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Full text of "Marketing entry strategy formulation : a hierarchical modeling and consumer measurement approach"

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MARKET ENTRY STRATEGY FORMULATION: A HIERARCHICAL 
MODELING AND CONSUMER MEASUREMENT APPROACH 

Glen L. Urban// 
Philip L. Johnson//// 
Richard H. Brudnick// 



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W.P. No. 1103-80 



December 1979 



THE MARKETING CENTER 

Massachusetts Institute of Technology 

Alfred P. Sloan School of Management 

50 Memorial Drive 

Cambridge, Massachusetts 02139 

(617)253-6615 



MARKET ENTRY STRATEGY FORMULATION: A HIERARCHICAL 
MODELING AND CONSUMER tffiASUREMENT APPROACH 

Glen L. Urban// 
Philip L. Johnson//// 
Richard H. Brudnick// 

W.P. No. 1103-80 December 1979 



// Alfred P. Sloan School of Management, M.I.T. 
//// Management Decision Systems, Inc. 



ABSTRACT 



New product development requires large amounts of money and time and 
presents major risks of failure. An effective strategy for market entry 
can increase the likelihood of success and improve the potential payoff 
by focusing development efforts on attractive market opportunities. This 
paper describes a system of models and measurements designed to support 
the formulation of such a strategy. 

A hierarchical approach to defining the competitive structure of 
a market is proposed based on Tversky's (1972) theory of choice by elimi- 
nation of aspects. In our model, product attributes, usage situations, 
or user characteristics can define the competitive structure. Individual 
probabilities of purchase are estimated by logit procedures, and alterna- 
tive hierarchies are tested based on their ability to describe choices 
when consumers are forced to switch from their favorite product. Statis- 
tical tests are developed and choices in a laboratory shopping environment 
are utilized in a convergent analysis to select the best hierarchical 
description of the competitive structure. 

Opportunities for new product entry depend on the vulnerability of each 
section of the competitive structure and on the economics of introducing a 
new product in each. Competitive vulnerability is assessed with perceptual 
maps, and an order of entry model estimated based on 42 new consumer products 
is used to reduce the sales potential of later entrants. Profit potential is 
calculated and a tradeoff of risk, return, and investment is conducted to 
support formulation of an entry strategy. 

In an application to the coffee market a statistically significant and 
managerially relevant competitive structure is identified. Implications for 
new product development and research needs are discussed. 



-1- 



INTRODUCTION 



In many companies new product development is an important activity 
in generating growth in sales and profits. Despite the development of 
management science methods to improve forecasting, the risks remain high 
(see Urban and Hauser, 1980, for a review of the state of the art). 
Recently, A. C. Nielsen (1979) reported that of a sample of 228 frequently 
purchased consumer products which were test marketed in 1977, 64.5 
percent were not launched nationally. Since a test market may cost over 
one million dollars, these losses are substantial to the innovating firms. 
Losses also occur earlier in the process due to failures in R & D and 
consumer tests, but the most noticeable, embarrassing, and costly failures 
are those that occur after a national launch. For example, Polaroid 
probably lost over 150 million dollars on Polavision instant movies. 

The costs and risks of new product development can be considered 
within the sequential decision process shown at the top of Table 1. The 
first phase is opportunity identification. This activity includes the 
selection of a market and the generation of ideas for possible new pro- 
ducts. The second phase is design and consists of applied research and 
the specification of the physical characteristics of the product along 
with its psychological positioning of benefits to a designated target 
group. Testing is the third phase and it includes product and adver- 
tising evaluation, pre-test market laboratory simulation of consumer 
response, and test marketing. After all these steps are successfully 
completed, the product is launched. Table 1 shows the average costs 
and time for an industrial and a consumer product to go through each step 
in the process. The times, costs, and probabilities for industrial pro- 
ducts are adapted from Mansfield's studies of new chemical, machinery. 



-2- 



and electronics products (Mansfield et. al, 1971, Mansfield and Wagner, 1975, 
Mansfield and Rapoport, 1975). The data for consumer products are judgements 
based on the authors' experience with over 150 new products, most of which were 
packaged goods. The variances on these estimates are very large and depend 
on specific product and company characteristics so the data must be inter- 
preted cautiously. 

The average cost to reach the national launch phase for a product suc- 
cessful in each phase is about one million dollars for an industrial product 
and 1.3 million dollars for a consumer product. But each phase will not be 
successfully completed for each new product project. The probabilities for 
successful completion to the launch phase are about -37 (.57 x .65) for an 
industrial product and .23 ( .5 x .45) for a consumer product. This means 
each phase will be done more than once, on average, before a successful product 
is developed. The expected cost is the fixed cost of opportunity identifi- 
cation plus the expected costs of each phase. The expected cost of a phase 
is the cost of the phase divided by the product of the probabilities of com- 
pleting the remaining steps in the process. Similarly, the expected time 
is the time for opportunity identification plus the expected time for each 
phase. This is the time for the phase divided by the product of the proba- 
bilities. These calculations indicate about 3 to 3.8 million dollars should 
be budgeted for development of a successful product. The expected time to 
develop a product is about 5 years for a consumer product and 10 years 
for an industrial product. For development and launch, 4.6 and 9.6 million 
dollars for an industrial and consumer product, respectively, should be bud- 
geted, on average, for a typical successful entry into market. 

As indicated in note three of Table 1 the costs and time for a consumer 
product can be reduced to 2.7 million dollars and 4.6 years by use of pre-test 



Table 1 
Costs and Risks of New Product Development 
(adapted from Urban and Hauser, 1980) 
PHASES IN DEVELOPMENT PROCESS 











Subtotal 








Opportunity 






to 








Identifi- 






Launch 








cation 


Design 


Testing 


Decision 


Introduction 


TOTAL 


Cost ($000 's) 














Industrial 


50 


620 


290 


960 


1,270 


2,230 


Consumer 


100 


200 


1,000 


1,300 


5,000 


6,300 


Time (mos.) 














2 
Industrial 


5 


27 


9 


36 


15* 


51 


Consumer 


5 


6 


12 


23 


4* 


27 


Probability 














Industrial 


# 


.57 


.65 


— 


.74 


— 


Consumer ^ 


# 


.50 


.45 


— 


.85 


— 


Expected Cost 


($000's) 












Industrial 


50 


2,261 


603 


2,914 


1.716 


4,630 


Consumer ^ 


100 


1,046 


2,614 


3,760 


5,882 


9,642 


Expected Time 


(mos. ) 












Industrial 


5 


98 


18 


121 


20 


141 


Consumer 3 


5 


31 


24 


60 


5 


65 



NOTES: * Includes time from completion of testing phase to the beginning 
of launch . 

# Opportunity identification is an activity assumed to produce at 
least one market worthy of design effort. 

1 These figures are adapted from Mansfield and Rapoport (1975, p. 1382- 
1383) by allocating 50»000 from his applied research classification to opportunity 
identification and grouping the remaining to applied research and specification 
under design. Prototype plant is termed testing here. 

2 These times are adapted from Mansfield et. al (1971, p. 120) by allo- 
cating the total of 51 months to phases assuming no overlap in the launch, manu- 
facturing tool up, or prototype phases. The applied research and specification 
times were derived by allocating the remaining time proportionally to the percen- 
tage of time in these phases. 

3 Does not include consideration of pre-test market analysis. Based 
on a pre-test procedure costing $50,000 with a .6 success probability and a 
subsequent .8 test market success rate, the expected cost is $2,672 (100 + 
(200/(.5 X .6 X .8 X .85)) + (30/. 6 x .8 x .85)) + l,000/(.8 x .85)). This is 
over a one million dollar saving. The expected time is 55 months assuming the 
pre-test analysis takes 3 months. 



-3- 



market models, but in any case the costs and time requirements are large 
and emphasize that the new product process should be carefully managed. 
Quantitative and qualitative methods should be used to improve the probabili- 
ties and rewards of success at the design and testing phases. Careful atten- 
tion should also be focussed on the identification of opportunities before a 
firm commits approximately three million dollars and five years to develop a 

product. The opportunity identification phase should include the considera- 
tion of alternative markets, assigning priorities to these markets, and consi- 
deration of the competitive structure and new product opportunities in 
the selected markets. Careful development of a market entry strategy 
can reduce failures in the development process and improve the profits 
from successful products by targeting development activity to attractive 
markets that show vulnerabilities to new product innovation and potential 
to generate a high return on investment. 

In some firms, entry is based on technological innovation. Although 
success can be obtained with this approach, recent studies indicate that 
60 to 80 percent of technological innovations are the result of percep- 
tions of market needs and demands (Utterback, 1974, Von Hippel, 1978). 
This suggests that it is appropriate for an entry strategy to give heavy 
emphasis to market characteristics and then to target technological inno- 
vation at filling these needs. 

The purpose of this paper is to develop a market model and 
measurement system to support the formulation of an effective entry strategy. 
We assume that a large number of markets have been screened to iden- 
tify the two or three that most closely match the company's unique capa- 
bilities, have desireable market characteristics, and have financial potential 
(see Urban and Hauser, 1980, for a detailed description of a "market 
profile analysis" to consider the factors in screening markets) . In 



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each of these two or three markets a model-based study of the competitive 
structure and entry potential would be conducted. 

Some of the basic questions to be addressed in this paper are: What 
products compete with each other in the market? On what basis do they compete? 
Is there an opening for a new product entry? Are the incremental profits 
that may be earned worth the risks and costs of development and entry? 
We will develop a model of the structure for hierarchical competition 
in a market and a model to estimate potential payoff of a new entry in 
this market. If the market is permeable to entry and a financial payoff 
is likely, the resources would be committed to develop a successful 
new product entry. 

This paper begins with a review of existing approaches to hierarchi- 
cally defining a competitive structure. Building on the positive features 
of these approaches, a new model is formulated and its hierarchical 
specification, measurement, estimation, and testing procedures 
are described. Then, a model of profit potential based on modeling competi- 
tive vulnerabilities and the effects of the order of entry of a new product 
is specified. Risk/return/investment tradeoffs are considered and the 
entry strategy implications of the models are discussed. An application 
of the models to the coffee market (four billion dollars in annual sales) is 
reported, and the paper closes with a consideration of future research needs. 



-5- 



HIERARCHICAL MODELS OF COMPETITIVE STRUCTURE 



Many approaches have been used to define a market and the competitive 
relationship between products within it. The most common is based on 
similarities of materials or production. For example, the market may 
be defined as aluminum gears or diesel autos. In many cases, the standard 
industrial codes (SIC) are used to identify markets. 

These are insufficient for new product analysis since they do not 
reflect the market response which is critical to the success of an inno- 
vation. For example, a new plastic gear may compete with aluminum and 
steel gears for many uses. A VW Rabbit diesel may not compete with a 
Mercedes Benz 300D although they both have diesel engines. While consumers 
may see the Mercedes as a part of the luxury car market in which Cadillac, 
Lincoln, Chrysler, Oldsmobile, Buick, and Jaguars compete, the VW may 
be viewed as an economy car competing with Datsun, Toyota, Chevette, 
and Fiesta. 

Consider further the structure of the luxury auto market. Figure 
1 shows two hypothetical competitive structures for this market. We 
shall call such structures "trees" and indicate that "branches" divide 
the products in the market into subsets. In the first tree, the market 
is grouped by size of car and then by brands, while in the second, the primary 
grouping is by U.S. or foreign. The strategic implications are very 
different. Consider G.M.'s situation. If the first structure is correct, 
it has covered all major sections of the market and has 

positioned Seville to compete with Mercedes Benz. However, if the second 
tree is true, CM. is largely competing with other domestic manufacturers 
and its own brands compete heavily among themselves. In this second 
case, the Seville is not competing with Mercedes Benz, and G.M. could 



-6- 



consider importing a foreign car to sell in competition with Mercedes 
or developing a car that would be perceived as "foreign." The second 
structure would imply a new entry in the foreign luxury market would 
have a small negative effect on the existing G. M. business and be a 
possible strategy for increasing sales. 

This example emphasizes the need to understand the true competitive 
structure before committing to new product development. This paper will 
propose a market-based method for deriving a hierarchical description 
of the competitive relations between products to support the formulation 
of a market entry strategy. 
Alternative Approaches 

Market-based methods of defining competitive structure draw on the 
fields of economics, psychology, choice theory, and marketing. We briefly 
review several approaches and indicate each ones strengths and weaknesses. 
Then we propose a method which builds upon these strengths and attempts 
to overcome their weaknesses. This review is organized around the criteria 
used to model competition between products. 

Purchase Behavior : The most direct measure of competition is the change 
in sales of one product due to a change in sales of another (9q./3q., 
where q. is sales of product i) . Economists operationalize this notion 
by the cross price elasticity: 

dq. dp 
\ Pk 

where q. = sales of product i 
p = price of product k. 

K. 

If it is positive, the products are substitutes and if negative, complements. 



Figure 1 



Hypothetical Competitive Structures 
for the Luxury Auto Market* 



Luxury 
Auto 



Small 



Jaguar 



Cadillac 
Seville 



Medium 



Mercedes Olds Buick 



Cadillac 
Eldorado 



Large 



Lincoln Chrysler 



Cadillac Olds 



U.S. 



Buick 



Luxury 
Auto 



Foreign 



CM. Lincoln Chrys 



ler i 



aguar Mercedes 



Seville 



Eldorado 



* For illustrative purposes, this example only includes some of the over 30 
models that might compete in this market. 



