Modeling multiple category brand preferenc

Modeling Multiple Category Brand with Household Basket Data

Preference

GARY J. RUSSELL University of lowa

WAGNER A. KAMAKURA University ol Pittsburgh

Household basket datu contain important information about the structure of brand preferences both

within and across product categories. This research exploits the information in long-run basket .VIM-

mar-~ dutu to segment consumers with respect to brand preferences. The approach provides insights

into the competitive structure of brands within euch product catcgon: and identifies potentiul synergies

acm.cs product categories. The model is upplied in an analysis of retailer and national brand numc

preferencesforfourpaper goods ccrtegorirs. We discuss implicationsforjoint promotion, product bun-

dling and product assortment decisions.

INTRODUCTION

Category management is increasingly advocated as a marketing strategy concept which has

the potential to revolutionize retailing (Harris and McPartland, 1993). Simply put, category

management is the notion that retailers should evaluate specific brands both in terms of

contribution to product category profitability and in terms of contribution to overall store

profitabililty (Nielsen, 1992). From a marketing theory perspective, category management

builds strategies which integrate three basic marketing concepts: consumer preference seg-

mentation, demand substitutability (within product categories) and demand complementa-

rity (across product categories). The focus is on understanding the underlying determinants

of consumer behavior and planning marketing activities which exploit the way that con-

sumers assemble a basket of purchases.

Gary J. Russell is Associate Professor of Marketing at the College of Business Administration. University of

Iowa, 108 Pappajohn Business Administration Building, Iowa City, IA 52242. Wagner A. Kamakura is Thomas

Marshall Professor of Marketing at the Katz Graduate School of Business, University of Pittsburgh. 318 Mervis

Hall. Pittsburgh. PA 15260.

Journal of Retailing, Volume 73(4), pp. 439461, ISSN: 0022-4359 Copyright 0 1997 by New York University. All rights of reproduction in any form reserved.

439

440 Journal of Retailing Vol. 73, No. 4 1997

Cross Category Marketing Strategy

From the retailer’s perspective, an impo~~t implication of category management is the c~rdination of marketing strategies (product assortment, pricing and promotion) across product categories (Blattberg, 1989; Blattberg and Neslin, 1990; Zenor, 1994). Our research addresses the central role of cross-category preferences in the design and implementation of these strategies. In particular, knowledge of preference correlations is essential in evaluating the profitability of joint product promotions. If preferences for two complements (or inde~ndent) products are negatively correlated across the consumer population, then product bundling {selling two products as one unit at a single price} can be a profitable strategy (Nagle, 1987; Braden, 1993). In contrast, if preferences for a set of complementary (or independent) products are positively correlated across the consumer population, the retailer may be able to target a particular consumer segment by only promoting one product in the set. The increased store traffic by this segment may then increase the sales of all products in the set.

Knowledge of multiple category product preference patterns also allows the retailer to predict the likely composition of market baskets. Loblaws, a major Canadian grocery retailer, studies the make-up of consumer market baskets to understand the cross category product preferences of consumers who typically buy its President’s Choice store label (Goldberg, Urban, and Wertz, 1995). Such information is used in both product assortment and store layout decisions. Catalina Marketing Coloration, a retailing indust~ consultant, sells point-of-purchase electronic couponing systems which can be programmed to issue coupons in a given category based upon the consumer’s purchase behavior in other categories (Catalina Marketing, 1997). The coupon program is designed to encourage consumers to increase the number of categories considered on a shopping trip. In essence, the system allows the retailer to impIement a cross-category marketing strategy based upon correlated

category usage patterns.

Measuring Multiple Category Preferences

Our research develops an approach for analyzing multiple category brand preference using long-run purchase summaries on consumer market baskets. Consistent with the logic of Grover and Srinivasan’s (1987) approach to market structure, we build a consumer preference segmentation model and use the model output to study patterns in brand preferences. Our goal is the development of a marketing research tool which uncovers interesting patterns of preference correlation across product categories and thereby provides a basis for identifying potentially profitable cross-category marketing oppo~unities.

The proposed approach has two important features. First, the analysis is based upon a general model of multiple category demand. In contrast to earlier work in the market structure literature (Urban, Johnson, and Hauser, 1984; Grover and Srinivasan, 1987; Kamakura and Russell, 1988; Ramaswamy and DeSarbo, 1990; Russell and Kamakura, 19941, demand relationships among brands are unrestricted: brands can be substitutes, complements or independent. This feature is essential in any model of multiple-catego~ demand.

Modeling Multiple Category Brand Preference with Household Basket Data 441

It allows our model to represent consumer preferences for all brands of interest to the

retailer.

Second, our procedure only requires information on brand consumption. Marketing mix

variables (e.g., price and promotion data) are not used in this analysis. Although these vari-

ables affect the composition of market baskets on a week by week basis, we show analyti-

cally that a representation of brand preference segmentation can be recovered without

explicit knowledge of marketing mix activity. Because our procedure places light demands

on data collection, it can be used when marketing mix data is incomplete or missing alto-

gether. Examples of such data sources include A.C. Nielsen wand panels (in which the con-

sumer records purchases by scanning UPC product codes at home) and consumption data

obtained from a retailer’s “buyer club” participants. Thus, the procedure can be used when conventional panel data models are impractical.

Overview

We begin our discussion by formulating a general consumer purchase model for brands

in multiple product categories. We then specialize the model to the analysis of long-run

purchase volumes of brands in multiple product categories observed in a consumer panel. To illustrate the potential of the approach, we study consumer preferences for national and

retailer brand name extensions across four paper goods product categories. Our results

show that the cross-category pattern of preferences for national brand names are consider-

ably different from the cross-category pattern for retailer brand names.

A MODEL OF MULTIPLE CATEGORY PURCHASING

On a typical shopping trip, consumers make multiple purchases, both within and across

product-category boundaries. Clearly, category incidence plays an important role; consum-

ers rarely purchase products in all available categories on the same shopping trip. In addi-

tion, category incidence is conditional upon a number of factors such as household

inventory and marketing mix activity (both within and across categories), which are not

always observable. Thus, we seek a model which simultaneously accounts for category

incidence and product choice over a predetermined time period.

