Discussion Paper No. 70
An Integrated Model for
Discontinuous Preference
Change and Satiation
Nobuhiko Terui
Shohei Hasegawa
Adam N. Smith
Greg M. Allenby
September 28, 2017

Data Science and Service Research
Discussion Paper

Center for Data Science and Service Research
Graduate School of Economic and Management
Tohoku University27-1 Kawauchi, Aobaku
Sendai 980-8576, JAPANAn Integrated Model for Discontinuous Preference
Change and Satiation
byNobuhiko Terui
Tohoku University
Sendai, Japanterui@econ.tohoku.ac.jp
Shohei Hasegawa
Hosei University
Tokyo, Japan
shasegawa@hosei.ac.jp
Adam N. Smith
University College London
London, Englanda.smith@ucl.ac.uk
Greg M. Allenby
Ohio State University
Columbus, Ohio
allenby.1@osu.edu

September 28, 2017

An Integrated Model for Discontinuous Preference Change and Satiation

Abstract
We develop a structural model of horizontal and temporal variety seeking using a dynamic
factor model that relates attribute satiation to brand preferences. The factor model employs a threshold specification that triggers preference changes when customer satiation
exceeds an admissible level but does not change otherwise. The factor model is developed
for high dimensional switching data encountered when multiple brands are purchased
across multiple time periods. The model is applied to two scanner-panel datasets where
we find distinct shifts in consumer preferences over time where consumers are found tovalue variety much more than indicated by traditional models. Insights into brand preference are provided by a dynamic joint space map that displays brand positions andtemporal changes in consumer preferences over time.

Keywords: Dynamic Factor Model, Horizontal Variety, Product Attributes, Threshold
Switching Structure

1

Introduction

Consumers purchase a variety of goods in every product category, and invariably switch
brands at some point in time because of deals or because they get tired of consuming
the same things. Temporary changes in preference have been the subject of a long literature on variety seeking in marketing, with reasons ranging from the presence of multiple
needs, persons and contexts, to changes in tastes, constraints and available offerings (see
McAlister & Pessemier, 1982). This paper investigates the relationship between satiationand preference as an explanation for why people seek variety. We find that consumer
satiation affects preferences in a predictable way up to a point, after which consumer
preferences abruptly change and consumers switch to varieties that are distinctly different from those consumed in the past. Our findings have implications for the breadth of
products carried by retailers.
Existing models of variety seeking assume that changes in the demand for varieties
can be explained by a continuous model structure with predictable changes in preference.
Models of horizontal variety seeking (Kim et al., 2002; Bhat, 2005), for example, assume
that diminishing marginal returns (i.e., satiation) explain why people purchase multiple
varieties at one time, where marginal utility is a function of quantity purchased. In
these models people are assumed to have stable preferences that diminish in intensity as
consumption quantities increase, leading them to tire of consuming large quantities.
Temporal variety seeking behavior is modeled by including lagged purchase variables
in models of discrete choice (Dubé et al., 2010; Chintagunta, 1998). A positive coefficientvalue for lagged purchase leads to higher repurchase probabilities for the consumed product while leaving the preference ordering for the remaining varieties unaffected. Models of
temporal variety seeking make relatively minor changes to the preference ordering unlessmultiple lagged variables are included in the model specification.
A problem common to the study of temporal and horizontal variation of brand pur-1

chases is with the dimensionality of switching behavior. The study of m brands is associated with m2 different possible “switches” for two time periods if only one brandis purchased. The dimensionality increases when considering the temporal variation ofhorizontal variety, where multiple goods are purchased in both time periods. Models ofswitching behavior are challenged by the large number of possible purchase outcomes,
even when the number of brands under study is relatively small.
In this paper we propose a model of preference change that distinguishes multiple formsof variety seeking and examines the temporal relationship between product satiation andbrand preference. We find that preference changes are initiated from a latent satiation
variable that varies over time, where consumer preferences are stable for a period of time
and then abruptly change when the latent satiation variable exceeds a threshold value.
This behavior is consistent with consumers becoming tired of consuming the same set of
products and then moving on to a new set. We address the issue of dimensionality byemploying a dynamic factor model that relates preference and satiation. We find that thebest fitting model has the preference factors changing only when the dynamic satiation
factor exceeds a threshold. We find that our threshold model has larger estimates ofcompensating value for varieties in the product line, and has implications for the breadthof offerings carried by retailers.
The organization of the paper is as follows. Section 2 provides a discussion of related
literature. In Section 3 we introduce our integrated model and contrast it to existingmodels of horizontal and temporal variety seeking. We include a discussion of alternativemodels examined in our empirical analysis that relax some of the assumptions of our
proposed model. Section 4 presents empirical results using scanner panel data from two
product categories: carbonated beverage and yogurt. In both cases we find significant
improvement in model fit over existing models. Section 5 contains a discussion of theresults from both data sets to illustrate the insights provided by our approach. Concluding
remarks are offered in Section 6.