-7- 



The notion that the higher the cross elasticity, the more competitive 
two products are, could be used to describe competitive relationships. 
It is attractive since it is based on actual sales changes, but presents 
practical difficulties. The econometric estimation of cross elasticities 
is difficult for a market of many brands since many cross elasticities 
must be estimated and these are second order effects relative to direct 
price and advertising elasticities. New advances in measurement due 
to electronic retail checkout data and uniform product codes (UPC) may 
make estimation more feasible in the future for consumer products. Even 
if the elasticities are estimated, a method to process a matrix of cross 
elasticities (e.g. 20 x 20) to succinctly define the structure of competi- 
tion has not been proposed. This is further complicated when one considers 
cross elasticities due to advertising or promotion are also possible 
measures of substitution and complementarity (Urban, 1969). 

In frequently purchased goods markets, it is feasible to observe 
sequences of consumer buying based on consumer diaries of purchases. 
Estimated probabilities of repeat purchasing and switching brands can 
be derived. Pairs of brands which experience high switching may be considered 
in competition. Clustering of the observed switching matrix to specify groups 
of brands which compete has been proposed (Rao and Sabavala, 1978, Kalwani, 
1979). Hierarchical clusters could be derived, but in practice the matrix 
is not very large and many cells may be estimated by small samples. Some 
of the clusters may be difficult to interpret since all products may not 
share an observed attribute that can be used to identify it for strategic 
purposes (e.g., all toothpastes in a cluster may not be anti-cavity brands). 



-8- 



A more theoretical approach to defining a hierarchical competitive 
structure based on switching has been proposed by Butler (1976). In this 
approach the criterion is that brands are in competition if switching is 
proportional to the product of their shares. The method entails testing 
alternative hierarchical descriptions and selecting the one that best fits 
the criterion (Morrison and Kalwani, 1977, Rubinson and Bass, 1978). Empir- 
ically observed switching can be used if the market is in equilibrium or if 
it is not, Butler proposes switching rates be derived by maximizing the 
entropy of the system subject to constraints on market share. 

This is an interesting method, but it, as well as other methods based 
on brand switching, is subject to measurement and estimation limitations. 
The measures of switching from diaries of consumer purchases reflect house- 
hold purchases. Individual preferences and usage associations are lost. 
For example, if the household switches at every purchase opportunity be- 
tween Crest toothpaste and Colgate, brand switching approaches would find 
a competitive condition between the brands. But this will not be true if 
the children are perfectly loyal to Crest and the adults are perfectly loyal 
to Colgate. 

Another difficulty with the method is that the assumed equilibrium con- 
dition may not occur often in frequently purchased brands where over 50 per- 
cent of the volume is sold on special promotions. In these cases the maxi- 
mum entropy procedure can be invoked, but one study based on simulations 
from known structures indicated this procedure was not effective in identifying 
the hierarchical structure (Rao and Sabavala, 1979). 

A final weakness is the lack of statistics to test if one hierarchical 
structure is significantly better than another. It is not difficult to find 
a hierarchy that adequately fits a set of data, but in practice other hier- 



-9- 



archies also display this adequacy of fit. There is a need for statistical 
tests to discriminate between alternative competitive structures. 

Choice Processes ; 

One approach to overcoming some of the measurement and estimation prob- 
lems in methods based on observed sales is to develop models of the individual 
choice process. Early research led to non-hierarchical models, but recent work 
has led to models that explicitly consider the hierarchical relationship 
between products. 

Luce (1959) has proposed a choice model that states that the probability 
of purchase of an alternative is determined by its preference relative to the 
sum of preferences of all alternatives. This model assumes the relative 
probabilities of choice between pairs of alternatives do not vary with the 
size of the set of alternatives offered. This is called the assumption of 
independence of irrelevant alternatives. This assumption is violated when 
an alternative competes more with some alternatives than others. For exairple , 
Debreu (1960) posed a counter example in the choices between three records: 
a suite by Debussy (D) and two different recordings of the same Beethoven Symphony 
(B',B"). If all are equally preferred. Luce's model would imply a probability 
of choice of 1/3 for each. However, if the two Beethoven records compete with 
themselves and if the first selection is between either a Beethoven or a Debussy 
record, the probabilities would be P(D) = ^, P(B') = ■!$, and P(B") = k- This 
second condition violates Luce's model and the assumption of the independence 
of irrelevant alternatives. The violation shown by this example could be 
rectified by a model based on a hierarchical choice process of first Beethoven 
versus Debussy, and then the choice between the two Beethoven records when 
Beethoven is selected over Debussy. 



-10- 

Tversky (1972, 1979) has developed a theory called "elimination by aspects" 
which models choice as a hierarchical process in which all stimuli with a given 
aspect are eliminated and then choices are made among the remaining alternatives. 
In an experimental setting in which respondents made repetitive choices from pairs 
and triples of stimuli (i.e., college applicant profiles on intelligence and moti- 
vation) maximum likelihood procedures were used to estimate an elimination by as- 
pects model. The elimination by aspects model could be rejected for only 2 of 24 
respondents at the 10 percent level. This notion of elimination by aspects also 
has received research support from psychologists (e.g., Wickens, 1971). 

McFadden (1980) has recently conceptualized the elimination by aspects 
theory within a framework of generalized extreme value models. His tree 
extreme values model is a nested sequence of multinomial logit models. 
A hierarchical structure is posited and probabilities are estimated itera- 
tively by applying the multinomial logit estimation procedures within 
branches. In an application of these models to transportation mode choice 
data from San Francisco, he found his tree extreme value model and Tversky's 
elimination by aspects, produced similar estimates of individual probabili- 
ties. Alternative orderings in the hierarchical models did not exhibit 
significantly better fits (log likelihoods) or lower standard errors 
than non-hierarchical multinomial logit, but a specific parameter to 
reflect the hierarchical specification was significantly different from 
zero. This supports the theory of hierarchical choice. The application 
also demonstrated the difficulty of discriminating between alternative 
trees. The significance levels were similar for trees with very differ- 
ent hierarchical orderings and, consequently, very different implications 

of competitive structure. 

The theoretical foundations of hierarchical choice models make them 

attractive approaches. In addition, McFadden 's model is feasible to 

apply based on observed last choices and measured attributes. Algorithms 

now are being developed to obtain computational efficiency. 



-11- 



Information Processing : Although a hierarchical model may fit choice 

data, the hierarchy need not necessarily represent the sequence of 
decisions individual consumers make. The fact that several trees may 
fit the data emphasizes this. One should also recall that McFadden's 
choice model is an aggregate model. It may not represent how individuals 
behave unless all respondents are homogeneous. An idiosyncratic approach 
to describing the hierarchical decision process can be made by considering 
information processing (Bettman, 1979) . 

Applications have been reported in marketing (Bettman, 197 9, Haines, 
197 1) based on developing a protocol from consumers' statements about 
what they are considering as they go through a shopping experience. A 
lexicographic model then is developed to describe their order of considera- 
tion of product and use attributes. 

Payne (1976) used such a protocol procedure to study choices of apart- 
ments, but supplemented it by an information seeking measure. The respon- 
dent was asked to choose from a set of apartment alternatives. A matrix of 
information was presented, each row an apartment, and each column an attri- 
bute. Each cell contained a blank card and if a card was turned over, an 
attribute of an apartment was revealed (e.g., rent or number of rooms). The 
number of apartment alternatives and the number of attributes was varied 
across respondents. Payne found that as the number of alternatives and attri- 
butes increased, the proportion of cards overturned decreased. For two al- 
ternatives, the same number of cards were overturned for both choj.ces, but for 
larger numbers of alternatives, some alternatives were searched more than 
others and the chosen alternative was searched most thoroughly. This sup- 
ports the notion of a lexicographic choice process for complex problems and 
a trade-off process for simple choice tasks. 



-12- 



Information processing represents the most behaviorally detailed 
approach to developing a hierarchical model, but it is subject to limita- 
tions due to the cost of collecting the information which limits sample 
sizes and the difficulty of aggregating the findings into a description 
of a market which is useful to managers (Bettman, 1974). 
Use Substitution : Examining protocols often indicates the importance 
of the specifics of the use situation for a product. Situational effects 
are important in understanding choice behavior (Belk, 1975) . Stef f Ire 
(1972) has proposed in-use substitution as a measure of competition. 
If two products are substituted for the same use, they may be viewed 
as rivals. Stef fire studied 52 prescription drugs by having doctors 
judge their appropriateness to 52 patient symptoms. A multidimensional 
scaling of the data indicated groups of products that were deemed to 
be appropriate to groups of sjnnptoms. Day, Shocker and Srivastava, (1979) 
applied a similar approach based on a factor analysis of judgements of 
the appropriateness of brands of products that could serve as a breath 
freshener under specific use situations. 

These approaches emphasize the importance of a situation specific 
measures in defining a competitive structure, but they restrict their 
attention only to use similarity and do not reflect purchase behavior or 
hierarchical choice processes in their definition of competition. 
Perceptions : One method of analyzing the appropriateness of products 
to specific uses is to develop a matrix of similarity between the products 
(e.g. Z.. = number of situations in which products i and j are appropriate 
for the same uses divided by the number of uses) . A perceptual map can 
be derived from such a matrix by the application of non-metric multidimen- 
sional scaling procedures (e.g.. Bourgeois, Haines, and Sommers, 1979). 



Figure 2 
Perceptual Map of Coffee Market 



• High Point (RD) 
•Brim (GD) 
• Sanka (RD) 

Sanka (FD) • 



MILDNESS 



Sanka (GD) • 



Nescafe (RD) 



Private Label 



Hills (GC) • 



• Tasters' Choice (FD) 



•Brim (FD) 



Folgers' (RC) 

• Tasters' Choice (FC) 
_► TASTE 



Nescafe (RC) 



(GO 



• Maxim (FC) 



• Maxwell House (GC) 

• Instant Maxwell House (RC) 

• Chase (GC) 

• Folgers' (GC) 



, A & P (GC) 

• Chock Full of Nuts (GC) 



» A & P (RC) 



NOTE: 



GC = ground caffeinated 

GD = ground decaffeinated 

RC = regular caffeinated instant 

RD = regular decaffeinated instant 

FC = freeze-dried caffeinated instant 

FD = freeze-dried decaffeinated instant 



-13- 



Products that are close together could be viewed as more competitive 
than those farther apart. Products on such perceptual maps can be clus- 
tered to define groups of competitive brands or recent hierarchical multi- 
dimensional procedures (Carroll, 1976) can be used directly to estimate a 
competitive structure. 

Perceptual mapping methods have been widely used in marketing (Green 
and Rao, 1972, Stefflre, 1972, Urban, 1975) based on similarity judgements 
or ratings of products on attributes. In some applications it is assumed 
the market share of a new product will come from brands inversely propor- 
tional to the distance between the new brand and old brands (Urban, 
1975). The notion of rivalry between products being represented 
by the distance between them was proposed initially in economics by 
Hotelling (1929). His linear model has been extended recently to the multi- 
dimensional attribute cases (Lancaster, 1971, and Schraalensee ,' 
1977). 

Perceptual similarity is an attractive criterion for defining competi- 
tion, but it is an intermediary measure of substitution and may not be 
as valid as actual purchasing. Perceptual maps are commonly used to 
model choice as a compensatory process by defining directions 
of increasing utility or maximum utility points (called "ideal" 
points — Carroll, 1972). The research on information processing and the 
experiments by Payne cited earlier cast doubt on such a structure in 
situations with a high number of stimuli. For example, consider the 
map of the coffee markets shown in Figure 2. This map is based on 
a factor analysis of ratings of products on 12 attitude scales obtained 
from interviews of coffee drinkers. (See measurement and application 
section for description of data collection procedures.) Two dimensions 



-14- 



explained 84.3 percent of the variation In the data. Dimension one was 
most correlated (factor loadings greater than .7) to "taste" scales 
(fresh tasting, full bodied flavor, rich, right strength of flavor, ground 
aroma, stimulating, overall taste), and dimension two correlated (loadings 
greater than .7) to "mildness" scales (does not upset stomach, not bitter). 
The factor scores for each product are shown in the figure. Note the 
large number of brands and the lack of obvious clusters of brands that 
could represent distinct competitive sets. In the authors' experience, 
these results are typical for a category of many brands. Although percep- 
tual mapping is attractive, it is not the best method for representing 
competition at the overall level. As Payne's work suggests, it may be 
an effective method to represent tradeoffs when a lexicographic elimination 
procedure has preceded it and a simple choice task remains. 



-15- 



Summary and Proposed Approach : Many attractive features are represented 
in the existing approaches and it is not possible to select one 
method as best in all situations. If the problem is how to allocate 
promotional funds across an existing product line, it suggests the appro- 
priateness of research to develop procedures to estimate cross elastici- 
ties based on electronic checkout (UPC) data. If the problem is one 
of identifying and modeling behavioral phenomena, information processing 
appears attractive. For the problem of market entry, a criterion reflect- 
ing switching is useful since the new product must cause people to switch 
from their existing first choice. 

This paper will develop an approach based on Tversky's (1972) theory 
of elimination by aspects. In an effort to obtain power in discriminating 
between trees, aggregate switching probabilities will be calculated to 
represent the situation when the first preference product is unavailable 
to a consumer. This forced switching scenario will represent the basis 
for differentiating between hierarchical representations of competitive 
structures. Specific statistics will be developed to test significance 
within and between trees. Survey measures of preference and choice will 
be taken for specific usage situations so the hierarchy can reflect situ- 
ation specific groups of products that may compete for separate 
uses. A convergent validation procedure is facilitated by another measure 
of forced switching based on observation of purchasing in a store when 
the respondent's first choice is "out of stock." This model is hierarchi- 
cal, but at the lowest level of the tree where the choice task is simpler, 
perceptual maps will be added to represent attribute tradeoffs and position- 
ing opportunities. 



