Dewey
A DYNAMIC ATTRIBUTE SATIATION MODEL
OF VARIETY SEEKING BEHAVIOR*
by
Leigh McAlister*
Sloan W.P. No. 1283-82
September 1981
THE MARKETING CENTER
Jassachusetts Institute of Technology
Alfred P. Sloan School of Management
50 Memorial Drive
Cambridge, Massachusetts 02139
(617)253-6615
A DYNAMIC ATTRIBUTE SATIATION MODEL
OF VARIETY SEEKING BEHAVIOR*
by
Leigh McAlister**
Sloan W.P. No. 1283-82 September 1981
*The author wishes to acknowledge the financial support provided by the
University of Washington Graduate School of Business Summer Research Fund
and the valuable guidance of Professor James Bettman of UCLA in stimulating,
developing and presenting these ideas.
•^Visiting Assistant Professor of Management Science, Alfred P. Sloan School of
Management, Massachusetts Institute of Technology, Cambridge, Massachusetts
02139
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A DYNAMIC ATTRIBUTE SATIATION MODEL
OF VARIETY SEEKING BEHAVIOR
ABSTRACT
This paper presents a model of individual consumer choice behavior for
separate choice occasions. Contrary to the popular notion that each choice is
essentially independent of its predecessors, that very dependence is proposed
as the key to variety seeking behavior. From the consumption history one can
infer which valued attributes the subject has recently consumed and in what
quantities. Comparing this to the ideal amount of each attribute for that
subject gives an indication of the attribute combination that would be most
preferred by that subject at that point in time. As the consumption history
evolves, the pattern of attribute accumulations will change, leading to
preference for items rich in different attributes at different points in
time. The model is operationalized and specific parameterizations are
inferred from a collection of soft-drink consumption diaries. The proposed
model is shown to predict choices better than a model which ignores the
dependence among choices.
074391^^
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A Dynamic Attribute Satiation Model
of Variety Seeking Behavior
INTRODUCTION
An excerp from a soft drink consumption diary indicates that the subject
drank a Coke on Monday, a Coke on Tuesday, a Dr. Pepper on Wednesday, a 7-Up
on Thursday, a Pepsi on Friday and a Club Soda on Saturday. Further
questioning of the subject reveals that Dr. Pepper was selected on Wednesday
because it was offered that day at an especially low price. Seven-Up was
chosen Thursday as a change of pace. The subject wanted a Coke on Friday but
settled for a Pepsi because Coke was not available. Saturday night the
subject chose Club Soda to mix in her Scotch drink.
This pattern of switching among brands is not atypical for frequently
purchased, non-durable goods. Switching can be induced by the manipulation of
marketing variables, by the accessibility of the product, by the situation in
which the product is consumed or by the desire for variety. It is switching
for the sake of variety with which this paper is concerned. In particular, it
is proposed that such switching is not completely random. A deterministic
process which would lead to variety-seeking is proposed,' modelled and
empirically tested. The process differs from traditional models in its
consideration of the impact of previous selections.
The hypothesized effect of consumption history on variety seeking is based
on three assumptions. Following Lancaster (1971) it is assumed that items can
be represented by the values they take on for their constituent attributes.
Similarly, a collection of items can be represented by the sum of values,
across items in the collection, on those constituent attributes.
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A consumption history, which is a collection of items, can therefore be
represented by the attribute accumulations or attribute "inventories" it
generates.
Consider the simplified example in Tables 1 and 2. Individual soft drinks
are described by the two attributes fruit flavor and caffeine. At any point
in time, the consumption history can be summarized by the amounts of those two
attributes that have been accumulated. On day 1 only one Coke has been
consumed so the accumulated inventories would be 2 units of fruit flavor and 9
units of caffeine. The consumption of another Coke on day 2 would raise the
inventories by 2 and 9 units respectively. After the consumption of a
Dr. Pepper on day 3 the fruit flavor inventory would be incremented by 5 units
and the caffeine inventory by 7 units, etc.