2

2

Related Literature

Models of discrete behavioral changes, characterized by thresholds and switching regimes,
have been found to provide an accurate description of many aspects of consumer behavior. Behavioral decision theory (Einhorn & Hogarth, 1981), for example, describes theeffects of framing on consumer decision processes that reflect discrete differences in how
consumers view consumption opportunities. The most widely known example of this is
how consumers react to gains and losses (Thaler, 1985). More broadly, the similarity,
attraction, and compromise effects regularly documented in models of choice (Roe et al.,2001) point to discrete and discontinuous effects in the decision process. The behavioral
decision theory literature (e.g., Kahneman & Tversky, 1979) indicates that human behavior reflects discrete, not continuous changes as choice alternatives are described, framed
and presented to consumers.
The modeling literature in marketing has also found that models with discrete thresholds provide a good description of marketplace behavior. Switching regression models(Terui & Dahana, 2006), models of structural heterogeneity (Kamakura et al., 1996),
and Markov switching models (Frühwirth-Schnatter, 2006) all describe different response
processes among and within respondents. Fong and DeSarbo (1981) propose a model ofchoice in which consumers can enter a passive state of response once they become fatigued.
Gilbride and Allenby (2004) propose a choice model with a screening component that sets
the choice probability to zero if a brand does not enter a person’s consideration set. Teruiet al. (2011) find that media advertising for mature products affects brand considerationand choice as long an advertising stock variable is above a threshold variable. We contribute to this literature by showing how these discrete thresholds can be incorporated
into the class of direct utility models. In addition, we introduce discrete thresholds in thecontext of dynamic factor models that allow us to identify the source of abrupt changes
in preferences.

3

Recently, Hasegawa et al. (2012) employ a dynamic factor model on the satiation
parameters of a direct utility model to describe changes in preferences over time. Their
specification of factor dynamics roughly approximates a smooth time transition function
and thus only allows for smooth preference changes. In contrast, our goal is to model
discrete shifts in preferences. We do this by integrating the dynamic satiation model ofHasegawa et al. (2012) with a second factor model on baseline preference parameters that
contains a discrete switching structure.
Our formulation is consistent with existing models in the marketing and psychology literature. The dynamic attribute satiation (DAS) model of McAlister (1982) and McAlister
and Pessemier (1982) predicts that variety seeking occurs as a respondent’s consumption
history evolves. Sarigollu and Schmittlein (1998) extends the DAS model to include a
discrete choice model where preferences are related to an inventory of past attribute accumulation. Our formulation includes the discrete choice model as a special case, andincorporates threshold effects leading to discrete changes in preference. In contrast to
Fader and Hardie (1996), we employ a dynamic factor model instead of observed product attributes to deal with high dimensionality of the choices and to allow for temporalvariation in demand. One possible motivation for our model is the single peak model by
Coombs and Avrunin (1977) in which consumers reach an optimal level of an attributeand then, because of their satiation, decide to consume a different attribute on the next
purchase occasion. We investigate changing preferences for brands through a dynamic
factor model that, as we see below, helps visualize spatial patterns of competition.