Household Purchase Model

Our model is developed in terms of purchase quantity. Let X [h (s), i(m), t] be the volume (in equivalent units) of brand i purchased by household h during week r. This notation emphasizes that each household h is a member of some consumer segment s (s = 1,2, . . . S).

Moreover, each brand i can be placed in a known category m. For example, in our empirical


work, m represents one of four paper-goods categories: toilet paper, paper towels, facial tis-

sue or paper napkins.

We assume that X 11% (s), i(m), t) is distributed as a Poisson random variable with mean

h[h(.s), i(m), t] = h[h, m, t]cY[s, i(m) t] (1)

where

h ih, m, tl is a time varying category purchase rate (which includes seasonality and

inventory effects),

a[s, i(m)1 is the stable intrinsic preference of segment s for product i(m), and

P[i(m), fl is a time varying attractiveness of product i(m) due to marketing mix

activity.

That is, the mean is decomposed in terms of two time-va~ing components (category pur-

chase rate and marketing mix activity) and one stable component (intrinsic product

preference). Because the goal of this research is a representation of product preferences, our

primary interest is the estimation of the segment-specific product preferences a[.~, i(m)].

The Poisson distribution used here has found considerable application in models of con-

sumer purchase behavior (e.g., Ehrenberg, 1972; Lenk, Rao, and Tibrewala, 1993).

Although the Poisson assumption makes the model more tractable, the key equation of our

market basket model (equation (5) below) does not depend upon distributional form.’

We also assume that, conditional upon the means h[h(s), i(m), t], the observed purchase

quantities X[h(s), i(m), t] are statistically independent with respect to household h(s), prod-

uct i(nrj and time f. This conditional independence assumption is commonly made in the

context of repeated observations on individuals {Fahrm~ir and Tutz, 1994, section 5.2). It

is important to recognize that this assumption &es not rule out correlations among the

observed X[h(s), i(nz), t]. Rather, conditional independence requires that any correlations

in the observed quantities X[h(s), i(m), t] be induced by correlations among the purchase

quantity mruns h/z(s), i(m), t&not by correlations among the purchase quantity residuals

X[h(s), i(m), t] - h[h(s), i(m). r] (see Gelman et al., 1996, section 5.2). In general, a retailer should expect to observe correlations among purchase quantities due to: (a) inter-category

correlations in purchase rates h[h, m. t], (b) inter-segment correlations in product prefer-

ences a[~, i(m)], and (c) inter-brand correlations in marketing mix activities P[ i(m), t]. Our

model allows for correlations of this sort.

Model Characteristics

Our model formulation has three desirable features for multiple-category analysis. First, a proportional intensity relationship is used to model the means in equation (1). The base

rate of category purchasing h[ h, m, f] is muItiplicatively adjusted for both intrinsic preference a[.~, i{m)] and marketing activity P[ i(nz), t]. Although the marketing activity compo-


nent is independent of household (or segment), the model does not imply that all consumers are equally affected by marketing activity. Note that the derivative

13h(h(s), i(m), t)/ap[i(m), t] = h[h, m, t]a[s, i(m)]

depends both upon the household and the consumer segment. In terms of the absolute change in the overall purchase rate A[h(s), i(m), t], our framework implies that consumers with a higher propensity to buy the category (large h[h, m, f]) or the product (large a[s, i(m)]) will be more affected by changes in marketing mix activity. Thus, the model allows for a natural interaction in category base rate, product preference and marketing activity.2

Second, the model does not force products to be substitutes. Looking over time, the model views the quantities purchased of different products i(m) as correlated time series where the pattern of correlations depends upon the time varying means a[h(s), i(m), t].

Because this approach allows for simultaneous purchasing of different products, it can accommodate complementary and independent products. This feature allows the model to accommodate all items in a consumer’s market basket.

Third, the model implies that category incidence depends upon the household’s pattern of intrinsic preferences. Using standard results on the Poisson distribution, it is easily

shown that Fi,,X[ h( s), j( m, t)], the total volume purchased in category m by household h

in week t, also follows a Poisson distribution with mean Ej ,h[h(s),j(m), t]. Conse-

quently, the probability of purchasing category m is an increasiig function of

where the summation is over all products in category m. Intuitively, category incidence is more likely when marketing mix activity makes a high preference brand more attractive (i.e., a[s,j(m)] and Pu(m), t] are simultaneously large for some brandj.) This structure is similar to a nested logit formulation (cf. Bucklin and Gupta, 1992) in which category incidence depends upon category purchase propensity h[h, m, t] and a preference-weighted index of current category attractiveness CjE,a[s, j( m)] prj( m), t].

ANALYZING MARKET BASKET INFORMATION

Multiple category preference patterns can be understood by analyzing the inter-segment pattern of intrinsic product preferences a[s, i(m)]. Clearly, we could obtain this information first by specifying the components of the purchase rate decomposition (equation (1)) and then estimating a fully-specified demand system using weekly marketing mix information. However, when the researcher’s primary goal is to recover estimates of the a[ s, i(m)],

it is much simpler to work solely with long-run summaries of household basket data. In this section, we use the general multiple category purchase model to justify this simpler approach.


long-run Basket Data

We define a household’s market basket as the set of observed purchase volumes X[h(s), i(m), t] for all brand i and category m combinations i(m) in a given week f. A long- run market basket is defined as the purchase volume Q[h(s), i(m)] for each product i(m)

over some time horizon,

Q[W, i(m)1 = ~C,X[h(s), i(m), 11 (4)

where the summation is over the t = 1, 2, . . . . T periods of the available data. Because the

weekly volumes X[h(s), i(m), t] may be equal to zero in certain time periods, Q[h(s), i(m)] represents an aggregation over both purchase and non-purchase occasions.

long-run Purchase Behavior

Given the structure of the multiple category purchase model of the previous section, we can infer a logically consistent model for the long-run basket data. The analysis here rests upon two key assumptions. First, as discussed in the previous section, the weekly volumes X[h(s), i(m), t] are conditionally independent Poisson variables with time-varying means described by equation (1). Second, looking over time, the household’s category base rate h[h, m, t] is uncorrelated with the marketing mix attractiveness P[ i(m), t].