[Tables 1 and 2 About Here]
The second assumption concerns the continual depletion of the inventories
through physiological processing or forgetting. This depletion can be
conceptualized as the discounting of older consumption experiences. That is,
the soft drink that a subject consumed a week ago has a smaller residual
impact on her current attribute inventories than one she consumed yesterday.
Similarly, that soft drink she consumed yesterday would have a smaller
residual impact than one she consumed one hour ago. Figure 1 describes the
ups and downs of the inventory of caffeine generated by the consumption
history in Table 2. From day to day the inventory drops by half to
represent the physiological processing or forgetting of the attribute. With
each consumption there is a discrete jump upward in the level of the inventory
equal in size to the amount of the attribute in the soft drink consumed.
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[Figure 1 About Here]
Finally, it is assumed that there is a decreasing marginal relationship
between the attribute inventories that would result from the consumption of a
particular item and preference for that item. Figure 2 depicts two possible
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decreasing marginal relationships:
1) A finite ideal point that lies within the achievable range of the
attribute inventory (given by the dashed curve).
2) A finite ideal point that lies beyond the achievable range of the
attribute inventory (given by the broken curve).
Consider a single attribute. When the inventory of that attribute is very
low this assumption implies that preference for a unit of that attribute is at
its highest. As the inventory of that attribute grows, perference per unit
drops. Should the inventory reach its ideal level or point of satiation, the
marginal impact of adding a unit of the attribute is zero. Beyond the point
of satiation, preference decreases. This phenomenon explains why a cola might
be very appealing at times (when the inventory of caffeine is low and
therefore the marginal impact on preference of adding to that inventory is
relatively high) and less so at other times (when the inventory is high
implying that additions will have a relatively small marginal impact on
preference).
[Figure 2 About Here]
The amalgamation of these three assumptions is a dynamic attribute
satiation process. It holds that preference for an item at a point in time is
a function of the preference contributions of that item's constituent
attributes. The preference contribution of each attribute is, however, a
function of the consumption history (summarized by attribute inventories) and
the point of satiation for that attribute. Since the configuration of
attribute inventories can change dramatically as the consumption history
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evolves, it is not surprising that shifts in preferences among choice
alternatives (and resulting variety seeking) are observed.
In this paper the dynamic attribute satiation process is operationalized
as an estimatable model. Soft-drink consumption diaries are used to infer
individual specific parameterizations of that model. The ability of the
proposed model to predict actual choices is shown to be superior to that of a
model based on the assumption that each choice is independent of prior
selections. The managerial implications of this finding are discussed.
LITERATURE REVIEW
As mentioned earlier, brand switching is sometimes induced by the
manipulation of marketing variables (price, product design, promotion,
distribution) and sometimes by changes in situational variables. Early
studies of brand loyalty (Tucker 1964, McConnell 1968) and a similar study in
social psychology (Brickman and D'Amato 1975) controlled for these factors and
still reported switching. In those studies subjects were asked to make
repeated choices from a set of unfamiliar stimuli. Two distinct phases of
switching behavior were apparent in the data. Initially, subjects
systematically explored the stimuli. Later in the experiment, subjects tended
to alternate among the elements of their favored subset of the stimuli. Much
of the consumer behavior literature on variety seeking, novelty seeking,
innovativeness, etc. focuses on switching like that of the first phase (e.g.,
Robertson 1971, Venkatesan 1973, Hirschman 1980). This phase can be
distinguished from the later one by the information acquisition motive. It
is switching like that of the second phase (switching among familiar items
that is done simply for "variety") with which this paper deals.
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Bass, Pessemier and Lehman (1972) studied choice from a familiar product
class controlling the impact of marketing and situational variables. Subjects
in their study chose the brand they reported as their favorite only about half
the time. The authors attributed the switching to and among reportedly less
preferred brands to "a stochastic component of choice which arises because of
variety seeking" (Bass, Pessemier and Lehmann 1972, p. 538). This line of
reasoning gave rise to Bass' (1974) "Theory of Stochastic Preference and Brand
Switching". According to that theory, relative preferences dictate the
proportion of times each brand is chosen. Any particular selection, however,
is at the mercy of a "stochastic element in the brain". Blin and Dodson
(1980) propose a specific functional relationship between the frequency with
which a brand will be chosen and the importance weights in an individual's
linear compensatory preference function. In a variation on this theme Huber
and Reibstein (1978) propose that the item selected is a deterministic
function of parameters of the preference function of the person doing the
choosing. Those parameters, however, are assumed to change in a random
fashion.