-16- 

Model Formulation 

In this section we define the competitive structure model called PRODEGY 
( PRODu ct strat EGY ) and its associated measurement, estimation, and testing pro- 
cedures. Later in the paper, market entry analysis procedures based on this 
model and an application of the model to the coffee market are reported. 
Criteria for Hierarchical Specification ; Our criterion to judge the appropri- 
ateness of a hierarchical tree structure is based on the probability of an 
individual buying a product in the branch that contains that individual's 
first preference product under the condition that the first preference product 
is not available. We aggregate these probabilities across individuals to 
obtain an average probability for each branch. 

(la) P., = y p.. 

lb >„ 11 
■^ 1 

ieB, 

D 



(lb) P.. = P../(l-P..*) 

iJ iJ iJ 



P, = for individuals who have their first preference 
in branch b, the probability of buying a product 
in branch b when their first preference brand is 
unavailable . 

P., = for individual i who has his or her first prefer- 
ence in branch b> probability of buying a product 
in branch b when his or her first preference brand 
is unavailable - 

P.. = probability of individual i buying product j. 

P..* = probability of individual i buying the first 

preference product 
\, 
P. . = conditional probability of individual i buying 

product j when the first preference is not 

purchased (unavailable). 



-17- 



I = set of individuals whose first preference product 
is assigned to branch b 

B, = set of products contained in branch b 
b 

C. = set of products individual i would consider buying 
J.* = individual i's first preference product 



Equation lb defines the conditional probability of buying a product (j) given 

the first preference product is not purchased. The unconditional probability 

(P..) is the product of the probability of buying product j given the first 

preference product (j*) is not purchased (P. .) times the probability of not 

buying the most preferred product (1-P..*) and therefore P.. = P../(l-P..*) 

ij ij ij' ij 

Equation la calculates an individual's probability of buying in the 

branch which contains his or her most preferred product under the condition 

that the first preference product is unavailable; it sums the probabilities over the 

products in that branch which the individual would consider. Table 2 gives an example of 

these calculations to make the implications of the equations more clear. 

Individual one considers five products (j = 1 to 5) and the most preferred 

product is product one (P.. is greatest for j=l) ; it is a type A product. 

For illustrative purposes. P., is calculated for a two-way branching of 

products with attribute A versus those with AA. The value of P., = .67 

lb 

probability of buying a product of type A if product one were unavailable. 
Similarly P., is calculated for individual two, but here the most preferred 
product is of type AA, so individual two's probability of buying is calculated 
by equation la over products of type AA. 

Equation 1 averages the probabilities for individuals whose first 
preference product is in a given branch (e.g. A or AA in Table 2 ). In the 



Table 2 



Examples of Calculation of P., 



Products (j) 


Product 
Type 


Individuals 

1 


(i) 
2 


1 


A 


^1 = '' 


X 


2 


AA 


hi = ■'' 


^22 = -^^ 


3 


A 


^3 = ''' 


X 


4 


A 


h, = ■'' 


P24 = -^ 


5 


AA 


h5 = ''' 


^25 = -3^ 


6 


AA 


X 


^26 = -1 










^ib 




.67 for bM 

. .15 .05 . 
^(l-.7)'(l-.7)^ 


.81 for b^AA 

. .35 .1 . 
^(l-.45)'(l-.45)^ 



X = not in individuals consideration set 



-18- 



two cases in Table 2 the probabilities (P.. ) are high. If this were true 
for all individuals, it would suggest high values of P, and that branching of 
attribute A versus AA is a good candidate for the hierarchy. 

To obtain an overall measure, the probability of buying in branch b 
when the first preference products are not available (P,) is averaged across 
branches to produce an aggregate tree probability of buying in the branch 
when first preference is not available: 

(2) p = K^b ' K 

b b 

A good tree structure will have a high value of P. We seek to find the 
tree with the highest P and assure ourselves that it is significantly better 
than a random market classification and other possible hierarchical descriptions. 

The branching probability in Equation 1 is a function of the assignment 
of products to branches (P,)j products individuals consider (C), and choice proba- 
bilities (P--). To test the significance of a tree we compare P, for a specific tree 
ij b 

to a random assignment of products given no information on consideration sets and 
choice probabilities. In this case, products would be randomly assigned in equal 
numbers across the branches and the conditional choice probability calculated. 
For example, for a two-branch tree., each branch would contain one-half of the 
brands. Randomly taking away one product from some one arbitrarily designated 
branch represents the condition of the most preferred product being unavailable. 
The number of products in this designated branch is (n/2)-l and (n/2) products 
are in the other. Given that all products are considered and preferences are 
equal, the branching probability is the number of products in the arbitrarily 
designated branch divided by the number available for choice (n-1) . The random 
probability (R, ) is calculated by: 



-19- 



R, = random probability for branch b which is subdivided to 
contain branch b at next level below it. (b=0 at top 



of tree and R =1.0) 
o 



H, 



, = number of products contained in branch b 
b — • 

G, = number of subdivisions of branch b at the next level 

h u 1 -^ ~" 

— below It 

For the two branch tree and six, products shown in table two, the random 
probability is .4 [ 1 .0( (6/2)-l)/(6-l) ) ] • In most cases the number of 
products is large and random value would approach R, /G, . If P, is greater 
than R^, this represents better assignment than random and if less than R, , 
worse than random assignment. The average random probability (R) for the tree is: 

b b 

The random probability reflects assignment of the products to branches 
without regard to attribute commonalities while the tree is an assignment with 
at least one common attribute. It should be noted that the random probability 
used to test significance does not depend on the particular set of brands 
individuals consider buying or existing market shares. For example, if two 
branches exist, the number of products is large, and the market shares of 
products in each of the branches for the hypothesized tree are .9 and .1 
respectively, the random probability of buying for those individuals assigned 
to a branch when their first preference is unavailable would be approximately 
.5 in each branch. This is consistent with the elimination by aspects notion 
which indicates the selection of a branch reflects a decision between attributes 
and not specific products. Use of the market shares of evoked brands 
in the random value would result in building a very high information alternative 



-20- 



since the major determinants of share and the model proposed here are the con- 
sideration set (C.) and the individual choices (P..). The random assignment 
probability (R) represents the best null hypothesis to test the significance of 
the hierarchical market structure model presented in this paper. 

P can be compared to R statistically since its approximate distribution 
is given by the central limit theorem. In the sample sizes and proportions 
represented here (n>300, .1<P<.9), the proportions are normally distributed. 
If we assume the probabilities (P..) to be multinomially distributed and 
that trials are independent, the standard deviation of P, is 



b 7 lelb 



and the standard deviation of P is 



a = / E P.. (1-P., )/ZN, 2 

P s/ i ^^ ^^ b ^ 



(see Appendix One for proofs). One can also test the significance of given 
branches against the random assignment probability (P, versus R.) if the sample 
size is not too small and the probabilities are not too skewed (Drake, 1967). 
These statistical tests give a basis for determining if a given tree is 
statistically significant relative to a random assignment. Similarly, the 
difference in the overall probabilities (?) from two trees can be tested 
by standard procedures to determine if one proportion is significantly 
better than the other. 

Branching Procedure : The first step in developing a tree structure to describe 
a market is to designate the possible alternatives. Any attribute can be used 
to define a branch, but each product must be uniquely assigned to a branch 
before the tree can be evaluated. An alternative is rejected if in any branch 



-21- 



the probability of buying in the first preference branch (P, ) is not signifi- 
cantly greater than the random probability (Ri^) at the ten percent level. A 
second rejection criterion is used to eliminate trees where the switching from 
the first preference branch is high relative to the random probability. The 
probability of switching from the first preference branch (b) to another 
branch (bb) is: 

(^) \,bb = ^ ^ ^J / 'b 

j^^b 

W, , , = probability of switching to branch bb from the 
' first preference branch b. 

For a tree to be acceptable, we require that the switching probability (W^^ ^■^) 
not be significantly greater at the 10% level than the random probability of buying 
in the branch switched into when the first preference is not available 
(R, , ) . After the alternatives have been screened for the rejection cri- 
teria, the tree with the highest average probability of purchase in the 
first preference branches (P) is identified. 

The application of the rejection criteria and identification of 
the best branching is carried out at each level of the tree from the top 
to the bottom. This procedure insures that the least switching occurs 
at the top branches of the tree and that switching increases as one 
divides the market more finely. In the market definition problem consi- 
dered in this paper, the order of branching is important. The sequential 
procedure assures that the probability of repeat buying (P) is highest 
and that the market division is strongest at the top of the tree. 

After the top level is considered, alternates rejected by the criteria 
discussed above, and the best branching identified, we determine if the 



-22- 

best branching is significantly better than its nearest rival at the ten per- 
cent level based on the overall probability (P). If so, the analysis moves to 
the second level based on branching from this alternative. If the best tree is 
not significantly better than the next alternative, both alternatives are con- 
sidered for further branching at the next level. Branching stops when no 
further divisions will satisfy the two rejection criteria given above, when 
sample sizes become unacceptably small, or when no more candidate hierarchies 
are available. This typically allows branching to no more than three levels 
unless a large sample of consumer surveys is collected (greater than 500). If 
one tree is not significantly better than others at the ten percent level, the 
tree with the highest probability (P) is selected and a sensitivity analysis 
is performed during the entry strategy analysis to determine the effects of 
the second best alternative on the recommended strategy. 

Branching by Uses ; As indicated earlier, the specific uses of products can be 
important in defining a market since positioning a product for a particular use 

may be a good entry strategy. In this model, uses can be the basis for 
defining the structure of competition by formulating a tree in which 
the branches are defined by specific sets of uses, and products are uniquely 
assigned to branches. For example, in the home cleaner market, cleaning the 
kitchen may be one branch and cleaning the bathroom another. This would 
be a good definition if the probability of buying the products assigned 
to a branch was high for the set of uses that defined that branch and 
low for buying products assigned to another branch. 

This notion is implemented by calculating the individual probabilities 
of buying again in the "use branch" (products assigned to a particular use) 
when the most preferred product in that branch is not available. This is 
analogous to the probability defined in Equation 1. In this formulation, 
however, individuals are assigned to a branch for a use if they evoke it. 



-23- 



Probabilities are conditioned on each use evoked. For an individual, the 
probability of buying again in the branch when the most preferred product for 
a specific use is removed is determined and then the overall probability of 
trying again in the branch is calculated. The branching probability for the branch 

defined by use situation P, (U) is: 

o 

(6) P (U) =E Z Z) Pi- / E N 

b ueU, i£l(u) jeC. ^" ueU '^^ 
b ^ ' -^ lu b 



where P . 





JEBb 




im* 


^iu 




1-p.. 


u 



iju 



Pj^. = probability of individual i buying product j for use u and 



I ^ju ■ 1-° 



jeC. 

■' lU 

P** = probability of individual i buying the most preferred 

brand of the set of products assigned to the branch b 

for use u contained in U, 

b 

U, = set of uses that define branch b 
b 

I (u) = set of indivduals who evoke use u 

C. = set of products Individual i considers for use u 



lU 



B, = set of brands assigned to branch b 

J. **= individual i's most preferred product for use u that 
is contained in branch b 

N = number of people in branch b with use u. 

Note that the probability is conditioned on the most preferred product 
in the branch being unavailable rather than the overall first preference. 
This is because it is not necessary that the respondent's first preference 
product for a use be one of the products assigned to that usage branch. If 



-24- 

it is not, however, the probability (P.. ) will be low when summed over 

the products in the branch. If this phenomena is widespread, the overall 

probability P>,(U) will be low and the tree structure will be rejected 

as it should be. 

The overall probability (P(U)) can be compared to the random probability 

(R(U)) and probabilities (P) from other trees where branching is not based 
on use, but on attribute branching. A statistical judgement can be made 
as to whether use is a significant method of defining the competitive 

structure and if it is significantly better than other tree structures. 
The association of products (B, ) and uses (U, ) in a branch (b) can 
be made by prior grouping or by a factor analysis of a matrix of the 
average ratings of appropriateness of each product ( j ) for each use (u) . 

(See application reported later for empirical example.) The factor loadings 
will reflect the intercorrelations of the uses and are the basis for 
grouping uses into larger sets. The factor scores will indicate the 
position of each product on the use dimension and products can be assigned 
to use set based on their highest factor score. This provides a set 
of uses and products for definition of branches for evaluation by Equation 6. 
Branching by Users : Similar procedures can be used to group users and assign 
products to branches to test structures based on users. For example, children and 
adults are two possible definitions of branches for breakfast cereal. 
If products can be uniquely assigned to one group or the other, the proba- 
bility of buying again in a branch can be calculated. This probability is: 

b -^ 1 
^'\ 



where 



-25- 



^ = hi 

ij 1-P..** 
ij 

I, (s) = set of individuals with characteristics (s) that are assigned 
to branch b 

J^* = individual i's most preferred product of those assigned 
to branch b 



p ** 

ij 



probability of individual i buying the most preferred 
product of those assigned to branch b. 



Individuals can be grouped into sets for the definition of branches by 

a priori designation or cluster analysis of individual characteristics. 

If clustering is used, those who have similar patterns across products 

could be grouped together and products would be assigned to the group which 

has the highest average preference for them. This branching alternative 

can be evaluated by Equation 7. If the assignment and clustering is good, the 

branching probability will be high; if not, the probability (P, (S)) will fail the 

statistical criteria for branching and the user based tree rejected. 