This second assumption is based upon the observation that h[ h, m, t] is an idiosyncratic household purchase rate which reflects current category inventory. In contrast, P[i(m), t] is identical for all households. Although the retailer can coordinate the marketing activity of various brands (leading to correlations across the various product P[i(m), r] components), the retailer cannot coordinate marketing activity to match each household’s idiosyncratic category base rate. Hence, h[ h, m, t] and P[i(m), r] should be uncorrelated over time.3 This assumption does not imply that a household’s category incidence is independent of brand marketing activity. The relationship shown in equation (3) remains valid even when h[ h, m, t] and P[i(m), t] are assumed to be uncorrelated.

Define Q[ h( s), m] = Cj ,Q[ h( s), j( m)] as the total volume purchased in category m by household h over the time’ horizon of the data. Using these assumptions, the Appendix derives the following key result. Conditional upon the household’s category m volume Q[ h(s), m], the observed long-run product volumes Q[ h(s), i(m)] within category m follow a multinomial distribution with means

O[s, i(m)] = M.Y, i(m)lZ[i(m)l

(5) C M.cAm)lZU(m)l

jEt?i

where


Z[jh)l = Et{ P[i(m), fl>

is the time average of the marketing mix effects for product i(m). For purposes of model

identification, we assume (without loss of generality) that X;E,log{ as,j(m)} = 0.

This result brings out two important features of long-run basket data. First, by condition-

ing upon the household’s observed total volumes in each category m, the researcher need

not explicitly model the category base rate h[h, tn, t]. Second, by aggregating over time,

the long-run basket data are affected by a summary index of each brand’s marketing activ-

ity Z[i(tn)]. Notice, however, that Z[i(m)] depends only upon the brand-not upon the

household or segment. Thus, conditional upon the total category volumes, a household’s

long-run basket data depend only upon two components: the intrinsic preferences of the

household’s segment CI[S, i(m)], and the common product-specific effects of marketing

activity Z[ i(m)].

Implications for Preference Segmentation

The key implication of this analysis is that long-run basket data can be used to segment

consumers with respect to product preferences a[.~, i(m)]. Suppose we find two households

(1 and 2) whose long-run basket data follow multinomial processes with identical means

0[ 1, i(m)] = 8[2, i(m)]_ Algebraic manipulation of equation (5) implies that a[ 1, i(m)]/ a[ 1, ,j(m)] = a[2, i(m)]la[2, j(m)] for any two products i(m) and j(m) within each

category tn. Because Ejj, ,,,log{a[.s,j(m)]} = 0, it then follows that a[ I, i(m)] = a(2, i(m)] for all products. Thus, equivalence of multinomial means implies equivalence of intrinsic

product preferences.

The above result is important because it allows us to create a preference segmentation of

the market on the basis of long-run multiple-category basket data. This is done by sorting

households in terms of similarities in the multinomial means associated with each house-

hold’s long-run basket data. These groups of households will automatically be homoge-

neous in terms of intrinsic preferences. Hence, the market structure in a multiple category

setting can be found using simple summaries of household purchase behavior.

MODEL CALIBRATION

We analyze the long-run basket data by classifying households into homogeneous preference segments and studying the resulting inter-category patterns in product preference. The

approach used is a simple variant of latent class analysis (e.g., Kamakura and Russell, 1988;

Grover and Srinivasan, 1989; Ramaswamy and DeSarbo, 1990; Russell and Kamakura,

1994) for the analysis of multiple product categories.


latent Class Framework

The key to our empirical analysis is the direct correspondence between our long-run con-

sumption model (equations (Sj-(6)) and the standard setup of a latent class model. Latent

class models assume that each consumer can be assigned to one of S segments. Each seg-

ment s has a distinctive size n, and is homogeneous with respect to underlying segment- specific parameters. The problem facing the analyst is the classification of consumers into

segments and the estimation of segment-level parameters.

We have previously shown that, c~~nditional upon the total category pn consumption

@[h(s), pn], the individual brand consumptions Q[h(s), i(rtz)] follow a muitinomial distri-

bution with means Q[s, i(m)]. Moreover, because all the underlying weekly purchases

X[h(s), i(m), t] are conditionally independent, the multinomial distributions for each cate-

gory are also conditionally independent.

The likelihood of the household’s long-run basket data, conditional upon the member-

ship in some segment s, is computed as

(7)

where N denotes the number of product categories and I(m) denotes the number of brands

within category 112. Here, we have suppressed the segment index in &[ h(s), i(m) 1 to emphasize that only the purchase quantity of the household is observable; segment m~tnb~rship

is unknown. Because the segment s is unknown, a latent class model is based upon the

unconditional likelihood

where group size n, is interpreted as the prior probability that a randomly selected house-

hold belongs to segment s. The product of equation (8) over all households yields the

likelihood for the entire sample of long-run market baskets.

In our empirical work, we use the well-known E-M algorithm to obtain parameter estimates (Dempster, Laird, and Rubin, 1977). The E-step {expectation step) updates the

household segment-membership probabilities ~~~~ = ~s~{~(.~)}/~,s = ,, Sn L{h(s)}. New estimates of the segment sizes and brand shares within segments are obtained in the M-step

(maximization step) as R, = C,r = l,Nz,,,/N and

Q(k i(m)& = I, NT,,,\f2( t%s, i(wz)) = C, = l.Nr,,

h, m) . Final estimates are obtained by iterating these two steps.

The number of segments IS chosen by maximizing the likelihood conditional upon a variety of values of S and then choosing the model which minimizes the Consistent Akaike Infor- mation Criterion (Bozdogan, 1987).

Estimating Intrinsic Brand Preference

As noted in equation (3, the estimated segment volume shares t3l.r. i(m)] are biased away from the intrinsic segment preferences a[s, i(nz)], due to the impact of each brand’s mar-


keting mix activity Z[i(m)]. However, a simple transformation of the O[s, j(m)] estimates across brands and segments wirhin each curegory m can be used to remove the biases.

Define t3im,s = log (O[s, i(m)]). Using these log variables, let 8+,n,s be the equal-weighted (weights = i/I(m)) mean over brands (for a given segments) and eim+ be the size-weighted (weights = 7~~) mean over segments (for a given brand i). Further, let 8+,,+ be the grand mean over all segments and brands (using the weight ~,ll(m) for brandj in segment s).