3

Model Development

We develop our model within the framework of direct utility maximization (Kim et al.,
2002; Bhat, 2005; Hasegawa et al., 2012). Consumer h’s utility over j = 1, . . . , m varieties4

at time t is defined as:
U (xht ) =

m
X
ψjht
j=1

γjht

ln(γjht xjht + 1)

(1)

where xht = (x1ht , . . . , xmht )0 is the vector of quantity demanded by consumer h at timet, ψjht is the baseline value of marginal utility when xjht = 0, and γjht is a satiation
parameter that affects the rate at which marginal utility diminishes. Both ψjht and γjht
are restricted to be positive.
A stochastic model is obtained by assuming that the baseline utility parameter has∗+ εjht )an error term. To ensure strictly positive marginal utility, we let ψjht = exp(ψjht∗
where ψjht
is unrestricted and εjht follows an EV(0,1) distribution, as in Bhat (2005).

Then the likelihood function is obtained by maximizing (1) subject to the budget constraint p0ht xht ≤ Eht where pht is the price vector and Eht is total expenditure. This isaccomplished by creating the following auxiliary equation.

Q = U (xht ) − λ(p0ht xht − Eht ).

(2)

By employing the Kuhn-Tucker conditions of constrained utility maximization, we obtainan expression that relates the observed demand to the error terms as follows:∗εjht = ψjht
− ln(γjht xjht + 1) − ln pjht if xjht > 0(3)∗εjht < ψjht
− ln(γjht xjht + 1) − ln pjht if xjht = 0(4)

The likelihood function is then composed of a combination of density and probability
mass, arising from the interior and corner solutions, respectively.

3.1

Satiation Dynamics

We begin our model specification by allowing for satiation dynamics as in Hasegawa etal. (2012). In particular, we let γ ∗ht = log(γ ht ) follow a dynamic factor model with a5

time-invariant factor loading matrix a and a one-dimensional factor fht .
γ ∗ht = afht + εht , εht ∼ N (0, Σ = diag{σ1 , . . . , σp })(5)fht = fht−1 + νht , νht ∼ N (0, 1)(6)

The satiation factor score fht is specified a priori in (6) as a random walk, which imposesa smoothness prior on changes in the factor over time. The random walk specification
also allows for the accumulating effects of past purchases, where parameter values of highlikelihood rationalize the observed choices. Equation (6) defines a non-parametric modelfor temporal dynamics, and it accommodates a trend component locally linear over timein the non-stationary part worth and satiation parameters. This specification has beensuccessfully used in state space modeling (e.g., Harvey, 1989; Kitagawa & Gersh, 1984;
West & Harrison, 1996; Terui et al., 2010; Terui & Ban, 2014).
The factor score moves rather smoothly when the variance of factor score is smaller
than the part worth’s variance, as is employed and discussed in Hasegawa et al. (2012).
When multiplied by the factor loading matrix a, the result is a vector of attribute satiation
coefficients that evolve through time with expected value afht . Thus, the factor loading
matrix a can indicate for which of the product alternatives consumers experience temporalvariation in satiation.

3.2

Baseline Preference Dynamics with a Switching Structure

In order to relate satiation dynamics to preference, we specify a second factor model tobaseline preference parameters. That is, we assume that the baseline parameters are also
well projected into a lower-dimensional space, as is done in a choice map when conducting
a market structure analysis (Hauser & Shugan, 2008; Elrod, 1988; Chintagunta, 1994;

6

Wedel & DeSarbo, 1996).

ψ ∗ht = bg ht + δ ht , δ ht ∼ N (0, V = diag{v1 , . . . , vm })(7)

Each row vector of factor loadings matrix b defines the coordinate of brand position andcorresponding factor score vector g ht , indicating consumer h’s preference direction at timet. We will refer to g ht as the preference direction vector. We assume that the preference
direction will change when consumer satiation level exceeds the admissible level rh , butdoes not change otherwise. Factor dynamics can then be described as

g ht =
 β f ∗ + ω ht , ω ht ∼ N (0, I)
h1 ht−1∗
if fht−1≥ rh g ht−1

otherwise(8)

where β h1 = (βh11 , βh12 )0 . We set rh = 0 for identification in the empirical application.
Our model of dynamic preference change integrates two factor analytic models – one forthe satiation parameters γ ∗ht in equation (5) and one for baseline preference parameters ψ ∗ht
in (7). These parameters are related to each other by (8) where dynamics are explained interms of the respective factor scores. In our proposed model, the scores for the satiation
parameters induce abrupt changes to baseline utility through a threshold model. The
dimensionality of the factor models is set to two for the baseline preference parameters
for ease of interpretation, and one for the satiation parameters to extract a scalar satiation
score. Below we examine alternative specifications for these model components, including
the model by Hasegawa et al. (2012) who consider a factor model for the baseline utility
preference parameters only.