In searching for the best hierarchical structure to define a market, 
alternatives based on product attributes, uses, and users can be compared. 
The branching procedure across these alternatives will use the probability 
of buying again in the branch (P (U,S) to find the best tree definition at 
each level. The highest average probability (P(U,S), Equation 2) represents 
the best tree and the statistical significance of differences between 
alternatives can be calculated. 

Heterogeneity : The procedures outlined above assume that consximers have 
a homogeneous view of the competitive structure of the market. This 
assumption can be tested by modeling the heterogeneous segments with 
separate trees and determining if this heterogeneous description is signi- 
ficantly better. First, alternative hierarchical structures (H) are posit- 
ed and then individual probabilities (P^h' ^^ation la) are calculated for 
each alternative. The result is a probability for each individual of buying 



-26- 



in the branch to which he or she was assigned under each alternative tree 
(P.,(H)). Each individual is assigned to the overall tree hypothesis (H) 
he or she most strongly supports. This is where his or her probability (P-vCH)) is 



ib^ 

4 
highest. These probabilities are aggregated for the individuals assigned 

to each tree (P(h)) and then combined as a weighted average to obtain an 
overall goodness of fit measure (P). The significance of the gains due to 
allowing heterogeneity can be tested on an overall basis by a 
significance test for the differences in proportions (P versus P) . 

If heterogeneity is significant, the heterogeneous description would 
be subjected to managerial analysis. If heterogeneous groups can be 
demographically or attitudinally identified, separate products could 
be targeted to each of them. If not, one product would be developed 
based on the weighted average response from the heterogeneous description 
of the competitive structure. Sensitivity analysis would be used to 
see if the inclusion of heterogeneity changes those market entry strategies. 

Measurement, Estimating and Testing 

The hierarchical model input requires individuals' evoked uses, 
the set of products considered and their appropriateness for each use, 
and the probability of purchases of each product considered. Survey 
measures and statistical estimation procedures provide these inputs. 

Direct survey measures are collected at a central location for a 
sample (n>^300) of category users. See Silk and Urban, 1978, for more 
detailed description of such sampling and measurement methodology. In 
order to determine the products consumers would consider for specific 
uses, respondents describe their last and other uses of the product. 

4 

An alternate approach is to cluster individuals based on their patterns 
of fits (P^^(H)), See Brudnick (1979). 



-27- 



An interviewer classifies the specific use situations into one of a set 
of more general usage classes . Pre-testing and focus group interviews 

are conducted to assure that all the use situations are identified and 
classified. For each use the respondent indicates what product she last used, 
ha« on hand or would consider using in the situation. (See Appendix Two for 
an example that shows coffee use situations and the proportion of people who 
would consider each coffee product for each use.) 

Given the consideration set (C.) and uses (U), the next task is to 
estimate the probability of purchase (P..). Several measures may be utilized. 
The most elementary is to assign a probability of 1/n., where n. is the number 
of products in the consideration set C, to each product in an individual's 
consideration set. This makes the restrictive assumption that each product is 
equally preferred, but if it gives results (P, ,P) that are not significantly 
inferior to other methods, considerable measurement costs could be reduced by 
not collecting preference data. The equal preference assumption can be relaxed 
by collecting rank order or scaled preferences. If rank order preferences are 
collected along with the identification of the respondent's last purchase, a 
probability can be estimated when i is the r ranked product by: 

(8) P., =w (j)/x; w (j) 

^ jeC. 
where W (j) = percent of respondents who last purchased their r 

preferred product and where in a specific case product 

j is r ranked 

This assumes that preferences are constant (zero order purchasing process) 

t"Vi 
and all individuals have the same probability of buying their r ranked 

product. 

The most attractive model of probability of purchase is the logit 

model : 



-28- 



exp ( B In A . . ) 
^^^ ^ij " V exp(B In A^.) 



A is the measured preference for brand j and individual i 

B = parameter 
To support this model last purchase and constant sum preference measures 

(Torgerson, 1958) would be collected. Maximum likelihood procedures are 

available to estimate the parameter 3 (McFadden, 1970, McFadden and wills). 

and statistical tests of the goodness of fit of the model can be applied 

(McFadden, 1970, Hauser, 1978). 

The logit model allows each individual to have different probabilities 

of purchase over their consideration set of products, but the model assumes 

independence of irrelevant alternatives. In each empirical case, tests 

should be conducted to determine if the assumption is violated. Specific 

tests can be applied based on the structure of residuals (McFadden, Train 

and Tye, 1977) or differences in estimates when enlarging the evoked 

set (Silk and Urban, 1978). If independence of irrelevant alternatives is 

violated, another problem appears in the calculation of the individual set 

of probabilities of choice when the first preference is removed (P..) since 

Equation la assumes a proportionate reduction in all other probabilities after 

removing one product. 

If the assumption is violated, one possible recovery procedure is to employ 

a hierarchical logit model (McFadden, 1980) to estimate the choice probabilities 

(P..). Theoretically the hierarchical logit is the best way to estimate the 

individual probabilities, but the properties of the hierarchical logit in the 

face of the heterogeneity that is to be encompassed in this model are not 

well known. In addition, the use of the hierarchical logit becomes rather cum- 

bersome because for each hierarchy tested, the probabilities (P.. and P..) 

ij ij 



-29- 



must be re-estimated by the hierarchical logit procedure. In practice, if the 
probabilities (P..) estimated by the multinomial logit (Equation 9) and the 
hierarchical logit are highly correlated, this cumbersome procedure can be 
avoided along with the need to assume homogeneity of the hierarchy across 
individuals. This issue will be considered further in the application section 

of this paper. 

With measures of consideration sets, evoked uses, and estimates of proba- 
bility of choice based on measured preferences for products for each use and 
the last produce used, the branching procedures and criteria can be applied. 

During the survey of respondents, ratings of products on selected 
attribute scales and demographic data are collected. The ratings are 
used to characterize product perceptions (see entry analysis section) 
and the demographics to identify the composition of branches. 

The procedures outlined above derive a hierarchical tree that best 
fits the measured preferences and choices. In order to gain confidence 
in this description, an experiment is conducted at the end of the respondent 
interview. Respondents are given an opportunity to purchase a product 
in a simulated retail store with coupons given them as compensation for 
the interview. This procedure has been successfully used to estimate 
trial of new products (see Silk and Urban, 1978). In this case it is 
modified by removing each respondent's most preferred product from the 
shelf in the lab store. This simulates forced switching and the observed 
proportions who remain in a predicted branch can be calculated. These 

observed proportions (P, ' ) can be used analogously to the proportions 

b 

from the choice model (P, in Equation 1) to find the best tree. If 

b 

the best tree in both cases agrees, confidence in that hierarchical structure 
increases. If the solutions are different, possible biases in data collection 
or estimation should be examined to see if one solution should be rejected or 
modified. If both solutions are acceptable, the initial proportions (P^^) are 



-30- 



considered as priors and updated by Bayesian procedures (Raiffa and Schlaiffer, 
1961) to be: 

(10) Pb" = ^h\^KK^/^\ + V 

P' = proportion who buys product in branch when shopping 
in environment where most preferred product is 
removed from shelf 

P, " = updated probability, of buying product in branch when 
most preferred product is not available 

N, = number of individual observations in branch b in 
choice model 

N' = number of individual observations in branch b 
in shopping environment 



This is equivalent to the classical procedure of pooling the data. Based on 
the updated probabilities (P."), the branching procedure is again applied to 
define the best hierarchical description of the competitive structure. 

The outcome of the measurement, estimation and testing is the specifica- 
tion of a hierarchical structure that is statistically significant and sup- 
ported by convergent estimation from the choice probability model and testing 
from the observed forced switching measures. 



-31- 



ESTIMATING NEW PRODUCT ENTRY POTENTIAL 

After establishing a hierarchical model of the structure of competition, 
we next must determine if there are opportunities for new product entries. 
The profit potential of a new entry will depend upon the existence of 
a vulnerability of existing products to a superior product, growth in 
the market, costs (production and marketing^ and margins. In this section, 
we discuss these profit factors, risk/return tradeoff s, and entry strategies 
that can be utilized in response to the identification of an entry opportunity. 
Competitive Vulnerability 

A number of products will be competing in each of the submarkets 
defined by the final branches in the tree used to define the structure 
of competition. In each of these submarkets the relative position of 
products can be represented by a perceptual map derived from factor analysis 
of consumers' product attribute ratings (Urban, 1975). Figure 3 shows 
a perceptual map for regular instant coffees. This is based on the average 
factor scores of these individuals represented in the overall map in Figure 
2 who had a first preference for a regular caffeinated instant coffee. 
The perceptual maps give the coordinates of each product on the two under- 
lying dimensions. The importance of each of these dimensions can be estimated 
by correlating the product coordinates with consumer preference in a compen- 
satory model of attribute tradeoffs. A linear form of such a preference 
model is: 

(11) A. . = Za.X. .^ + E 
ij ^ d ijd 

A. . = preference for product j and individual i 



a. 



= "importance" of dimension d 



Figure 3 
Perceptual Map of Caffelnated Regular Instant Coffees 



MILDNESS 
A 



• Nescafe 



• Folger^^ 



• IMH 



-> TASTE 



Figure 4 
Perceptual Map of Caffelnated Freeze-Drled Instant Coffees 



MILDNESS 

▲ 



• Tasters 'Cb<»«e' 



« Maxim ^ -.p-p 
-* ► iASTE 



-32- 



X. . , = attribute score of product i on dimension d by 
individual i. 

2 
e = error term, N(0,a ) 

More elaborate models could be used to represent nonlinearity . (See Hauser 
and Urban, 1977, for a review.) 

This use of a compensatory model of preferences at the bottom of the tree 
is consistent with Tversky's (1972) and Payne's (1976) findings that lexico- 
graphic procedures are used for complex tasks and compensatory procedures for 
simple tasks. The vector in Figure 3 reflects the relative importance of taste 
and mildness. The further out the perpendicular projection of each product 
on this line, the higher the preference. The importances shown in Figure 3 

were derived by a regression of observed preferences against the individual 

2 
factor scores in Equation 11 (F(2/173)=33, R =.27, t^=7.3, t =3.3). 

Nescafe is positioned as being the mildest, but it is not perceived as 
having as good a taste as Instant Maxwell House. The competition is vulnerable 
to a new brand that can achieve the mildness of Nescafe and the taste of Instant 
Maxwell House. Figure 4 shows a map of caffeinated freeze-dried instant coffees, 
assuming it is in a different product segment. It is similarly derived from 
Figure 2 for those who have first preference for a freeze-dried, caffeinated 
instant coffee, and it shows little vulnerability since Taster's Choice is 
very well positioned on the tradeoff between taste and mildness. In this 
illustrative example both segments value mildness and taste, but the competi- 
tive product sets are different. 

If the new product is positioned exactly at the same point as Taster's 
Choice in Figure 4, it probably would not gain the same share since it would 
be competing against a long-established brand without offering any apparent ad- 
vantages. To capture phenomena of positioning and order of entry, we model potential 



-33- 



as a function of the magnitude of the positioning opportunity and the 
number of brands previously entered in the market. The market share 
potential for the new product is: 



(12) M' = M*(S/S*)E 



(12b) 



e 



where ^t _ relative share potential for new entrant in branch 



E = order of entry index 
e 



M* = existing market share for first product in market 

S* = predicted share of purchases for the first product in 
market among those who would consider ; it . 



(12a) S* = E P /N 

ieF ^^ 

where F = set of individuals who have the first product in 
market within their consideration set (C^) 

N = number of individuals in set F 

P = probability of purchase of first product in market 
by individual i (Equation 9) 

S = predicted share of purchases for those who would 
consider new product: 

S = E exp(6 In A )/ z exp(6 In A ) 1 

iL "-^ jeC. iJ J 



/N 



where A. . = preference for product j by individual i 
■^ (Equation 11), j = k for new product 

N = number of respondents 

6 = logit parameter (Equation 9) 
The S/S* term is the share of the new product relative to the first product 

in the market. It reflects the positioning advantage of the new product because 

the new product share depends upon the preference that positioning earns. This 

positioning opportunity is usually estimated under the scenario that the new 

product could combine the maximum levels of the attributes now present in 



-34- 



existing products (e.g., in Figure 3 — the taste of Maxwell House and the 

mildness of Nescafe). These maximum levels (X.-O are substituted in Equation 

a 

11 to estimate the preference for the new entrant (A.,). In some cases where 
R&D capabilities and potential are high, preference may be predicted based 
on greater than the observed best levels (X,*). In others it may be deemed 
technically impossible to achieve the best values (^J') iri both dimensions and, 
therefore, an intermediate combination would be used to predict preferences. 
With the first procedure, S/S" is greater than or equal to 1.0. If the fit of 
the model used to predict preference (Equation 11) is not good, the amount 

by which S/S* exceeds one will be subject to error. In the case shown in 

2 
Figure 4, the t's are significant, but the R is not high. Care should be 

exercised if the decision to enter is sensitive to S/S'«. In this case 
S/S* = 1.01 and low sensitivity is present. The conservative position is to 
set S/S* =1.0 and this should be done if the F statistic or coefficents for 
the preference model are not significant. This is equivalent to assuming 
our position will be equivalent to the first product in the market. 