Recall from equation (5) that we may assume (without loss of generality) that CjEmlog{a(.s, j(m)} = 0. Then, an algebraic manipulation of equation (5) shows that the deviation scores

are consistent estimates of (x[.s, i(m)] - a[+, i(m)] where a[+, i(m)] is the average intrinsic preference for brand j across all segments. That is, we can recover a relative measure of each segment’s intrinsic brand attractions-free from the influences of brand marketing mix activity, by row- and column-centering the logarithms of the volume shares Ells, i(m)] sepurately for each category m. Because these deviation scores can be interpreted as deviations around the mean preferences of the consumer population, they can be used to construct inter-brand preference correlations for all brands in all product categories.

APPLICATION

To illustrate our approach, we study consumer preferences for national and retailer brand names across four categories of paper-goods. Results of the analysis show that cross category preferences for retail brands are positively correlated. In contrast, national brand preferences show a mixture of positive and negative correlations.

Data Description

The data analyzed here are taken from a panel of 626 Canadian households in one market area. The data consist of the total volume (in equivalent units) purchased of brands in four paper goods categories (toilet paper, paper towels, facial tissue and paper napkins) for a S2- week period. In addition, for each household, we know the total dollar amount spent on groceries (for purchases in any category-not just the four paper good categories) and the allocation of this total across the four major groceries chains in the market area (denoted A, B, C and D). Our segmentation is based upon the purchase volumes observed in the paper goods categories. The remaining information is only used to provide insight into the segmentation solution.

In preparing the data for analysis, we selected 12 brand names with aggregate market share (on a volume basis) greater than 0.5% in at least one product category, and combined the


TABLE 1

Brand

Ketail B

Retail Cl

Retail C2

Retail D

Facelle

Scott

White Swan Cotton-Elle

Delsey

Hi Dri

Majesta

Kleenex

Other

Volume Market Shares

kikt fdper PdJJW Toweh ljC;d/ Jk~c /%,!lC’~ !hdpkinS

2.2 3 .1 4.3 12.9

5.9 2.3 0.8 3.8 0.7 4.0 4.5 15.4

3.0 3.7 0.8 4.9

33.1 12.7 14.2 4.5 2.1 22.4 9.9 14.9

7.5 21.4 7.7 7.9 20.8 _ _

14.b _ _

_ 17.3 _ 14.7 _ 2.9 _

_ 54.9 5.3 10.1 10.2 2.9 10.7

remaining brands into an “Other” brand group. The resulting array of brands is shown in

Table 1.

Notice that seven of the brands compete in all product categories. As shown in Table 2,

four of these brands are distributed exclusively by one retailer (Retail B, Retail Cl, Retail C2, and Retail D). The remaining 3 brands (Facelle, Scott and White Swan)-with one

exception in one product category-are distributed by all grocery chains. We focus most of

our comments on these seven brands. We refer to the four limited-distribution brands as

retailer brands; the three widely-available brands are called national brands.

Segmentation Solution

Segments were constructed by analysing the cumulative equivalent unit volumes of the 626 households for the brand-categories of Table 1. We selected a 7-segment solution on

the basis of the Consistent Akaike Information Criterion (CAIC) (Bozdogan, 1987).4 We also computed an entropy-based goodness-of-classification index based upon the posterior

segment membership probabilities Ths as

(10)

where N = 626 and S is the number of segments. This index ranges between zero and one. A value of G = 0 implies random classification into segments (with probabilities l/S). A value of G = 1 implies perfect classification of each household into only one segment.


TABLE 2

Distribution Coverage

Brand Toilet Paper Paper Towels Paper Napkins

Retail B

Retail Cl

Retail C2

Retail D

Facelle

Scott

White Swan

Cotton-Elle

Delsey

Hi Dri

Majesta

Kleenex

Other 4

1

1 1

1

4

4

4 _

-

4

3 -

4

Note: Coverage is defined as the number of retail chains carrying the brand. Retail brands are only carried by the retail chain

with the corresponding letrer (e.g., Retail Cl is carried by Chain C). In all cells where Coverage = 3, Chain C does

not carry the brand.

Although the CAIC is not quite minimized with seven segments, we observed that the G

index became worse after seven segments were extracted. For our seven segment solution,

we obtain excellent separation among segments (G = .937).’

The output from the latent class procedure is found in Table 3. For comparison purposes,

we also include the aggregate volume market shares in the column labeled “Total.” Infor-

mation on segment size, total expenditures, and allocation of grocery dollars across the four

food chains is found in Table 4.

A clear correspondence between chain preference and overall volume shares is evident.

We show in Figure 1 a visual display of the percentage deviation of each segment’s chain

allocation from the market average. For example, segments 5 and 7 allocate relatively more

grocery dollars to Chain C than the market in general. These are also the two segments

whose volume shares of the Chain C retailer brands (Retail Cl and Retail C2) are quite

large relative to the market average (Table 3).

The results in Table 3 show that the presence of retailer brands creates a segmentation

structure which is organized along the lines of grocery chain preference. However, it is

important to observe that segments do not show extremely strong store loyalty. The alloca-

tions in Table 4 indicate that less than 50% of a segment’s expenditures is allocated to any

one chain. Hence, the pattern of cross-category brand preferences (to be discussed next) is

influenced-but not completely determined-by grocery chain preference.

Cross-Category Brand Preferences

Our primary interest in these data is understanding the cross-category pattern of prefer-

ences for national and retailer brand names. However, recall (from equation 5) that the esti-

450

TABLE 3A

Journal of Retailing Vol. 73, No. 4 1997

Segment Volume Shares (Toilet Paper)

Seg 1 Seg 2 Seg 3 Seg 4 Seg 5 Seg 6 Seg 7 TOtd

Retail B 0.7 1.4 9.9 0.6 0.9 0.1 0.2 2.2

Retail Cl 0.5 0.6 1.1 1 .o 47.9 1.4 6.3 5.9

Retail C2 0.4 0.9 0.2 0.4 2.5 0.3 1.2 0.7

Retail D 0.3 0.0 0.1 13.6 0.5 2.5 0.0 3.0

Facelle 32.9 41 .b 25.0 18.3 16.8 62.9 47.8 33.1

Scott 2.5 0.5 1.3 3.0 1.9 2.9 1.3 2.1

White Swan 9.7 2.9 5.8 9.9 6.9 2.8 8.5 7.5

Cotton-Elle 21.7 32.7 22.1 19.7 9.7 10.9 27.1 20.8

Delsey 25.0 15.9 16.9 15.3 5.0 8.6 4.9 14.6

Other 6.5 3.5 17.6 18.2 8.0 7.5 2.7 10.1

Note: Table shows the raw output of the latent class malysis of the household basket data. Entries in the table are the per-

centage of each segment’s total category volume attributed to a particular brand. The column labeled “Total” contains

the volume shares of the brands observed at the market level.