3.3

Alternative Models

We consider six alternative models in addition to our proposed model. All models differ
on the basis of dynamics, switching behavior, and flexibility. The first alternative model

7

employs a static preference direction using an ordinary factor model, and is denoted as(Static).
ψ ∗ht = bg h + δ ht , δ ht ∼ N (0, V = diag{v1 , . . . , vm })(9)Here preferences are assumed to have constant expected value bg h that is unrelated tosatiation effects.
The second alternative is a dynamic model that assumes the preference direction vector
g ht follows a random walk:g ht = g ht−1 + ω ht , ω ht ∼ N (0, I)(10)This specification is identical to a non-parametric model of a stochastic trend in timeseries {g ht }. Equation (10) has no causal variables or structural parameters, and we referto this model as a non-parametric dynamic factor model (NDF). This specification was
successfully employed in Hasegawa et al. (2012) to capture the locally linear stochastic
trend for a non-stationary series.
The third model specifies the preference direction vector g ht as being related to satiation in the previous period:∗
g ht = β h1 fht−1+ ω ht , ω ht ∼ N (0, I)(11)

We call the model represented by (12) as the structured dynamic factor model (SDF).
Both the NDF and SDF have a common property that preference changes whenever a
consumer purchases a product.
The next set of models include a switching mechanism regarding the timing of preference change. We assume that satiation drives the change when its level exceeds athreshold value, and does not drive the change otherwise. These models have various
forms, or types. The first is an SDF model with threshold switching, called a switching8

non-parametric dynamic factor model (SNDF):

g ht = ght−1 + ω ht ,ω ht ∼ N (0, I) g ht−1∗
if fht−1
≥ rh

(12)

otherwise

The second model is our proposed switching structured dynamic factor model (SSDF1)
shown in (8). The third model is composed of the two previous models, called a hybrid
dynamic factor model (SSDF2):g ht =
 β f∗ + g
h1 ht−1
ht−1 + ω ht , ω ht ∼ N (0, I)∗
if fht−1≥ rh g ht−1

otherwise(13)

This model provides a flexible specification of the preference vector updating equation,
allowing the current preference vector to be influenced by both the satiation variable andthe past preference vector. It allows the expected preference vector to the informed by
the satiation variable but not entirely dependent on it.
The fourth model includes an autoregressive term β h2 in the model to allow for greater
flexibility relative to equation (14). This model is referred to as SSDF3:

g ht =
 β f ∗ + β g ∗ + ω ht , ω ht ∼ N (0, I)
h1 ht−1h2 ht−1∗
if fht−1≥ rh g ht−1

otherwise(14)

These models provide a comprehensive set for assessing the benefit of the proposed dynamic model for describing preference change. Table 1 provides a summary of all models
that are fit to the data.

9

Table 1: Summary of Models
Model
Static
NDF
SDF
SNDF
SSDF1
SSDF2
SSDF3

Dynamic
No
Yes
Yes
Yes
Yes
Yes
Yes

Switching
No
No
No
Yes
Yes
Yes
Yes

Equation
(9)
(10)
(11)
(12)
(8)
(13)
(14)

Specification
g ht = g h
g ht = g ht−1 + ω ht∗
g ht = β h1 fht−1+ ω htg ht = g ht−1 + ω ht∗
g ht = β h1 fht−1+ ω ht∗g ht = β h1 fht−1 + g ht−1 + ω ht∗∗
g ht = β h1 fht−1+ β h2 fht−1+ ω ht4