The order of entry index (E ) reflects the share of the new entrant 
relative to the first product in the market when they are positioned identi- 
cally. The index may be expected to decline due to difficulty entrants exper- 
ience in gaining awareness, evoking, and trial in the face of consumer loyalties 
and retail distribution inertia built up by the first product in the market. 
For example, in the coffee market, Sanka was the first decaffeinated coffee 
and retains a dominant share despite a number of similar subsequent entries. 
The penalty probably would be greater for the third entry (e = 3) than 
the second (e = 2), but not twice as great. The exponential form (exp ) 
is an appealing model for this decay since it declines nonlinearly and asym- 
totically approaches zero. 



-35- 

Although there is a penalty for later entry, it can be offset by a posi- 
tioning that is superior to the first product (represented by S/S="f >1) . 
For example, Maxim was the first freeze dried instant coffee, but Taster's 
Choice, although second in the market, achieved a better positioning and 
a greater market share. The model in Equation 12 allows both positioning 
and entry effects to operate. 

In order to preserve the requirement that shares sum to 1.0, we 
normalize new product share to get the entry share potential (M) : 

(13) M = M'/(l + M'). 

Estimating Entry Order Effects 

The ratio of shares of the first product and later entrants can 

be observed (R = M'/M*). If relative positioning effects (S/S*) also 

have been measured, the index of entry (E in Equation 12) can be estimated 

e 

empirically. Solving Equation 12 provides a set of observed values of 

the index (E ) . 
e 

(14) E = (M'/M*)/(S/S=^) 

e 

If we assume the decline in the index is exponential we have: 

-a(e - 1) 

(15) E = exp , where E is the predicted order of entry 

index. Alpha (a) can be estimated by a log linear regression of Equation 

15. 

Data on purchase and preferences for established brands were available 
from pre-test market analyses conducted in 16 markets of frequently purchased 
brands (e.g., dandruff shampoos, fabric softeners, light beer, acetominaphen 
pain relievers, dry bleach, high filtration cigarettes). Market share 
and perceptual ratings data were available for 42 products (see Silk and 



-36- 
Urban for tha measurement procedure used in collecting this data). Alpha 

was estimated by the regression equation: 

a6 ) ln(R /(S /S*)) = a(e - 1) + e 
ec ec c 

R = share of last purchases for entrant e divided by the 
share of purchases of first product in market in 
category c. 

S* = predicted share of purchases for first product in 
category c (see Equation 12a) 

S = predicted share of purchases for product entry e in 
category c (Equation 12b) 

e = e product to enter category c (e > 1). 
The results were statistically significant at the ten percent level (t=1.6, 
25 degrees of freedom). The estimated a of -.53 implies entry index values of; 

E = 1.0 

E^ = 0.58 

E^ = 0.34 

E, = 0.20 
4 

The input to this estimation was based on relationships at a point 
in time and does not represent the patterns of share change over time. 
It assumes that if positioning is equal, the ratio of the share of an 
entrant relative to the first product is constant as new products enter. 

An alternative estimate of a was obtained using a robust method. 
Since e in Equation 16 takes on discrete values (2, 3, . . .) and since 
most of the products were drawn from positions 2 and 3, we have distinct 
groups of values for the dependent variable — one group for position 2 
and one group for position 3. Medians were calculated for each group, 
and a was fit to them. The resulting estimate was -.54 — almost duplicating 
the log regression results. 

Techniques for systematically identifying outliers in the data were explored. 
The "hat" matrix, a usually helpful instrument in this area, was of no value 
to this application, since it depends only on the values of the independent 
variables and its diagonal was constant at each entry position. 



-37- 



The entry index values demonstrate the substantial penalty apparent 
in these markets for later entry if a parity positioning is used. However, 
as Equation 12 indicates, this can be overcome with superior positioning. 
In four of the categories studied, a later entrant achieved greater 
share than the first product. In all these cases, the positioning (S/S*) 
was superior to the leader. 

To simulate the share potential of a new entry, substitute the appro- 
priate E value in Equation 12 and multiply by estimated share of choices 
e 

for the new product relative to the first entrant (S/S*) and the first 
entrant's share (M*) . The share of choices of the new product is a func- 
tion of preference for it, which in turn can be estimated from the model 
that relates perceptions into preference (Equation 11). 
Profit Potential and Risk/Return Tradeoff 

Given an estimate of the share potential for a new entry (Equations 
12 and 13), our next task is to calculate the expected profit and rate 
of return on investment that would result from a commitment to develop 
a product entrant for this market. Then a tradeoff between risk and 
return must be made and an entry strategy designated. 

We utilize a simple model to calculate total profit returned over 
the product's life cycle: 



(17) TP = E (M W (K - Z. ) - Y )D 
t=l ^ ^ ^ 

TP = total discounted profit 

M = market share of new entry in year t (t = I, 2, . . . L) 
where L is end of life cycle 

W = industry sales volume in year t 



-38- 



K = price in year t 

Z = unit cost in year t 

Y = sustaining advertising, selling, and promotion 
costs in year t 

D = 1/(1 + TR) = discount factor, where TR = target 

rate of return on investment 



Industry sales are usually subject to a life cycle of birth, 
growth, maturity, and decline (Polli and Cook, 1969, and Cox, 1967). Life 
cycle models such as the one developed by Bass (1969) can be used to 
forecast the sales of a total submarket based on previous history. In 
very new markets where little previous data exists, judgement is 
required. 

The market share (M) for the entrant can be estimated as indicated 
(Equations 12 and 13) , but this eventual share must be reflected in the 
annual share (M ) growth to its ultimate value (M) . In frequently purchased 
products, this happens rapidly over the first two years. In other product 
areas share growth may be expected to be slower. 

The costs of achieving the share potential are related to advertising 
and promotion. In the introductory period costs usually are higher than 
sustaining levels. The costs corresponding to this share potential achieve- 
ment could be approximated by the past industry spending rate per share 
point for introduction marketing expenditure multiplied by the share 
potential. Analogously the sustaining level is the ultimate share (M) 
times the industry spending rate per share at maturity. This assumes 
the new entrant will experience industry average efficiency in its market- 
ing spending. 



-39- 



Product costs (Z ) and price (K ) may be judged to be similar to 
existing industry norms in calculation of profit. If new innovations 
are to be made in costs, these can be reflected in the calculation. One 
phenomenon that may affect the costs is economies of scale in production. 
In some industries costs decline as production volimes increase (Boston 
Consulting Group, 1970). These learning phenomena also affect prices 
since as volumes and costs decrease, competition will lower prices. In 
markets where such phenomena exist, establishing a substantial share 
position is important. The share potential (M) must be high to justify 
entry and must be heavily funded to retain a significant industry presence. 
In industries where these phenomena exist, the simple model (Equation I7) 
must be expanded to consider the simultaneous effects of price on sales, 
sales on costs, and costs on price (Bass, 1978, Dolan and Jeuland, 1979, 
and Robinson and Lakhani, 1975). The result in some analyses will be 
a full venture simulation to reflect these effects and other cost and 
distribution complexities. 

The final adjustment to profit in Equation 17 is to discount (D ) 
at the firm's target rate of return. This discounted cash flow can be 
compared to the required investment to evaluate the desireability of 
committing to entering this market. The investment is the cost of fixed 
production facilities and the expected cost of developing and introducing 
the product. Table 1 provides average expected costs which include 
the initial marketing expenses and development costs. (Note Equation 
17 includes only the sustaining marketing costs (Y ).) At the time of 
formulating an entry strategy, the introductory marketing expense should 
be considered as an investment. 



-40- 



The decision to commit to development should reflect a balancing of 
risk and return. Several methods exist to make this tradeoff. (Keeney 
and Raiffa, 1976, Hertz, 1969, and Pessemier, 1977.) The simplest approach 
is to consider the amount by which expected return exceeds investment 
and judge whether it is enough of a margin of safety to cover unforeseen 
events. This approach can be formalized by estimating a distribution around 
each variable in Equation 17 and calculating the standard deviation of 
the discounted profit (see Urban, 1968, Seattle, 1969). If the distri- 
bution is assvfflied to be normal or derived by Monte Carlo analysis, the 
probability that the discounted profit exceeds investment can be calculated. 
This is equivalent to the probability that the rate of return exceeds 
the target rate of return. If this probability is above the firm's cri- 
teria, entering this market would be recommended. 
Entry Strategies 

The most obvious strategy is to fill the opportunity described by 
the hierarchical market definition and entry potential analysis. This 
is appropriate if the probability of achieving the target return on invest- 
ment is high. Resources could be devoted to idea generation and design 
activities to develop a product to fit the vulnerability in the competi- 
tive structure. (See Hauser and Simmie, 1979, for a modeling approach.) 

This single product strategy may not be appropriate if the firm 
offers an existing product line. In this case the incremental effect 
should be considered. The major market branches should be covered by 
products from the line, but multiple entries should be minimized unless 
they are clearly differentiated in their positioning within the markets. 
If duplication exists, resources should be concentrated on one product 



-41- 



in each market subseginent . Products could be dropped or repositioned to achieve 
effective coverage of the market opportunities. The maps and hierarchical tree 
provide the information needed to assess the duplication and coverage across 
the market components. 

Another possible product line strategy is to deter competition by filling 
all possible openings even if duplication results. We do not recommend such a 
strategy because it will produce duplication while risking antitrust actions 
(Schmalensee , 1977). We recommend innovation rather than deterence as a source 
of profit and direction for resource allocation, but if deterence is the 
selected strategy, the maps and branchings can point out gaps to fill in pre- 
empting competition. 

Product line effects may also be present in firms which are entering 
a market for the first time. If the dimensions are the same in each 
branch, it may be highly efficient to position a product line because 
the overall advertising expenditures will payoff in several rather than 
only one branch. Another justification for a line is if one of the common 
dimensions is the availability of a full line of products. Then the 
perception of comprehensiveness that is necessary can be fulfilled by 
a product line. In these cases, the ROI would be calculated for the 
line with due regard for demand and cost interdependencies (Urban, 19 69). 

Another entry strategy is by acquisition. If the maps show a well- 
positioned brand produced by a regional firm, the acquisition and national 
marketing may pay off. Similarly, if users see a product with low market 
share as well positioned, acquisition and application of marketing resources 
may pay off. The models allow calculation of ROI gains by national position- 
ing and gains due to marketing to achieve better positioning and evoking. 
Such input is very useful in negotiating an acquisition and determining 
how much should be paid. 



-42- 



All the above strategies are evolutionary since they work within 
the current market definition. Another approach is to revolutionize 
the market by creating new branches or new dimensions. For example, 
Contac's time release product revolutionized the cold remedy category 
and home pregnancy kits created a new market segment for health aids. 
Such a revolutionary approach to creating new markets can be very reward- 
ing, but it is also risky. Polaroid lost millions of dollars on 
Polavision, trying to revolutionize the home movie market by adding 
an instant development feature. 

We recommend a portfolio approach based on achieving growth and develop- 
ment goals with a combination of some projects based on positioning within 
the structure and some on changing it. Whether an evolutionary or revolu- 
tionary strategy is used, it is wise to understand the existing market 
structure and competitive dimensions. With an in-depth understanding of 
the current structure of competition, a revolutionary strategy can more 
effectively be pursued. 



-43- 



APPLICATION 



Problem Setting 

We assume we are in the position of a manufacturer of retail food products 
and that after evaluating many categories, found coffee to be desireable based 
on a set of overall screening criteria (see Urban and Hauser, 1980). Our ques- 
tion now is: Should we commit to develop a new entrant into the coffee market? 
If yes, should it be decaffeinated or caffeinated, ground coffee or instant, 
and if instant, freeze dried or regular instant. We apply our proposed model 
in this setting to evaluate the structure of competition, the potential for a 
new product, and entry strategies. 
Data Collection 

In accordance with measurement procedures outlined above, 295 users of cof- 
fee (those who drink more than one cup of coffee/per day at home) were inter- 
viewed in Springfield, Mass., and Indianapolis, Indiana in July and August of 
1977. Respondents were interviewed after being recruited in a shopping mall and 
quotas were set to assure at least 50 respondents used each major type of coffee 
(ground/instant, caf f einated/decaf f einated, freeze dried). It should be pointed 
out that this survey data was not used to estimate market shares — they were 
based on warehouse withdrawals. For each respondent uses were evoked, the products 
considered for each use, and the last product used were identified (see measurement 
section of this paper and Appendix Two). Preferences for products for each use were 
obtained on a seven point scale (extremely well liked to very much disliked). 
Brands were rated on 12 product attribute scales (see discussion of Figure 2 for 
identification of scales). After providing demographic data and answering ques- 
tions on coffee consumption, respondents were given an opportunity to purchase 
coffee for their most frequent use with a two dollar coupon they were given as 
compensation for participating in the interview. When the respondents reached the 
shelf, they fourtd their first preference product "out of stock." Eighty-five 



-44- 



percent of the people made a purchase in the lab and seventy percent 
noticed their favored brand was missing. At the close of the lab phase, 
respondents were requested to participate in a usage panel in which they 
would record for a week each cup of coffee served at home in a diary 
(when, kind, brand, who present, how many cups, who prepared). Sixty 
percent returned a complete diary. Two weeks after the lab, respondents 
were called back to determine their home inventory of coffee (kinds, brand, 
open or not, size of package). The panel and pantry check were conducted 
in this application to provide additional insight into the effects of the 
use situation on product choice. In most applications, the evoking and 
preference by use would be sufficient to determine if use is the best basis 
of a hierarchical branching in a market. 
Estimation of Probabilities of Choice 

Based on these data, individual probabilities (Pij) were estimated 
based on the rank order preference model (Equation 8) . The fits were good 

based on Mauser's (1978) information theoretic test — 80% of the total 

2 
uncertainty was explained (U = .795). The standard deviation between actual 

and predicted market shares was .9 share points. The logit model was not 

used since the preference measures collected here may not be interval scaled 

as required for this model. In this application, the collection of constant 

sum preference judgements which would allow ratio (or at least interval) 

scale estimates was infeasible since the number of paired comparisons across 

products for all uses would be an intolerable respondent burden. In cases 

where fewer use situations are present or where pretesting shows use 

situation not to be a basis of competition, constant sum procedures are 



-45- 



practical. The rank order preference (Equation 8) model assumes the weak 
form of independence of irrelevant alternatives. McFadden, Train and Tye (1977) 
have developed a residual test procedure for the logit model (see Appendix Three 
for detailed description of test). We applied it here to the probabilities from 
the rank order preference model. Table 3 shows the chi-squared statistic 
associated with this test for the major products. In three cases (Maxwell House 
Ground, Maxim, and Taster's Choice caffeinated) violation of independence is 
indicated. In the other five cases, violation is not indicated. 