Under the theory of stochastic preference, variety seeking is viewed as
non-understandable. Other paradigms allow explanation of the phenomenon.
Predominant among the explanations is the notion of "optimal arousal" (Berlyne
1960, Hansen 1972). Individuals are hypothesized to select that collection of
items which will provide just the right amount of stimulation or arousal.
Optimal arousal is frequently conceptualized as a single peaked relationship
(Coombs and Avrunin 1977) between preference and the stimulation provided by
the collection selected. McAlister (1979) modelled the stimulation provided
by the collection as a function of the stimulation provided by attributes of
items in the collection. Her model predicts the collection of items a person
would select at a point in time.
Jeuland (1978) modelled variety seeking behavior across time. He
essentially proposed item (i.e., brand) specific stimulation optima. He
further proposed "inventories" of item stimulation which evolve dynamically in
a manner analogous to the just described evolution of attribute inventories.
Implicit in this formulation is the assumption that the consumption of one
item has no impact on the inventories of other items. As pointed out by
Hagerty (1980), this ignores the effect of item similarity. Under Jeuland's
model the preference for Coke should not be affected by consuming either
(Pepsi, Dr. Pepper, RC Cola, Pepsi) or (7-Up, 7-Up, 7-Up, Mountain Dew,
Sprite). Changes in preference result from changes in the relevant inventory
and in either of these cases the inventory of Coke would be zero.
In the proposed dynamic attribute satiation process inventories of
attributes rather than inventories of items are accumulated. The first
consumption history above would generate a large inventory of caffeine and a
small inventory of fruit flavor. The second consumption history would
generate a large inventory of fruit flavor and a small one of caffeine. The
evaluation of the caffeine and fruit flavor contributions of a Coke (and hence
the evaluation of Coke itself) will probably be very different with the first
consumption history than it would be with the second.
OPERATIONALIZING THE DYNAMIC ATTRIBUTE SATIATION MODEL
Consistent with models in the traditions of Fishbein (1963) and
Lancaster (1971), the Dynamic Attribute Satiation (DAS) model relates
preference for an item to the preference contributions" of the attributes of
that item. Assuming there are no interactions among the attributes,
preference for an item will be defined as the sum of the contributions to
preference made by each of the attributes. That is:
DA%k=j4^Tkj ^1>
where DASy[^ = preference for item k at time T assigned by the Dynamic
Attribute Satiation model,
J = the number of attributes over which items are described,
Pjl^j = contribution of attribute j to the level of satisfaction that
would result from consuming object k at time T.
The contribution of attribute j to satisfaction from consuming object k at
time T, Pji^-, is assumed to be a function of the inventory of attribute j at
time T, the ideal level of attribute j, and the amount of attribute j in
object k. It was argued that the particular functional relationship should be
marginally decreasing with a single optimum at the ideal point. A quadratic
relationship of the form presented in Equation (2) displays these properties
and is easily estimated.
P^kj = Wj [(I,j . X,j) - XjA-l) â– (2)
where Pj|^j = contribution of attribute j to the level of satisfaction that
would result from consuming object k time T,
w. = importance weight for attribute j,
I-J-. = inventory of attribute j at time T,
X. . = amount of attribute j in object k,
X. = ideal level for attribute j.
Note that when the current inventory of attribute j plus the amount of
attribute j in object k (ly- + X^.) exactly equals the ideal for attribute
j (X ), the term which is squared equals zero forcing P.,., . to also equal zero.
The more I . + X^ . differs from X., the more negative P_ . becomes. That is,
preference peaks at the ideal point. To either add to or diminish the
inventory reduces overall preference.
