loyalty dummy variable. The fit of the mode! improves significantly as price is included as an explanatory variable in M3. The addition ofthe promotion variables in M4 further improves goodness of fit. The adjusted likelihood ratio index (p^) (Kannan and Wright, 1991), as well as the maximized likelihood indicate that the full model (Model 4) provides a significant improvement over the other nested logit models. Although the magnitude of change in log-likelihood from M3 to M4 is relatively small, it and the /-values ofthe added variables are all highly significant, demonstrating, as expected, the infiuence of promotion and size loyalty on branch choice for coffee. The parameter estimates have values that are reasonable and consistent with previous studies. For example, price has a significant and negative coefficient while the promotion variables all have significant and positive coefficients. The coefficient for Psize is positive and highly significant, confirming the strong size lc^alty in coffee purchases found by Guadagni and Little (1983). In addition, as one would expect, brand choice is also affected l^ the household's overall preference for different brands as refiected in their past purchase history. As for the brand-size constants {BS2.. ,BS9), their relative importance decreases as more explanatory variables are added to the model. Overall, the results suggest that the brand choice model has fece validity. Moving to the upper level, we observe that the sign of the coefficient for PRepeat is negative; households who made more repeat purchases in Year 1 were less likely to switch brands in Year 2. The coefficient for RLength is also negative, indicating that households with longer strings of consecutive purchases ofthe last brand are less likely to switch brands. This implies that, after controlling for the consumer's long-term tendency to make repeat purchases, the sample, on average, exhibited an inertia or variety-avoiding tendency. This finding is consistent with other analyses of coffee purchases (e.g., Givon, 1984, p. 12). The significance ofthe coefficients of RLength and PRepeat demonstrate that both longterm and short-term variety-seeking and inertial tendencies influence the decision to repeat or switch from the current brand. The coefficient for IncVal (inclusive value) lies between 0 and 1 in each ofthe estimated models, indicating that the hierarchical structure specified in the model is appropriate for the data set. As mentioned earlier, the coefficient of the inclusive value measures the infiuence ofthe variables in the lower-level model on brand-switching decisions at the upper level. The substantial jump in the value of the coefficient from M3 to M4 shows that the promotional variables added to M4 not only affect brand choice but also influence the decision to repeat or switch. We also investigated modified versions of the model in which summary measures of the in-store marketing environment such as the number of brands on deal and the average fece value of available store coupons were included in the upper level of the model. None of these variables were however significant at the upper level.

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4.2. Validation and prediction

'

To assess the goodness of fit of the nested logit specification we compare it to a reference model that incorporates dynamic and static components of brand loyalty within a multinomial logit framework. >\fefollowBuckiin and Lattin (1991) and Deighton, Henderson, and Neslin (1994) and model the indirect utility for a brand-size as a linear combination of all variables in the lower level of Model 4 and a new variable, Pbrand that accounts for the last brand purchased by the consumer (irrespective of size). Specifically, we define Pbrand = 1 if brand was purchased on the previous occasion, 0 otherwise. The multinomial logit model was calibrated on Sample I and the parameter estimates and /-statistics are reported in Tiible 1, under the logit column. All coefficients have the expected sign and magnitude. Table 1 also shows the overall fit statistics for both models. Since the reference model and Model 4, are not nested, their likelihood values cannot be compared directly. We, therefore, use the Bayesian information criterion (Allenby, 1990) to compare the goodness of fit of these models. The nested logit mode! (model M4) has a better goodness of fit as evidenced by a higher BIC value. One reason for the higher BIC may be the inclusion of variables Prepeat and Rlength in the nested logit model. The parameters of the nested logit model (model 4) and the multinomial logit model, were used to predict whether a household will switch or repeat. The last column of T^ble 2 shows the overall accuracy with which the two models predicted repeat or switch decisions. This measure of overall accuracy is based on all observations in the sample, while the predictions reported in the columns labeled repeat and switch are based on only those observations on which consumers actually repeat purchased or switched brands. The nested logit model achieved an overall predictive accuracy of 86 percent in the calibration sample and 74 and 79 percent in the two holdout samples. Both models prediced repeat purchases particulary well; the nested logit predicted switches better than the logit. The high predictive ability of the model provides empirical support for the hierarchical structure. The table also shows that the overall predictions from the nested logit model are better than those of the multinomial logit model for all three samples. . Repeat/switch predictiotis for calibration and holdout samples (propordon correctly predicted). Model Sample I (N = 2224): , Nested Logit Logit