Table 3 Test of Independence of Independent Alternatives 

Product x^(df=9) 

Maxwell House Ground 17.1* 

Taster's Choice (Decaffeinated) 5.6 

Nescafe 11.7 

Maxim 17.2* 

Instant Maxwell House 3.3 

Chock Full O'Nuts (Ground) 6.4 

Taster's Choice (Caffeinated) 18.8* 

Sanka (Instant) 11.0 

* = significant at the 10 percent level 

These results are mixed, but indicate the independence of irrelevant alterna- 
tives assumption may be violated. In a later section we test the sensitivity of 
the hierarchical branching to this assumption. 

Hierarchical Definition of Market 

In this section we describe the application of the branching procedure, 
consider heterogeneity in consumers' views of the competitive structure, 
examine the convergence obtained from the data on shopping in the labora- 
tory store, and report a sensitivity analysis on heterogeneity and the possible 
violation oL the assumption of independence of irrelevant alternatives. 



-46- 



First Level Branching : At the first level of the hierarchy, three branch- 
ing hypotheses were tested based on product characteristics (see Figure 5). 
The ground /instant alternative passes the necessary tests (P > R at 10% 
level and P > R at 10% level). The caf feinated/decaf feinated alternative 
fails the necessary condition in the decaffeinated branch (P ;^ R^ at 10% 
level) and the brand structure fails in all branches. The best first level 
division is ground/instant; in it 71 percent of the respondents 
would buy another product in the branch where their first preference pro- 
duct resides if that most preferred product were not available. Use branch- 
ing was evaluated by factor analyzing the matrix of the proportion of people 
who would consider products for each use (see Appendix Two for data) and then 
assigning products uniquely to the use branches. One dimension of use 
was found (X = 6.45, A = .28), and all uses loaded heavily on that dimen- 
sion. This is not surprising since inspection of Appendix Two shows little 
variation in the proportions considering a given product across uses. If 
finer use classifications are considered and two dimensions are forced, 
the only use situation that loads heavily on the second dimension is the 
portion of supper use represented by dinner with guests (evoked by only 
10 respondents) . Branching by use was not indicated by the factor analy- 
sis. Prior grouping of occasions into two classes by time of day of use 
(A.M. and P.M.) was also evaluated. Brands were assigned to either an 
A.M. or P.M. branch based on whether they were most heavily 
evoked for A.M. or P.M. This branching failed the required test (P.w = 
.29, P = .27, R = .5). The absence of use as a major basis for defining 
the market was supported by the use panel which indicated 54% of the respon- 
dents used only one brand over all occasions in the week and 10% more used 
one brand for all uses until it ran out and then switched to a new brand 
for all subsequent uses. (See Laurent, 1978 for a more extensive discussion 



Figure 5 
First Level Branching - Product Characteristics 



Alternative 1: 



Ground/ Instant*** 



P = .71 R = .49 



Ground*** 

\= .49 
Nb = 97 



Instant*** 



Pb = -76 



Rb = .49 
\ = 198 



Alternative 2: 



Caffeinated*** 



Pb =^ -74 



Rb = .49 



N^, = 195 



Caffeinated/Decaffeinated 
P = .64 I R = .^'j 



AA 



Decaffeinated A 
Pb = .44 
Rb = .49 



N^ = 100 



Alternative 3: 



Maxwell 
House A 

Pb = -09 

% = .15 

Nb = 99 



Brands 



.07 



AA 



R = .143 



Tasters 
Choice A 

Pb = .04 
Rb = .15 
Nb = 49 



Sanka A Brim A Folgers A Nescafe A 



Pb = .07 
Rb = .15 



Nb = 49 



Pb = .08 
Rb = .15 
Nb = 19 



Pb = .04 Pb = .05 
Rb = .15 Rb = .15 
Nb =15 Nb = 17 



A = model probability not significantly greater than random value (Rb) at 
10 percent level. 

AA = at least one branch fails requirement (A) 

* = significant at 10% level 
** = significant at 5% level 
*** = significant at 1% level 



-47- 



of this data.) The shelf check indicated 43% had only one container of 
coffee on hand and 60.6% had only one container open. Although the usage 
situation is an important phenomena in understanding coffee consumption, 
it is not a good overall basis for hierarchically defining the competitive 
structure of products in the market. 

A first level branch alternative based on user association of pro- 
ducts was formulated by defining two branch segments based on their pur- 
chase rates (heavy — more than one purchase per two weeks, and light — one 
or fewer purchases per two weeks) . Products were assigned to the branches 
where their evoking rate proportion was highest. This branching failed 

the necessary criteria in the light branch (P = .65, P = .39, 

HEAVY LIGHT 

IL =.49, P = .53, R = .49). Further user segmentation was conducted by 
clustering individual responses to questions on coffee consumption (agree/ 
disagree to 10 statements, e.g. : (1) If I'm only going to make one or two 
cups of coffee, I usually use instant coffee, (2) Sometimes, when a friend 
drops in, I prepare coffee in a different way from the way I prepare it 
for myself, and (3) I use decaffeinated coffee on those occasions when 
I'm concerned about being able to get to sleep afterwards.). After assign- 
ing products to one of the two segments, the branching probabilities were 
calculated and found to be below the random levels (P = .45, P„= .48, R^ = .49). 

Second and Third Level : The best first level branching considering pro- 
duct characteristics, uses, and users was ground versus instant coffee. 
Figure 6 shows second level branching from the first level ground/instant 
split. The branching of ground coffee into caffeinated and decaffeinated 
fails in the decaffeinated/ground branch. Both the division of instant into 
freeze-dried and regular branches and into caffeiaated and decaffeinated branches 

pass the tests (P, > R & P > R & W, , < R , at 10% level). The regular 
b b b,bb bb 

versus freeze-dried is better, but not significantly. 



Figure 6 
Second Level Branching 



Alternative 1: 



P = .51 



Ground*** 



V -^ V -^9 



N^= 97 

D 



R = .32 



Instant*** 



Regular*** 

Pb = •" 
Rh = .24 



Nb = 111 



Freeze Dried*** 
Pb = .34 

Rb = -24 
Nb = 87 



Alternative 2: 



P = .525 



Ground*** 



P, = .6 R = .49 
b b 

N = 97 
b 



R = .32 



Instant*** 



Caffeinated*** 
Pb = .53 
Rb = .24 
Nb = 113 



Decaffeinated*** 



P, = .43 

D 



Rb = .24 



\- 85 



Alternative 3: 



Caffeinated*** 
Pb = .58 

Rb = -23 
Nb = 82 



P = .68 



Ground 



AA 



.41 



Decaffeinated 



P, = .194 
b 



Rb = .23 
Nb = 15 



Instant*** 



Pb = .65 Rb= .49 
N = 198 



-48- 



Figure 7 indicates the third level branching of caffeinated and decaf- 
feinated instant into freeze-dired and regular (Figure 6, Alternative 1) or 
freeze-dried and regular into caffeinated and decaffeinated (Figure 6, Alterna- 
tive 2) is justified. This branching also passes the test that switching to 
the other branches be less than that branch's random probability. 

Figure 7 shows the best branching. In this representation we use caffeinated 
and decaffeinated at the second level, but it should be recalled that freeze- 
dried and regular would also be acceptable. In either case, the end point 
branches are the same. The figure also shows the probabilities of buying 
when the first preference brand is available (PP and PP. from equations 1 and 2 
without restriction j?^j*). These values are high and indicate the expected pro- 
portion of next purchases in each branch without restricting the most preferred 
product . 
Branching Based Only on Consideration Sets: 

As indicated above, the probabilities of choice could be estimated by assum- 
ing each product in the consideration set other than the first preference has an 

equal probability of choice (P.. = ( 1-P. .*)/(n .-1) , where n. is the number of 

ij ij 1 ' 1 

products in individual i's consideration set). The branching procedure can be 
applied to these probabilities and compared to P, and P obtained from Equations 
8 and 9 which use information on preference as well as consideration set. 

Figure 7 shows in parentheses the branching probabilities derived from the 
consideration set information. The values are surprisingly close and indicate 
most of the information utilized in the definition of the hierarchy is contained 
in the consideration set. Preference information improves the values, but 
branching based on consideration produces similar results. 



84 


.94 


53 


.94 


1 


.85 



-49- 



Heterogenelty : Calculation of each individual's P., under the alternative 

first level branchings (see Figure 5) and assignment to the best fitting 

tree led to the identification of some differences in consumers' views 
of the competitive structure. Table 4 shows the number of people who fit 

one tree better than others. 

Table 4 Heterogeneity in Competitive Structure 

Number in Which One 
Dominant Tree Tree Dominates 

1. Ground/Instant 

2. Caffeinated/Decaffeinated 

3. Brand 

The value of P indicates that groups described by ground/instant and caf- 
feinated/decaf feinated branchings fit their respective branchings signifi- 
cantly better than in the homogeneous case (see Figure 5) . These two groups 
represent significant heterogeneity while the remaining 60 percent of the 
sample are not better described by one tree than others. (Eight-four people 
were equally well described by Alternatives 1 and 2, 6 people by Alterna- 
tives 2 and 3, and 6 people by Alternatives 1, 2, and 3.) 

The group best described by the caffeinated and decaffeinated struc- 
ture (Alternative 2 in Table 4) were subjected to second level branching. 
In the caffeinated branch, attempts to branch (ground/instant and by brands) 

failed to meet the required criteria (P, > R and W , , < R , ) . Second 

b b b,bb bb 

level splitting of the decaffeinated branch was not possible due to small 
sample sizes. In applications where heterogeneity is present, larger initial 
samples should be collected or supplemental sampling conducted if hetero- 
geneity is critical to the entry strategy decision. The sensitivity of 
entry strategy to the observed heterogeneity will be discussed in a sub- 
sequent section. 



-50- 



Convergent Analysis 

The trees evaluated based on preferences and past choices and shown 
in Figures 5, 6, and 7 were tested by repeating the branching procedure 
with probabilities (P ') measured by the proportion of people who purchased 
in the lab when their first preference product was not available. The 
analysis of the shopping data indicated that the tree in Figure 7 was the 
best. In Table 5 the probabilities from the preference analysis, 
shopping measures, the Bayesian update of the probabilities (Equation 10), 
and the random probabilities are shown. The values from the two analyses 
are similar. For example, for ground coffee, the preference analysis indi- 
cates 60 percent of people who have a first preference for a ground product 
would buy another ground if their first preference was not available ; 
in the lab, 60 percent of these people actually bought another ground when 
their favored brand was out of stock. This close correspondence was not 
found within the instant branches where substantial differences were observed, 
but the updated values (P. ") pass all the significance tests (P^" greater 
than R^ at the ten percent level) and continue to indicate the tree in 
Figure 7 as the best hierarchical description of the market. 
Perceptual Maps 

Perceptual maps were generated for each of the five end point branches 
in the tree. Figures 3 and 4 and their associated discussions have presented 
the factor analysis results and perceptual maps for the caf feinated/regular/ 
instant and caf feinated/f reeze-dried/instant branches. Figures 8, 9, 
and 10 show the perceptual maps for the remaining branches in the best 
tree (Figure 7). Next, we consider the implications of these maps and 
the hierarchical market definition for the formulation of entry strategy. 



Figure 7 



Best Hierarchical Description of Coffee Market 



Coffee*** 

P = .71 ( .70) 
PP= .93 
R = .49 
N = 295 



Ground*** 



P^ = .6 (.59) 



PP,= ,91 
b 

= .49 



\ 



N, = 97 

D 



Instant*** 

Pb = .76 (.76) 

PP,= .95 
b 



\ 



= .49 



N^^ = 198 



Caffeinated*** 



Decaffeinated*** 





Pb = 


.53 ( 


.55) 


Pb = .43 ( .39) 

1 




^\= 


.89 




PP,= .9 
b 




\ = 


.24 




h = -2^ 




\ = 


113 


1 


N, = 85 
b 




1 






1 I 


Regular*** 




Freeze 


Regular*** Freeze 






Dried 


f<** 




Dried*** 



Pb = .38 (.39) 
PP^= .86 



= .11 



N, = 68 
b 



Pb = .22 (.18) 



PP, 



\ 



.84 
= .11 
= 45 



Pb = .30 (.25) Pb = -24 (.22) 



PP, 



h 



.89 

= .11 



N^ = 43 
b 



PP,= .85 
b 

.11 



h 



N, = 42 
b 



) = values of branching probabilities estimated from consideration set 
information only. 