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Attribute Inventory
The attribute inventory is hypothesized to dwindle continuously and
experience discrete increments each time an item containing that attribute is
consumed (see Figure 1). A similar process was proposed by Little and Lodish
(1969) for the cumulative impact of advertising and by Jeuland (1978) for the
evolution of "experience" with a brand. The particular functional form used
here to convert a consumption history (X ., t=l, 2, ..., T) into an
*^tJ
inventory is given by Equation 3.
where I^. = inventory of attribute j at time T,
\. = inventory retention factor for attribute j, <_ x <_ 1,
k = item chosen at time t,
X, . = amount of attribute j in the item chosen at time t.
\^
The speed with which the inventory dwindles is an inverse function of the
inventory retention factor, X.. It seems reasonable that this factor
might differ across individuals and across attributes. For instance, one
might expect Xo^l-^j^ ^ ouenchino ^°^ athletically activp persons to be
smaller than X^^..^- i. . . for more sedate persons, indicating a more
rapid dwindling of the inventory of thirst quenchingness for athletically
active persons than for the more sedate. (In general the X's for heavy
users of a product class might be expected to be lower than x's for light
users.) Similarly, one might expect \^^^^^^^^ > X^arbination ^°^ ^"
individual indicating that the human body divests itself of carbonation more
rapidly than calories.
Unfortunately, the estimation procedure employed requires the a priori
specification of values for the X-'s. Receiving no guidance on the
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selection of such values from those who have proposed similar processes
(Little and Lodish 1969; Jeuland 1978) the value for X- was set
arbitrarily at 1/2 for all attributes and all individuals. This arbitrary
selection will impede the predictive ability of DAS. However, the objective
of this paper is to demonstrate that a process which considers the
interdependence of choices has greater predictive ability than one which views
each choice as independent of all others. If the process incorporating the
interdependence (DAS) is able to make better predictions in spite of a
handicap in parameter selection, the point will be made. Future research into
the pattern of variation of these parameters should provide insights useful to
researchers and managers and enhance the predictive ability of such models.
Parameters of the Model
Ideal Points . It is important to note that the ideal points in the DAS
model, (X.: j =1, 2, ..., J), do not necessarily reflect the amount of
attribute j that one would like to find in a single choice alternative.
Rather, they indicate the optimal level for the entire inventory of that
attribute. As the inventory level of an attribute decreases, the amount of
that attribute which is desired in a choice alternative increases.
Importance Weights . The difference between an inventory retention factor
and an importance weight should be noted. An importance weight reflects the
degree of disutility associated with being a given number of units from one's
ideal level. Comparisons among importance weights allow one to make
statements concerning the relative impact of each attribute assuming that all
else is held constant . But all else is not held constant, and inventory
retention factors determine the pattern of that inconstancy. For example,
being one unit away from one's ideal level of thirst quenchingness might be
less unpleasant than being one unit away from the ideal level of sweetness
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(importance weight for sweetness > importance weight for thirst
quenchingness). However, if this individual's X^^.^^^ quenchingness ^"^
X pg4-p,pss ^^^^ ^^^^ ^^^^ ^^^ inventory of thirst quenchingness depleted
much more rapidly than the inventory of sweetness, alternatives offering
relatively more thirst quenching ability than sweetness would probably be
chosen. This in spite of the fact that sweetness has a higher importance
weight than thirst quenching ability.
Confounding of Parameter Estimates when Inventory is Ignored .
If people do, in fact, evaluate choice alternatives relative to the
current state of their attribute inventories, one might expect bias to be
introduced by estimation procedures which do not account for those
inventories. In an appendix to this paper it is shown that the failure to
account for inventories will not bias importance weights but will bias ideal
points. The direction of ideal point bias will be downward from the true
ideal by an amount equal to the inventory at that point in time. For that
instant the bias in the parameter exactly makes up for the failure to include
inventory in the stimulus-attribute matrix. At later points in time the
inventory will be at different levels and the parameter's bias will not
exactly compensate. The managerial implications of this bias will be explored
in the "Discussion of Findings" section.