TABLE 3~

Segment Volume Shares (Paper Towels)

Retail B

Retail Cl

Retail C2

Retail D

Facelle

Scott

White Swan

Hi Dri

Majesta

Other

Seg 1 Seg 2 Seg 3 Seg 4 Seg 5 Seg 6 Seg 7 Total

2.4 2.4 9.8 1.1 1.0 0.2 0.2 3.1

0.1 0.0 0.4 0.0 15.3 1.8 7.8 2.3

0.8 0.8 1.3 1.6 17.2 1 .I 15.8 4.0

0.8 0.2 0.1 15.4 1 .o 4.9 0.2 3.7

8.9 37.8 10.5 3.0 7.7 31.7 10.6 12.7

24.4 41.7 22.9 17.2 17.2 20.1 16.9 22.4

25.0 5.9 16.0 24.6 19.1 12.2 39.0 21.4

22.8 7.5 29.3 14.9 9.4 9.6 6.4 17.3

1.7 1.7 1.8 9.2 1 .b 1.3 0.4 2.9

13.1 2.1) 8.1 12.9 10.6 17.1 2.7 10.2

Note: Table shows the raw output of the latent class analysis of the household basket data. Entries in the table are the per-

centage of each segment’s total category volume attributed to d particular brand. The column labeled “Total” contains

the volume shares of the brands observed at the market level.

mated volume shares in Table 3 are biased away from intrinsic brand preferences due to the presence of brand marketing activity. To eliminate these influences, we must work with deviation scores Dj,, constructed by row and column centering the logarithms of the four

subsections of Table 3 (see equation 9). A representation of the Dj,, matrix is found in Table 5. To focus attention on the rele-

vant managerial issues, we consider only those seven brand names which have products in each of the four paper goods categories. To emphasize the overall pattern, we adopt a “+” and “-” notation. Recall that Dj,,, is a consistent estimate of O$S, j (m)] - a[+, j (m)]where a[+, j (m)] is the average intrinsic preference for brand j across all segments. A “+” in Table 5 indicates that the segment’s brand preference is more than .5 standard deviations

“ above the market average; a - ” indicates that the segment’s brand preference is more

than .5 standard deviations below the market average.


TABLE 3c

Segment Volume Shares (Facial Tissue)

Seg 1 Seg 2 Seg 3 Seg 4 seg 5 Seg 6 Seg 7 Total

Retail B 1.5 1.9 16.2 2.5 1.4 0.2 0.0 4.3

Retail Cl 0.1 0.2 0.9 0.0 3.6 0.2 2.3 0.8

Retail C2 0.1 2.9 0.8 1.5 24.0 0.5 14.2 4.5

Retail D 0.2 0.0 0.1 3.3 0.0 0.7 0.1 0.8 Facelle 9.3 26.4 14.5 13.2 9.7 36.2 7.7 14.2

Scott 6.0 15.4 11.5 15.7 7.1 9.4 6.2 9.9

White Swan 4.1 0.6 6.1 12.9 9.2 11.9 a.7 7.7

Kleenex 72.5 52.6 48.4 47.3 44.3 37.8 60.7 54.9

Other 6.3 0.0 1.4 3.7 0.7 3.1 0.2 2.9

Note: Table shows the raw output of the latent class analysis of the household basket data. Entries in the table are the per-

centage of each segment’s total category volumeattributed to a particular brand. The column labeled “Total”contains the volume shares of the brands observed at the market level.

TABLE 3D

Segment Volume Shares (Paper Napkins)

Retail B

Retail Cl

Retail C2

Retail D

Facelle

Scott

White Swan

Hi Dri

Kleenex

Other

Seg 1 Seg 2 Seg 3 Seg 4 Seg 5 Seg 6 Seg 7 Total

5.5 6.4 52.3 3.5 0.0 0.4 0.b 12.9

0.0 5.6 0.0 2.1 39.9 0.0 0.9 3.8

0.0 0.0 2.3 9.0 28.4 0.0 74.1 15.4

1.1 0.0 0.0 14.6 0.0 18.1 0.0 4.9

16.2 6.0 6.8 10.0 2.7 15.0 3.3 9.5

11.1 39.3 10.9 15.6 15.3 24.7 6.7 14.9

6.0 23.0 5.4 6.4 7.7 9.1 a.7 7.9

38.1 0.0 13.0 10.1 0.6 14.0 2.0 14.7

9.2 18.0 3.1 3.9 2.4 3.6 1.9 5.3

12.9 1.7 6.2 24.7 3.0 15.3 1.9 10.7

Note: Table shows the raw output of the latent class analysis of the household basket data. Entries in the table are the percentage of edch segment’s total category volume attributed to a particular brand. The column labeled “Total”contains the volume shares of the brands observed at the market level.

TABLE 4

Segment Characteristics

Segment size Lxpenditure index Chdin Akdtion (‘% of Total Expenditures)

Chain A Chain B Chain C Chain D

1 23.3 98 21 32 28 18

2 7.6 106 15 38 31 15

3 16.4 90 16 48 26 10

4 17.8 110 9 25 17 49

5 8.6 93 16 35 38 10

6 10.8 100 14 31 33 22

7 15.5 103 11 34 46 9

All Households - 100 15 34 30 20

No@: Size is the percentage of all households belonging to the segment. Expenditure Index is the total dollar expenditure

on groceries per household (100 = average). Chain Allocation is the percentage of grocery dollars spent at the indi- cated chain. Allocations sum to 100% within each segment.