FlRure 9 

Perceptual Map For 
Decaffeinated /Regular/ Instant Coffee 



MILDNESS 



/ 



High Point • 

Sanka « 



/ 



/ 



« Nescal^ 

/ 

/ 
/ 



/ 



-> TASTE 



Fl£iire_IO_ 
Perceptual Map For Ground Coffees 



MILDNESS 



rvi LMiwCl • 



• Sanka 



-> TASTE 



• Chase , MH 
•Hills 



• Folgers 



• Chock 



-51- 



Entry Analysis 

With a clear understanding of the hierarchical structure of compe- 
tition and the positioning of products within each market, the next task 
is to calculate the potential profit for a new entrant and balance it 
against risk and investment considerations in making an entry commitment. 
Profit, Investment, and Risk : Table 6 depicts the calculation of profit 
in each market. Sales volumes were based on 1977 U.S. warehouse sales with- 
drawal data and, because population growth is balancing approximately the 
slow decline in per capita consumption, it is assumed that no significant 
growth will occur in the future. Share potential is calculated 
by applying the entry model (Equation 12). Recall these share potentials 
assume good positioning on the market maps (maximum of existing attributes). 
The entry order (e) was determined by presuming we are considering a major 
market entry. Therefore, the major brands in each market were counted 
along with an aggregate product to reflect existing regional and small 
brands (e = 5 for ground, e = 5 for instant /caffeinated/regular, e = 3 for 
instant/caffeinated/freeze-dried, e = 4 for instant/decaffeinated/ regular, 
and e = 4 for instant/decaf feinated/freeze-dried) . 

The share potentials vary from 3.5% to 12.8%, but the markets are of 
different size and have different prices/pound. Dollar sales volumes 
were based on an average retail price of $3/pound for ground coffee and 
$8/pound for instant coffees. The greatest sales potential is for a ground 
coffee (70 million dollars) and the lowest for freeze dried, decaffeinated, 
instant (8 million dollars) . Net contribution profit was simply calculated 
by assuming profit as ten percent of sales. This is a subjective estimate 
based on the assessment of the margin and competitive pricing practices 
in the industry. 



-52- 



Investment includes the expected development cost (Table one- note 3) , invest- 
ment in production facilities, and introductory marketing expenditures. 
The production investment is an estimated incremental expenditure to an 
existing facility to produce the new volumes required. If a firm now 
had no coffee production capability, the required expenditure could be 
much higher. On the other hand, if excess capacity existed in a facility, 
it would be much lower. The introductory marketing expenditure for adver- 
tising and promotion is based on twenty percent of the long-run annual sales 
revenue and is set to be consistent with past major national brand intro- 
ductions. 

The highest investment and profit potential are for a ground coffee. 
To compare return and investment, the simple payback period could be cal- 
culated. Ground coffee pays back the fastest (2.5 years based on the 
mature profit level) , regular/caf feinated/instant in less than three years 
(2. 8 years), and freeze-dried/decaf feinated/instant has the longest pay 
back (6 years). The others pay back in three to four years. 

Payback is indicative of return on investment, but does not reflect 
risk considerations or the time value of money. To include these factors, 
discounted profit was calculated at a target rate of return of 20 percent 
(see Equation 17) . The yearly profit was based on an eight year life 
cycle in which sales grow to full potential over the first two years (year 
one — 50% of potential and year two — 67% of potential) , stabilized at full 
potential for four years, and then fall over the last two years (year 
seven — 67% of potential and year eight — 50% of potential) . The total 
investment was divided by the total discounted profit. Based on this 
ratio, a share potential was found where the discounted profit just equaled 
the investment (ratio = 1.0). This break even ROI share was compared 



Table 5 



Lab Shopping and Updated Branching Probabilities 



Ground 



Insta:it 

Cafteinated/Rsgular 
Caffeinated/Freeze Dried 
Decaffeinated/Regular 
Decaffeinated/Freeze Dried 



Shopping 
Choice Observa- 
Model tions 
P^ 



.60 



■ b 



.38 


.25 


.22 


.24 


.30 


.21 


.24 


.32 



Updated Random 



.60 



.32 

.23 
.27 
.29 



.49 



.11 
.11 
.11 
.11 



Figure S 

Perceptual Map For 
Decaf {elnated/Freeze-Dried/Instant Coffees 



MILDNESS 



/ 



a Sanka 

• TCD / 

/ 

/ 

• Brim 



/ 



/ 



/ 



^ TASTE 



Table 6 Entry Analysis of Coffee Market 





Ground 


Instant 






Caffeinated 


Decaffeinated 






Regular 


Freeze 
Dried 


Regular 


Freeze 
Dried 


Volume (Millions 

of Pounds) 


663 


88 


29 


24 


21 


Entry Share 
Potential in Market 


3.5% 


6.2% 


9.3% 


12.8% 


5.0% 


Revenue - Ongoing 
(millions of dollars) 


70 


44 


22 


25 


8 


Profit - Ongoing 
(millions of dollars) 


7 


4.4 


2.2 


2.5 


.8 


Investment 
Development 
Production 
Introductory 
Marketing 

TOTAL 


2.7 
.5 

14.0 
17.2 


2.7 
.5 

8.8 
12.0 


2.7 
.5 

4.4 
7.6 


2.7 
.5 

5. 
8. 2 


2.7 
.5 

1.6 

4.8 


Probability of 
Achieving 20% Rate 
of Return 


80% 


70% 


45% 


45% 


10% 



-53- 



to the expected share potential. Subjective estimates of exceeding the 
breakeven ROI share were made in each market based on the margin of safety 
(share potential less breakeven ROI share) and the assessment of the risk 
in entering each market. These values are equivalent to the probability 
of exceeding the target rate of return. 

Entry Opportunities : Table 6 shows that the best chance (80%) for making 
20 percent ROI is in the ground coffee market. Examination of the map 
for ground coffee (Figure 10) indicates the positioning opportunity is 
for a "mild" coffee with "good taste." A partially decaffeinated ground 
coffee might be the basis of combining the mildness of Sanka and the taste 
of Folger's brands. The caf feinated/regular/instant market also is attrac- 
tive to entry since there is a 70 percent chance of achieving the target 
rate of return by investing in it. The positioning opportunity again 
is based on combining mildness and taste (see Figure 3). The freeze- 
dried/decaf feinated/instant market is the least attractive with only a 
ten percent chance of financial success. 

The appropriate entry strategy for a company depends upon what pro- 
ducts the firm now offers. Table 7 shows the existing brands (1977) of' 
three major manufacturers. If Nestle is considered, there is a clear 
match between the ground coffee entry opportunity and their existing pro- 
duct line since they now offer no ground coffee. On the other hand, General 
Foods already has many and perhaps too many ground coffee offerings. It 
has covered all the markets and its strategy for innovation should be 
based on revolutionizing the category. For example, a pre-brewed liquid 
coffee in a one-cup container that could be heated in a micro-wave oven 
might be the basis of creating a new market branch. Such a revolutionary 
strategy would be risky, but if General Foods wanted to grow in the coffee 



Table 7 



Brand Offerings by Selected Firms 





Ground 


Instant 


Caffeinated 


Decaffeinated 


Regular 


Freeze- 
Dried 


Regular 


Freeze- 
Dried 


Nestle 


No Brand 


Nescafe 


Tasters' 
Choice 


Nescafe 


Tasters' 
Choice 


Procter & Gamble 


Folgers' 


Folgers' 




(High 
Point) 




General Foods 


Maxwell House 

Sanka 

Yuban 

Brim 


Maxwell 
House 
Yuban 


Maxim 


Sanka 


Sanka 
Brim 



-54- 



raarket, this analysis suggests rather than looking for new positionings 
in the existing market, it should allocate effort to a major innovation 
to create new branches in the market structure. Procter and Gamble entered 
the market with Folgers' brand in the two most desireable markets — ground 
and caffeinated/regular /instant. At the time of this research, P & G 
had "High Point" test market. Our analysis would have suggested a 45 
percent chance for a new decaffeinated/regular/instant market entrant 
to be financially successful. 

Sensitivity to Heterogeneity : The entry opportunities were identified 
based on an assumption of homogeneity in consumers' view of the competitive 
market structure. As indicated in a previous section, 18 percent of the 
sample see the market differently. These people consider the market divided 
into two branches — caffeinated and decaffeinated. The new ground coffee 
and caffeinated regular instant coffee opportunities would enter in their 
caffeinated branch. In this branch, all caffeinated brands compete, and 
the new entry would have many competitors (10 major products) . The new 
product entry would be the eleventh entry in the market, and it could 
not expect to get a large share of this crowded market. The entry index ' 
(Equation 15) for the eleventh product would be .05. This inference is 
beyond the range of the data used to estimate the index, and in our opinion, 
may understate the potential, but we will use it in this calculation to 
determine sensitivity to heterogeneity. If the positioning (S/S*) is equal 
to the first product in this caffeinated market, the entry potential share 
(Equations 12 and 13) would be 1.15 percent. 

This share is lower than in the homogenious case (3.5 percent for 
ground, 6.3 percent for instant), but the caffeinated market is larger 



-55- 



than the ground or caffeinated/regular/instant branches. The weighted 
average total sales for a new ground coffee would be $63 million ($57.4 
million from the 82% represented by Figure 7 and $6 million from the 18% 
who had a caf feinated/decaf feinated branching) . The sales for the new 
caffeinated regular instant would be $42 million ($36 million from the 82% 
and $6 million from the 18%). The probability of achieving the ROI for 
a new ground coffee would drop to 70 percent and remain almost unchanged at 
67 percent for a new caffeinated/regular/instant. 

The effect of heterogeneity in this application is to increase the 
estimated risk, but the entry strategy remains unchanged. In other cases, 
decisions may be sensitive to heterogeneity and suggest the need for dif- 
ferent new product entries. Representing the heterogeneity by different 
trees and calculating the weighted average sales volume and profit provides 
a basis for evaluating strategies under heterogeneous conditions. 

Sensitivity to Assumption of Independence of Irrelevant Alternatives : As 
indicated earlier, McFadden's test of residuals suggest violation of the 
independence of irrelevant alternatives may have occurred (Table 3) . In 
order to determine the sensitivity of our hierarchical specification to 
this potential violation, we re-estimated the choice probabilities (P..) 
and the branching probabilities by hierarchical logit procedures (McFadden, 
1980). 

The use of the hierarchical logit model requires that we assume our 
preference measures (7 point) are interval scales. To investigate the 
effect of an interval scaling assumption, we compare the rank order prefer- 
ence and standard multinomial logit model in which the interval property 
is also necessary. The correlation of the choice probabilities (P. •) 



-56- 



estimated by the rank order model (Equation 7) and multinomial logit model 
(Equation 8) were highly correlated (P = .965), so the probability estimates 
do not appear to vary much when the interval scaling property is assumed. 

The correlation of the probabilities from the hierarchical logit 
to those from the multinomial logit model in the ground^nstant structure 
was .84. This is not as high as the previous correlation and use of the 
probabilities from the hierarchical logit led to different branching proba- 
bilities (P, ). For example, the branching probability for the ground 
b 

coffees was .42 — less than the random value of .49 This would suggest 
rejection of the first level branching previously indicated (Figure 6). 
However, before reaching this conclusion, recall that heterogeneity is 
present (see Table 4) . 

In order to investigate the effect of heterogeneity on hierarchical 
logit estimation, the hierarchical and multinomial logit probability esti- 
mates were obtained within the two heterogeneous groups — ground/instant 
(n=84) and caf f einated/decaf f einated (n=53). Despite the small samples, within 
these groups the correlation returned to high levels (^.96 for the ground/ 
instant group and P=.91 for the caf feinated/decaf feinated group) and the branch- 
ing probabilities were high (^= .84 for the ground/instant group and 
P = . 75 for caf feinated/decaf feinated group). These findings suggest 
extreme caution should be excercised in applying hierarchical logit pro- 
cedures when heterogeneity is possible, since it appears to bias the estimates. 

Once heterogeneity is considered, the sensitivity to possible violation 
of the assumption of independence of irrelevant alternatives is low since the 
hierarchical and non-hierarchical logit procedures yield very similar 
probability estimates (P.,). This result combined with the low managerial 
sensitivity to heterogeneity indicated in the previous section suggest 



-57- 



the overall hierarchical tree and maps are appropriate for entry strategy for- 
mulation in the case presented here. 

The absence of an empirical problem with the independence of irrelevant 
alternatives can be explained in part by the research design which measures 
preferences only over individual consideration sets (C.). The consideration set 
is the consumer's self-screening of the alternatives and the designation of those 
"relevant" to his or her choice. The empirical analysis here is consistent with 
the notion that a Luce model describes individual choices across the consideration 
set and that the hierarchy is primarily the result of aggregation of such indi- 
vidual Luce models rather than the sum of individual hierarchical choice models. 

Limitations of Application: This study was conducted to test and demon- 
strate the model and measurement methodology. Care should be exercised 
in taking specif ic marketing actions based on it since the sample is not 
representative of all regions of the U.S., and many financial estimates 
were made in calculated return on investment. In a company sponsored 
application, the approximate sample size could have been 1,000 respondents 
across 5 or 6 cities. This study was not sponsored by a manufacturer, 
so the sample was smaller and for research purposes only. The sample 
was collected (July - August, 1977) after a period in which coffee prices 
rose from two to four dollars per pound and then stabilized at three dollars 
a pound. It would be necessary to repeat the study under the current 
price and product competitive environment before it could be used in planning 
strategy in today' s market . Another caution is reflected in the margin 
and investment assumptions. These are subjective estimates and should 
be based on actual company cost, market prices, and facilities requirements 
before a firm contemplates utilizing the results in committing to design- 
ing a new product entrant into the coffee market. 