DATA
Data for the study reported in this paper were collected between October
and December, 1978. Twice in the course of this 81 day study (at the
beginning and half way through) subject perceptions of stimuli on relevant
attributes were elicited. Twice a week during the course of this study,
subjects were asked to rank order the stimuli from most preferred to least
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preferred and to report all items from the stimulus product class that they
consumed since they last gave data. Data from the first 50 days of the study
is used to estimate parameters of different models. These estimated models
are then employed to predict actual choices made during the last 30 days of
the study. Statistics based on those predictions allow comparison of models.
Subject Population
The subjects in this study were 36 graduate and undergraduate students
enrolled in the School of Business Administration at the University of
Washington during Fall Quarter, 1978. Twenty-two percent of the subjects were
females. No economic incentive was offered for participation in the study.
Motivation for accurate reporting of information was provided by having the
professor in a bi-weekly class begin each period by distributing data
collection forms and requesting that serious thought be given to the task.
Responses to a questionnaire administered at the end of the study indicate
that subjects were neither intrigued nor irritated by the tasks and tended
o
to report their preferences accurately.
Stimuli
This study, as did Bass, Pessemier and Lehamann's (1972), deals with
preferences for and choices among soft drinks. The 10 stimuli selected were:
Coke, Diet Pepsi, Dr. Pepper, Mountain Dew, Pepsi, Royal Crown Cola, 7-Up,
Sprite, Sugar Free 7-Up and Tab. These soft drinks were reported in Standard
and Poor's Industry Survey (1978) as having the ten highest market shares,
ranging from a share of 26.6% for Coke down to 1.2% for Sugar Free 7-Up. The
total of market shares for stimulus soft drinks is 69.2% with no excluded soft
drink receiving more than .9% of the market. These soft drinks include 6
colas and 4 non-colas and 3 diet drinks and 7 non-diet drinks.
The subjects were, on average, reasonably familiar with this product
class. Their self reported familiarity with the stimulus soft drinks.
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averaged across subjects and across soft drinks, is 2.8 on a scale on which 1
indicates that the subject had never tasted the soft drink and 5 indicates
that the subject often drinks it.
The attributes selected to describe the stimulus soft drinks are the same
as those used in the Bass, Pessemier and Lehmann (1972) study: carbonation,
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calories, sweetness, thrist quenching ability, and popularity with others.
Seventy-two percent of the subjects indicated that they thought that the
selected attributes were not the only factors they considered in selecting a
soft drink. Other attributes that they mentioned as important include (in
order of frequency of mention, most frequent first): taste, price,
availability, caffeine, saccharine, can size and nutrition.
Data Collection Instrument
The data collection instrument was made up of three documents. The first
document, administered at the beginning of the study and half way through,
elicited subject perceptions of attribute values for stimulus soft drinks on 6
point scales (0 to 5). Zero indicated that the brand possessed virtually none
of the attribute. Five indicated that the brand possessed a great deal of the
attribute. The order in which stimulus soft drinks were presented was
randomized across subjects.
The second document, administered bi-weekly for the 11 weeks of the study,
elicited a history of soft drink consumption since the subject last gave
data. It also requested that the ten stimulus soft drinks be rank ordered
from the brand a subject would most like to consume at that point in time to
the brand she would least like to consume at that point in time. The order of
presentation of soft drinks for the rank-ordering task was randomized across
data collection occasions.
The final document was administered at the end of the study to survey
subjects' attitudes about the study. It included questions regarding
familiarity with the stimuli, involvement with the experimental tasks, reasons
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for selecting a soft drink other than the one which had most recently been
reported as most preferred and factors other than experimental attributes that
influenced the subject's selection of soft drinks.
Model Estimation
The algorithm LINMAP was used to estimate parameters for DAS. Because not
all subjects reported preferences at every possible data collection
opportunity (due to class absences, etc.) the number of preference reports per
subject in days 1-50 of the study (the time period used to estimate
parameters) ranges from 5 to 11. Their respective stimulus-attribute matrices
were therefore made up from 50 to 110 stimuli (10 from each report,
corresponding to the perceptions of the 10 stimulus soft drinks augmented by
the inventories). This does not, however provide the information content of a
single ranking of 50 to 110 objects. Since no comparisons were made across
report periods, it is impossible to say whether the stimulus ranked third on
one day is more or less preferred than one ranked fifth on another day. The