Figure 7

The key finding is that preferences for retailer brand names exhibit strong consistency

across product categories. That is, if a segment has a strong preference for a brand name in

one paper goods category, the segment also has strong preference for the brand name in

other product categories. All retailer brands follow this principle (Table 5a). In contrast, the

pattern for national brands differs by brand name (Table 5b). Facelle products follow the

same pattern as retailer brands. Scott and White Swan products show less evidence for preferences organized by brand name. For example, segment 5 has high preference for both Scott and White Swan paper napkins-and low preferences for all other Scott and White Swan products. The results in Table 5 also emphasize that inter-segment similarity in pref-

erences for retail brands need not translate into inter-segment similarity in preferences for national brands. For example, segments 4 and 6 both prefer the Chain D retail brands, but

only segment 6 shows high preference for Facelle.

A summary of the preference pattern for the entire consumer market can be obtained by

using the 0jm.y scores to infer the market-level preference correlations.6 This approach is

Modeling Multiple Category Brand Preference with Household Basket Data

TABLE 5A

453

Cross-Category Retail Brand Preferences

Brand Category Segment Number

1 2 3 4 5 6 7

Retail 6

Retail 6

Retail 6

Retail B

Retail Cl

Retail Cl

Retail Cl

Retail Cl

Retail C2

Retail C2

Retail C2

Retail C2

Retail D

Retail D

Retail D

Retail D

Toilet Paper

Paper Towels

Facial Tissue

Paper Napkins

Toilet Paper

Paper Towels

Facial Tissue

Paper Napkins

Toilet Paper

Paper Towels

Facial Tissue

Paper Napkins

Toilet Paper

Paper Towels

Facial Tissue

Paper Napkins

+ + + +

-

- +

+ - - + - -

-

_ + _

+ + + +

-

+ - + - + - +

- _ -

+ + + +

+ + + +

+ + +

+ - +

+ - + _ +

+

+ _ + - + + -

Note: Table displays the pattern of the deviation scores computed by row and column centering the segment volume shares of Table 3 as per equation 9. A “+” indicates that the segment’s brand preference is more than .5 standard deviations

above the market average. A “-” indicates that the segment’s brand preference is more than .5 standard deviations below the market average.

useful because it implicitly weights each segment in terms of its relative size in the total

market. Consistent with Table 5, overall brand preference correlations are positive for

retailer brands and for Facelle. Scott and White Swan exhibit an interesting pattern of neg-

ative correlation. Toilet paper is an outlier with respect to Scott products; paper napkins is

an outlier with respect to White Swan products.

These differences in preference correlation patterns between retail brands and national

brands are not unexpected. Although the consumer segments identified in this market are

not store loyal, they clearly do have preferences for particular retail chains (Figure 1). If we

assume that relatively chain-loyal price-sensitive consumers represent a large proportion of

the sales volume of (limited distribution) retailer brands, then we should expect to see pos-

itive preference correlations across retailer brands in the market basket data. In contrast,

due to widespread product availability, national brand buyers have more discretion in mak-

ing choices. This greater freedom of action allows consumers to be less brand loyal when

selecting items across multiple product categories.7

Marketing Strategy Implications

Marketing strategies based on these results flow from two key assumptions. First, we

assume that households do not view the four paper goods (toilet paper, paper towels, facial

454

TABLE 5B

Journal of Retailing Vol. 73, No. 4 1997

Cross-Category National Brand Preferences

Brand Cdlegory Segment Number

1 2 3 4 5 6 7

Facelle Toilet Paper + - + +

Facelle Paper Towels + _ +

Facelle Facial Tissue + _ _ _ +

Facelle Paper Napkins + + - + -

Scott Toilet Paper + _ _ +

Scott Paper Towels + - _

Scott Facial Tissue + -

Scott Paper Napkins + - + +

White Swan Toilet Paper + _ +

White Swan Paper Towels _ _ +

White Swan Facial Tissue + + +

White Swan Paper Napkins + _ + +

Note: Table displays the pattern of the deviation scores computed by row and column centering the segment volume shares of

Table 3 as per equation 9. A “c” indicates that the segment’s brand preference is more than .5 standard deviations above

the market average. A “-” indicates that the segment’s brand preference is more than .5 standard deviations below the mar-

ket average.

tissue and paper napkins) categories as substitutes for one another. Second, we assume,

based upon the logic underlying equation (9), that the preference patterns found in Table 5

and Table 6 have been stripped of the impact of marketing mix activity (such as price and

promotion). That is, the results in Table 5 and Table 6 reflect consistent estimates of the

intrinsic preferences a(.~, i (m)) found in equation (1).

A pattern of positive correlations across the market (as in the retailer brands) suggests a

strategy for stimulating sales in several categories simultaneously. Recall from equation (2)

that consumers with higher intrinsic preference a(s, i (m)) respond more vigorously to the

marketing activity of product i(m). Given positively correlated preferences, consumers who

respond to a retail brand promotion in one category will generally have high preference for

the retailer brand name in several product categories. Accordingly, promoting the retail

brand in a single category may elevate retail brand sales in several categories simulta-

neously due to increased traffic from consumers with high retail brand preference.

The effectiveness of this store traffic strategy depends upon the positioning of retail

brands within the retail environment. Premium private labels (such as the President’s

Choice label of the Loblaws supermarket chain) have a value positioning (national brand quality at a lower price) and play an important role in positioning the retailer rel-

ative to its competitors (Hoch, 1996). Although promoting one category could attract

consumers to a store, a retailer concerned about rewarding consumers for store loyalty

may wish to promote several (positively correlated) product categories within the same week. The notion here is that loyal consumers represent substantial revenue for the

retailer. Hence, to prevent store switching, the retailer may wish to reduce the total mar-

ket basket expenditure for these consumers (O’Brien and Jones, 1995).


TABLE 6~

Brand

Retail B

Retail 6

Retail B

Retdil B

Retail Cl

Retail Cl

Retail Cl

Retail Cl

Retdil C2

Retail C2

Retail C2

Retail C2

Retail D

Retail D

Retail D

Retail D

Preference Correlations for Retail Brands

Category Toilet Paper Paper Towels Facial Tissue

Toilet Paper 1.00

Paper Towels 0.91 1 .oo

Facial Tissue 0.75 0.89 1.00

Paper Napkins 0.72 0.80 0.54

Toilet Paper 1.00

Pdper Towels 0.82 1 .oo

Facial Tissue 0.76 0.87 1 .oo


Toilet Pdper 1 .OO




Toilet Paper 1 .oo




Paper Napkins

1 .oo

1 .oo

1.00

1.00

Note: Table displays market level correlations in brand preference derived from an analysis of the volume share deviation

xores underlying Table L;. See text for computational details.