Repeat

Switch

Direction

0.91 0.90

0.79 0.75

0.86 0.84

0.89 0.91

0.48 0.29

0.74 0.68

0.91 0.91

0^

0.79 0.76

Sample D (N = 530): Nested Logit Logit Sample m (N = 571): Nested Logit Logit

'

0;5e

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ASIM ANSARJ, KAPIL BAWA. AND AVIJIT GHOSH

"Eible 3. Predidive accuracy for brand-size and bmnd names (hit rates). Modei

Brand Size

Brand Name

Sample I: Nested Logit Logit

0.78 0.77

0.83 0.81

Nested Logit Logit

0.63 0.59

0.70 0.66

Sample ni: Nested Logit Logit

0.69 0.68

0.75 0.73

Sample II:

Table 3 compares the two models in terms of their hit rates in predicting which brand size and which brand (regardless of size) would be chosen on each occasion/ In the calibration sample the nested logit model predicted the brand correctly on more than 82 percent of the purchase occasions.^ More than 70 percent of the predictions were correct in the two holdout samples. In each case the predictions from the nested logit model were better than those fiom the logit model. As one would expect, both models predict the brand more accurately than the brand-size. These results demonstrate that in terms of predictive ability the nested logit appears to perform better than the multinomial logit in predicting brand switching and slightly better in predicting brand choice. However, the real benefit of the nested logit model lies in its ability to provide some insight into the decision process and the fectors that influence brand switching. By allowing us to examine the long-term, short-term, and point-of-purchase influences on switching behavior, the model provides an improved understanding of the choice process.

5. Conclusions In this study we have demonstrated a methodology for modeling the effects of inertia, variety seeking, and marketing mix variables within an integrated framework in a relatively parsimonious manner. The fundamental premise of our model is that the presence of variety seeking or inertial tendencies affects the way in which consumers view the altematives in the choice set. From a conceptual standpoint this approach is useful because it allows for a hierarchical decision process and because it captures the correlations, if any, between unobserved components of utility. Empirically, our results appear to support our premise and suggest that consumer choice behavior is consistent with a hierarchical decision process. A possible limitation of our study is that although we attempted to consider consumer heterogeneity in variety seeking by measuring consumers' long-term propensities to make repeat purchases, this measure of variety seeking may not have adequately reflected the full extent of heterogeneity. Whether or not this is a significant limitation needs to be addressed in future research. However, our results demonstrate that the model has fece validity

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and good predictive ability and thus may provide a potentially useful framework for developing a comprehensive model of brand choice that integrates inertia, variety seeking, and marketing-mix variables.

Acknowledgments We thank Information Resources Inc. for making the data available to us. We also thank Charles Weinberg and S. Siddarth for their valuable comments on an earlier version of this paper. This research was supported in part by a grant from the Social Sciences and Humanities Research Council of Canada.

Notes 1. This differentia] coding is also necessary to estimate the coefficients as the nested logit model requires that variables take different values across the two nests. 2. For estimation purposes the constant for Brand 1 was excluded from the model. 3. These relatively frequent purchasers may not be representative of the entire panel in terms of price sensitivity and brand preference (Kim and Rossi, 1994). 4. In our data there wen nine brand sizes representing six brands. 5. On each purchase occasion the altemative with the highest utility was predicted to be the chosen brand.

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