-58- 



RESEARCH ISSUES 

This paper has presented a model and measurement methodology to esti- 
mate a hierarchical structure of competition and examine its implications 
for market entry strategy formulation. In its first application it pro- 
duced encouraging statistical significance and managerial insight; however, 
several technical issues require further research. 

One method has been proposed in this paper for hierarchical definition 
of a market. It would be useful to conduct a comparative empirical study 
to see if it is more powerful than other methods (see discussion of alter- 
native approaches) in identifying the hierarchical structure of competition. 

The entry model proposed here (Equation 12) demonstrated statistical 
significance, but research could be directed at improving it. The model 
now represents entry share by a proportionality to the first product in 
the market, and thereby, does not consider other products. Attention 
should be directed at extending this model to include the shares of all 
previous entrants, so their defensive reactions could be explicitly consi- 
dered. It also would be productive to model entry not only by an order 
interger, but also by the time (months) between successive entries. If » 
the second product in a market enters one month after the first, the effect 
is likely to be different than if the entry is 12 months after the first 
product. Finally the index (E ) includes all effects except positioning. It 
could be subdivided to consider phenomenon such as advertising and promotion 

expenditures . 

A third technical issue in the model is what to do if only one product 

defines a competitive market branch. In this case, the model criterion 
based on switching is meaningless. A single product branch would be indi- 
cated if consumers would consider that product as the only acceptable 



-59- 



alternative for a specific use. In terms of our measures, a consideration 
set of one brand and a large proportion of respondents refusing to buy 
in the laboratory store would indicate this condition. Research is needed 
to improve procedures for identifying and testing single product branches, 
but in practice, such branches are not often observed because competitors 
usually develop quickly if the product is successful. 

A final area of research is consideration of durable consumer, indus- 
trial, and service industries. The application reported here was a fre- 
quently purchased consumer product. The model criteria based on prefer- 
ences and consideration sets could be applied to other industries, but 
the laboratory procedures would be inapplicable to industrial and service 
purchases. Shopping for consumer durables would be possible by the use 
of lottery (e.g., one in n chances to win the product of your choice, 
or cash), but realism is lost. Another problem is the estimation of choice 
probabilities. If the product is a first time purchase, the logit model 
which uses last purchases and preferences to estimate probabilities could 
not be used. Direct estimates of probabilities of purchase from consumers 
(Juster, 1966, and Morrison, 1979) or the assumption of equal probabilities 
over the consideration set could be used to provide estimates of probabi- 
lities, and thereby, allow application of the branching procedure. The branch- 
ing based on consideration sets reported here (see Figure 7), indicate this 
approach may be feasible. 

New applications are underway in several frequently purchased consumer brand 
markets to further assess the empirical adequacy of the model and its managerial 
relevance. Testing in the consumer, industrial, and service industries is anti- 
cipated. If statistical and managerial significance is achieved, the proposed 
model will be a useful tool aid in market entry strategy formulation. 



ACKNOWLEDGEMENTS 

We would like to acknowledge the very valuable comments on our work 
received from Al Silk, John Hauser, Api Ruzdic, Len Lodish, and Manu Kalwani, 



-Al- 



APPENDIX ONE 



Mean and Variance of Purchasing in Branc h* 

First the distribution is established at the individual level (Lemma 1) 
and then aggregation under homogeneity is considered (Lemma 2). The theorem 
establishes the formulas for desired mean and variance with heterogeneity across 
individuals . 



Lemma 1: If X = (X,, ... X, ) are multinomially distributed random variables 
—Ik 

with parameters n=l and p=(p ,...,p ) , then y = T, X is a 
Bernoulli random variable with parameter p = Z„p, where the set S 

S o K 

is a subset of the original random variables. 



Proof; The probability distribution for X is given by 

X K 

f(x|i.p) = kl[ Pk ^ f°^ \ = O'l' ^ \ = 1 

k=l 

otherwise 



Since the X, are (0,1) r .v . and since Z,X = 1 we know that y is a (0,1) r.v. 

Furthermore y = 1 iff X, =1 for keS. Since the events X =1 are mutually 
■'s k k ^ 

exclusive we have that the probability that y = 1 is given by 

Prob{y =1} = I Prob^ =1. X =0. j^k}= I P, = P, 



Similarly, 



Prob{y =0} = Prob{X =0 ¥ keS} = I Prob{X =l,X.=0,J7^k} 



kps 
This is the definition of a Bernoulli random variable . Q.E.D. 



* These proofs were supplied by John R. Hauser and are gratefully acknowledged 



-A2- 



Lemma 2: Let X be a vector multinomially distributed random variable with 
parameters 1 and p. Let y = )^oX, . Let m = the number of times 
y =1 on n successive independent draws. Then m is a binomial 
random variable with parameters n and p where p = ) p, . 



Proof: By lemma 1 y is a Bernoulli random variable with parameter p , 

since the successive draws are independent, m is a binomial 

random variable with parameters n and p . For example see 

s 

Drake (1967, p. 129). Q.E.D. 

The probability distribution of m is given by: 



f(mln,p ) = '(")p "(1-p )" "■ m=0,l, 
' "^s m s s 

otherwise 



Theorem 1: Let X. =(Xi . ,X„ . , . . . ,X, . ) ' , i=l to I, be a series of indepen- 
—1 li 2i ki 

dent random variables each a multinomial random variable with 

parameters n. (the number of successive draws for i) and £. . 

Let S be a subset of the indices 1 to K. Let y . = ) ^X, . and 

•^si '-S ki 

I 

let Y = y y .. Then for large I and for p. not uniformly 

S.'^,S1 —1 

1=1 

I 

skewed, Y is approximately normal with variance / n.p„.(l-p„.) 
' s "^"^ ■' .^, 1 Si Si 

1=1 

I 

where p„ . = /„p, . and mean ) n.p„. ' 
Si ^S ki >, 1*^31 

1=1 



-A3- 



Proof: Y is approximately normal by the central limit theorem (Drake, 
1967, p. 212), since Y approaches normality as I increases 
without bound. Independence and not uniformly skewed are the 
conditions necessary for the CLT. The variance and mean are 
computed by summation since the random variables are indepen- 
dent (Drake, 1967, p. 108). Q.E.D. 



Corollary 1 ; Let X. be a series of independent multinomial random variables 

with parameters n. and p. Let S be a subset of the indices 1 to K. 

Let Y be defined as in theorem 1. Then Y is approximatley normal 
s s 

I I 

with variance ( T n.) p ( 1-p ) and mean ( J n.) p , where P„ = /.„Pr.« 

,^1S S .-IS SSK 

1=1 1=1 



Proof: The result follows directly from theorem 1 with the substitution 

of p . = p for all i. Q.E.D. 
SI s 

Corrollary 2: Let X. be a series of independent multinomial random variables 

with parameters n. and p. Let p' = Y /I where Y is defined by theorem 
1. s s 

one. Then the variance of p' is 

I 9 

I n.p .(1-p .)/I^ 

.^T 1*^81 si 
1 = 1 



Proof : It is known that the variance of ax, where x is a random variable 

2 
is a times the variance of x (Drake, 1967, p. 112). Let a=l/I 

2 
and X = Y . Then the variance of Y /I is l/I times the variance 
s s 

of Y or 
s 

I o 

y n.p .(1-p .)/I . Q.E.D. 

.'-, 1 81 Sl 

1=1 



-A4- 



APPENDIX TWO 



Use Data 

In interviews with 295 coffee drinkers (greater than one cup per day), 
808 uses were evoked across six major use classes (average is 2.7 uses 
per person). Table A-1 shows the proportion of the respondents who 
evoked each use and the proportion who evoked given brand for those who 
evoked given use. For example, 8.5% of the respondents who evoked 
breakfast as a use evoked Brim (Instant) as a product for this use. 



-A5- 
Table A-1 



Use and Brand Consideration by Occasion 

Day Others 
Breakfast Day Alone Present Lunch Supper Evening 



Percent Evoking 

Use 



96,3 



41.7 



23.4 



30.2 



43.7 



43.1 



Percent Who Would 
Consider Brand: 



Brim (Instant) 


8.5 


6.5 


12.1 


7.9 


8.4 


7.1 


Folger (Instant) 


6.3 


6.5 


3.0 


6.7 


6.7 


6.3 


Folger (Ground) 


7.7 


9.8 


9.1 


3.4 


5.9 


7.9 


Maxwell House 














(Instant) 


32.0 


26.8 


40.9 


36.0 


33.6 


27.6 


Nescafe 


10.6 


11.4 


18.2 


9.0 


8.4 


15.0 


Nescafe (Decaf) 


10.6 


8.9 


6.1 


12.4 


10.1 


7.1 


Maxim 


12.0 


15.4 


7.6 


13.5 


13.4 


11.8 


Taster's Choice 


20.1 


18.7 


24.2 


20.2 


18.5 


22.0 


Taster's Choice 














(Decaf) 


13.0 


17.1 


16.7 


20.2 


17.6 


17.3 


Sanka (Instant) 


22.9 


22.0 


18.2 


21.3 


20.2 


24.4 


Sanka (Freeze- 














Dried) 


7.7 


8.1 


9.1 


12.4 


11.8 


3.9 


Sanka (Ground) 


6.3 


7.3 


12.1 


5.6 


9.2 


4.7 


Chock Full '0 Nuts 


10.6 


8.9 


10.6 


6.7 


8.4 


9.4 


Hills Brothers 


7.0 


4.1 


1.5 


3.4 


6.7 


1.6 


Maxwell House 














(Ground) 


28.9 


32.5 


24.2 


29.2 


32.8 


26.0 



-A6- 



APPENDIX THREE 

McFadden, Train, and Tye Test for Independence of Irrelevant Alternatives 

McFadden, Train and Tye (1977) have suggested a chi-squared test of 
association for the logit model which was applied here to the probabili- 
ties obtained from the rank order preference model. The procedure begins 
by considering all individuals who have included alternative k in their 
choice sets. The individuals are then sorted in decreasing order of their 
probability of choosing k. The list of individuals is then sequentially 

subdivided into m cells with N individuals in each cell (i.e., take the 

m 

first 10 in the list and form cell 1, the next 10 and form cell 2, etc.). 

For each individual in the list, there is a 0-1 variable indicating 
whether in an observed choice situation the individual chose alternative k. 
A non-negative residual is generated whenever an individual actually chose 
k, since that individual's probability of choosing k is 0<P.,<1 and 
1-P >0. Similarly, a negative residual is generated when the individual 
did not actually choose alternative k. 

Within each cell for a particular alternative k, the number of non- 
negative and negative residuals are tabulated, and the average probability 
of choosing k is computed. The data for a particular alternative would be 
organized as follows : 

Table A-2 



Number of Residuals . 
Average 

Cell Non-Negative Negative Probability (P --) 

1 18 7 0.74 

2 21 4 0.73 

3 19 6 0.71 
etc. 



-A7- 



By construction, we might reasonably expect the number of non-negative 
residuals per cell to be highest in the lowest numbered cells, since where 
the average choice probability is higher, more people should be expected to 
have chosen alternative k in the observed choice situation. 

The chi-squared test proposed by McFadden et_ al_ determines if the pat- 
tern of non-negative residuals is significantly different from that which 
would be expected given the average choice probabilities. McFadden reasons 
that this would occur in situations where the independence of irrelevant 
alternatives property is violated. 

The chi-squared test of association for alternative j is: 

M 

X^ = y (S -N P. )^/N P. 
^ ^1 m m jm m in 

m=l -^ -^ 

m = index of cell 

M = total number of cells 

S = number of positive residuals in cell m 

m 

N = total number of observations in cell m 

m 

P. = average probability of choosing alternative j in 
jm 

cell m 
P. = average probability of choosing alternative j in 
in the total sample of individuals who included 
j in their choice set. 

The chi-squared statistic is in this case bounded by M-1 d.f. and 
M-K-1 d.f., where K is the number of parameters estimated in the choice 
mode 1 . 

In the case reported in Table 3, 10 cells were formed for each of the 
major brands of coffee tested. The chi-squared test is bounded by 9 and 



-Bl- 



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Identifying Product Markets," Journal of Marketing , Vol. 43, No. 4 
(Fall 1979), pp. 8-20. 



-A8- 



8 d.f., with critical values of 14.7 and 13.4 respectively at the 10% con- 
fidence level. If the test statistic for a particular alternative exceeds 
the critical value at 9 d.f., there is a clearly significant difference in 
the observed pattern of residuals versus the expected pattern. Similarly, 
if the test statistic is below 13.4, the observed is not significantly 
different from the expected. Values of the test statistic between 13.4 
and 14.7 yield inconclusive results. 

Table 3 shows the chi-squared statistic for the major products. In 
three cases (Maxwell House Ground, Maxim, and Taster's Choice caffeinated) 
significant statistics indicate possible violation of the IIA property. 



-B2- 



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Hauser, J. R. and G. L. Urban, "A Normative Methodology for Modeling Consumer 
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Kalwani, M.U., and D. Morrison, "A Parsimonious Description of the Hendry 

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Lancaster, K., Consumer Demand: A New Approach (New York: Columbia University 
Press, 1971). 



-B3- 



Laurent, G. , "A Study of Multiple Variant Consumption for Frequently 

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with Probabilities of Success in Industrial R and D," Journal of 
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McFadden, D., "Conditional Logit Analysis of Qualitati/e Choice Behavior," in 

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Travel Demand Forecasting Project, Institute for Transportation and 
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-B4- 



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pp. 542-573. 

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Science, Vol. 21, No. 8 (April 1975), pp. 858-871. 



-B5- 



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