6~

Preference for National

Brand

Facelle

Facellc

Facelle

Facelle

Category

Toilet Paper

Paper Towels

Facial Tissue

Paper Napkins

Toilet Paper

1 .oo

0.83

0.66

0.51

Paper Towels

1 .oo

0.89

0.61

Facial Tissue

1 .oo 0.55

Paper Napkins

1 .oo

Scott Scott SCon

Scott

White Swan

White Swan

White Swan

White Swan

Toilet Paper 1.00

Paper Towels -0.42

FdCidl Tissue -0.46

Paper Napkins -0.34

Toilet Paper

Paper Towels

Facial Tissue

Paper Napkins

1 .oo

0.83

0.52

1.00

0.93 1 .oo

0.24 0.47 1.00

-0.12 -0.34 -0.46 1 .oo

1 .oo 0.41 1 .oo

Note: Table displays market level correlations in brand preference derived from an analysis of the volume share deviation

scores underlying Table 5. See text for computational details.

In contrast, the promotional strategy for a brand with a mix of positive and negative pref-

erence correlations offers different possibilities. Consider, for example, Scott toilet paper

and Scott facial tissue. The negative correlation between preferences for these products

indicates that consumers with high preference for Scott toilet paper are unlikely to have


TABLE 7

Quality Ranks for Scott Paper Goods

Scott Quality Total Ranks

Toilet Paper Paper Towels

Facial Tissue

Paper Napkins

14 20

9 31

2 10

not available not available

Note: Table shows quality rank of Scott brand (1 = highest) relative to the number of products rated (Total Ranks). These

quality ranks were obtained from three issues of Consumer Reports magazine: August 1984 (toilet paper), lanuaty 1992 (paper towels), and May 1989 (facial tissues). No Consumer Reports quality ranks are available for paper napkins.

high preference for Scott facial tissue-and vice versa. (See, for example, segments 1 and 2 in Table 5.) Under these circumstances, the manager may wish to consider product bun-

dling: providing a discount to the consumer only if Scott toilet paper and Scott facial tissue

are both purchased (Nagle, 1987; Brader, 1993). The relevant economic theory indicates

that if the two products were sold separately, only one segment would be attracted to each

product. However, if the price of the bundle is set appropriately, each segment may decide

to buy both products. Bundling (under this negatively correlated preference scenario) rep-

resents a way of targeting a promotion toward consumers with low prior purchase proba-

bility for one of the components in the bundle.

Product bundling strategy, however, must be approached carefully, with due regard for

all aspects of consumer purchase behavior. A key assumption in product bundling is that

all items in the bundle are contained in the consumer’s consideration set. This may not be

true-particularly when perceived quality varies considerably across brands. We investi-

gated this issue by obtaining quality ratings for Scott paper products from Consumer’s Union (Table 7). It is evident the Scott quality is rated quite low in toilet paper relative to

other categories. To the extent that Scott toilet paper does not enter into the consideration set of national brand buyers, this bundling strategy will be ineffective. In addition, the strat-

egy could be detrimental to the image of the highly-quality component of the bundle.

A related use of preference correlation information is retail assortment planning. Recent

research suggests that there is little practical difference between the set of brands in a consumer’s consideration set and the set of brands for which a consumer expresses high pref-

erence (Horowitz and Louviere, 1995). Given this interpretation, brands with positively correlated preferences will tend to be found in the same consideration set. Thus, positive

preference correlations for a set of brands (such as Facelle paper products) suggest that the

retailer should seek to carry the full product line.

CONCLUSIONS

We propose and illustrate an approach for estimating the distribution of consumer brand preferences using long-run market basket data from a consumer panel. The analysis is


derived from a multiple-category purchase behavior framework which simultaneously incorporates the notions of consumer preference segmentation, within-category brand sub- stitution and product class complementarity. We applied the model in a study of cross-category preference for retailer and national brand names in four paper goods categories.

Methodological Contribution

Our work makes two important methodological contributions. First, we provide a general framework for constructing a multiple category forecasting system. This system improves on previous models because it does not assume a priori that all products are substitutes. Rather, it allows the researcher to model all items in a consumer’s market basket simultaneously-whether they are substitutes, complements or independent with respect to demand. This property is desirable in any forecasting system. It is essential in building a model for household basket data.

Second, we show that brand preferences can be extracted from long-run basket data without knowing the causal environment (prices, promotions etc.) in which the basket data were generated. Our key result (equation (5)) implies that the marketing environment biases long-run volume shares away from the consumer’s true long-run preferences. However, by transforming the data appropriately (as per equation (9)), the analyst can obtain an accurate picture of preference correlations across the market-free from the impact of marketing activity. This allows the retailer to study consumer preference patterns using summaries of consumer purchase behavior. Thus, the analysis developed here is ideal for consumer data- bases (such as loyalty programs) in which causal information is missing.

Marketing Strategy Implications

As explained earlier, consumer preference patterns can be used by the retailer both to plan product assortments and to develop cross-category marketing programs. Generally speaking, positive preference correlations imply that the products fall into the same consideration set. Negative preference correlations imply that different sets of consumers purchase the products. Based upon this information, marketing policies can follow one of two generic strategies. The retailer can seek to adapt to consumer behavior (e.g., by carrying the entire line of positively correlated products) or to change consumer behavior by offering special incentives (e.g. by bundling negatively correlated products and selling the bundle at an attractive price). The appropriateness of these strategies largely depends upon the retailer’s goals and upon the costs associated with varies programs. Nevertheless, knowing the pattern of consumer preferences across the population provides a basic input for the

design and implementation of innovative marketing strategies.

Limitations

In developing this methodology, we made a number of simplifying assumptions to permit cross-category preferences to be estimated only using long-run summary data. The two


most important assumptions concern the form of the marketing mix impacts (proportional

intensity representation) and the way retailers vary marketing mix activity over time (lack

of correlation between category base rate and marketing mix effect). Although we believe

that these assumptions will be reasonable in many applications, they may not be appropriate

in all applications. In addition, we assumed that purchase volumes are distributed as Pois-

son random variables with time varying means. Although the Poisson assumption has very

little impact in the present analysis (see Appendix), a more robust alternative such as the

Negative Binomial distribution (Lenk, Rao and Tibrewala, 1993) may be more realistic if

the general multiple category model of equation (1) were to be implemented.

Future Work

These concerns may be addressed by developing a more general methodology based

upon all information available in market basket data. For this reason, an important exten-

sion of our work is the construction of a sales-volume forecasting system based upon indi-

vidual purchase information and records of marketing activity (price, feature advertising,

promotions etc.) for brands in multiple product categories. The attractiveness of such a

model should be clear. The model would be able to identify consumer preference segments

and to link these segments to market response coefficients for price and promotion. It

would also allow the relaxation of the assumptions used in our long-run market basket

model. From a management perspective, building marketing mix response into a multiple

category model provides a way of conducting “what if’ analyses for proposed cross cate-

gory marketing programs. Certainly, an extended model of this sort is not trivial to con-

struct. However, the general multiple category purchase model which underlies our

analysis provides a framework for further research.

APPENDIX

Long-run Basket Model

The long-run basket analysis is based upon two key theorems about the Poisson distribu-

tion (see, e.g., McCullagh and Nelder, 1989). Let yl. . . ., y,, be independent Poisson distrib-

uted variables with means ht. Then, the sum Y = Zjyi has a Poisson distribution with mean

Zihi. Moreover, conditional upon Y, the vector lyt, . ., y,] has a multinomial distribution

with means pj = hi[Zihi] and scale parameter Y (i.e., I.LiY is the mean of y;).

In the multiple category purchase model, the weekly volumes X[h(s), i(m), t] are assumed

to be conditionally independent Poisson variables. It then follows that the long-run volumes

W(.r), i(m)I are conditionally independent Poisson variables with means

h[h(s), i(m)] = C&(s), i(m), t]. Hence, conditional upon the total category volume


Q[h(s), m] = Z&Q[h(s), i(m)], the long-run volumes Q[h(s), i(m)] collectively have a multinomial distribution with means

YIh(s), i(m)1 = h[h(s), i(m)l/Cje,hlh(s),j(m)l (Al)

where, using equation (1),

h[h(s), i(m)1 = MS, i(m)lX,Uh, m, rlP[i(mI, tl . (A21

Let T be the number of weeks in the consumer panel. Consider the probability limit

(plim) of (1/7)3h[h(s), i(m)] as T approaches infinity. Because h[h, m, t] and P[i(m), t] are

assumed uncorrelated over time,

plim (lIT)hVz(s), i(m)1 = a[s, i(m)1 E,{h[h, m, tl} E,{P[i(mh 4 1 (A3)

where Et{ .} denotes a long-run time average. Now, using the properties of plim,

plim y[h(s), i(m)1 = plim ( l/T)h[h(s), i(m)] / CjEmplim (1/7)h[h(s). j(m)]. 644)

Inserting (A3) into (A4) yields

plim y[W, ib>l = a[~, i(m)lZti(m)l / Zjma[s, j(m>lZMm>l W)

where Z[i(m)] = E,{P[i(m), t]}. Defining O[s, i(m)] = plim ylh(s), i(m)] gives the result in the text.

An examination of this proof highlights the role of our assumptions in the analysis. Con-

sider the observed volume shares VS[h(s), (im)] = Q[h(s), i(m)]l&Q[h(s), i(m)] for each household. Because plim VS[h(.s), (im)] = plim $h(s), i(m)], it follows that only the assumed zero correlation between h[h, m, t] and P[i(m), r] is necessary to obtain the formula for the long-run volume share probability limit (equation (5) in text).

Given this result, the Poisson distribution assumption is only needed to conclude that the observed purchase volumes follow a multinomial distribution. The assumption could be discarded entirely if model estimation were based upon quasi-likelihood theory (see Chap- ter 9 of McCullagh and Nelder, (1989)). This change would have little consequence for our analysis. The quasi-likelihood approach yields the same parameter estimates as shown in the text. However, standard errors will be larger than those predicted by maximum likelihood theory.

Acknowledgment: The authors thank seminar participants at the Stanford Camp, University of Texas (Dallas), University of Iowa and BCRST Conference for many useful comments. The authors also wish to thank Professor Andrew Mitchell, Director of the Canadian Centre for Marketing Infor- mation Technologies of the University of Toronto, for the data analyzed in this study. This research


was partially supported by a grant from the Social Sciences and Humanities Research Council of Canada (SSHRC) to the first author.

NOTES

1. Details are provided in the Appendix.

2. Although this type of proportional intensity representation is often used in consumer purchase models (e.g., Lenk, Rao, and Tibrewala, 1993), it may not be appropriate for all markets. For example, McCann (1974) provides an example of a market in which light buyers are more respon- sive to marketing actions than heavy buyers.

3. In a highly seasonal product category, h[h, m, t] will reflect the influences of seasonality as well as inventory. Because seasonality is common to all households, retailers could co-ordinate marketing activity in such a way that h[h, m, t] and Pu(rn), r] are positively correlated, thus violating the zero correlation assumption. In such cases, data should be collected over a shorter period of time (e.g., one quarter) in which seasonal effects are relatively stable.

4. A formal justification for the use of the CAIC in selecting the number of segments in a mixture model is presented by Bozdogan (1993).

5. The overall fit of the model to the data, measured by the CJ* information statistic (Urban and

Hauser, 1980), is U* = .47. In choice modelling, U* values of .5 or greater indicate excellent fit.

6. The correlations in Table 6 were calculated from a table of deviation scores Dims in which all segments s were placed in the rows and brand-category names (for all defined j and m combinations) were placed in the columns. Because Oj,, is a consistent estimate of a[s, j(m)] - a[+, j(m)], each column of this table contains deviations around the market average for the corresponding combina- tion of brandj and category m. Inter-brand correlations were obtained by computing weighted Pear- son correlation coefficients for all pairs of columns using overall segment sizes (Table 4) as weights.

7. We thank Professor Charles Ingene of the University of Washington for this insight.

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