Empirical Applications

4.1

Data Description∗
if fht−1≥ rh∗
if fht−1 ≥ rh∗
if fht−1≥ rh∗
if fht−1 ≥ rh

We apply the model to the carbonated beverage and yogurt categories in the IRI household
panel data set (see Bronnenberg et al., 2008 for a detailed description). The productcategories are chosen because of their wide assortments and high frequency of purchaseamong households. We use data over a two-year period from one store in Pittsfield,
Massachusetts.
In the carbonated beverage category, we restrict our analysis to 12-packs of cans (themost common form) and select the top 30 varieties based on total volume. The resulting
product set consists of nine national brands (7Up, A&W, Barqs, Coke, Mountain Dew,
Mug, Pepsi, Schweppes, Sprite) and one private label brand. A complete descriptionof the product set is provided in Table A.1. A total of 607 households are included inour data set after removing those with less than five purchases over the sample period.
Moreover, 56% of purchase occasions correspond to interior solutions in which more than
one variety is chosen.
In the yogurt category, we select six national brands (Colombo, Dannon Fruit on the
Bottom, Dannon Light and Fit, Stonyfield Farm, Yoplait, and Yoplait Light) and one
private label brand. We then choose the top five varieties within each brand based onmarket share. A complete description of the resulting 35 products is provided in Table A.2.

10

This data set contains 387 households and 80% interior solutions. The overwhelming
majority of interior solutions in both data sets points to the need of a demand model that
can accommodate this multiple discreteness.
We also observe characteristics in the data which point to the need to accommodate
temporal variety seeking. For example, in the two-year sample period, 92.1% and 83.9%
of households have purchased more than one brand in the carbonated beverage and yogurt
categories, respectively. Further evidence is shown in Figure 1, which plots the purchases
for a single household (ID#50) in the yogurt category. We find concentration among
Private Label varieties for the first 10 trips, and then a shift to Dannon and Yoplait
varieties during the last 10 trips. This type of demand pattern is consistent with abrupt
shifts in preferences over time.
PL Strawberry
PL Raspberry
PL Peach
PL Cherry
PL Blueberry
Colombo Classic Strawberry
Colombo Classic Peach
Colombo Classic Blueberry
Colombo Classic Vanilla
Dannon LNF Vanilla
Dannon LNF Strawberry
Dannon LNF Raspberry
Dannon LNF Blueberry
Dannon LNF Strawberry Banana
Dannon FOTB Raspberry
Stonyfield Farm Blueberry
Stonyfield Farm Raspberry
Stonyfield Farm Peach
Stonyfield Farm Strawberry
Stonyfield Farm Vanilla
Colombo Classic Blackberry
Dannon FOTB Mixed Berry
Dannon FOTB Peach
Dannon FOTB Blueberry
Dannon FOTB Strawberry
Yoplait Light Peach
Yoplait Light Blueberry
Yoplait Light Red Raspberry
Yoplait Light Vanilla
Yoplait Light Blackberry
Yoplait Original French Vanilla
Yoplait Original Key Lime Pie
Yoplait Original Mixed BerryYoplait Original Mountain BerryYoplait Original Strawberry

0

5

10

15

20

trips

Figure 1: An example of temporal changes in household purchases (ID#50) in the yogurt
category.

11

4.2

Identification Conditions and Prior Specification

We fit seven models to the data as described in Section 3.3. All models are specified as
Bayesian models and Markov chain Monte Carlo methods are used to sample from eachposterior distribution. Descriptions of the algorithms used are provided in Appendix B.
For the two-factor model applied to baseline parameters, we restrict the loadings to achieve
statistical identification.
10b21 1 b31 b32 
b=

 ..
.. 
 .
. 
bp1 bp2(15)This restriction due to the factor model being applied to parameters of a latent utility isstronger than Geweke and Zhou (1996) condition for the conventional factor model. We
define the prior distribution on this factor model’s parameters as follows:
vk2 ∼ IG(nv0 /2, sv0 /2)
b21 ∼ N (b0 , B0 )(16)

bk = (bk1 , bk2 )0 ∼ N (b0 , B0 ) for 3 ≤ k ≤ pwhere nv0 = sv0 = 2, b0 = 0, and B0 = 100I. The same type of priors are applied to the
one-factor model for satiation dynamics:
σk2 ∼ IG(nσ0 /2, s0σ /2)(17)

ak1 ∼ N (a0 , A0 ) for 2 ≤ k ≤ pwhere nσ0 = svσ0 = 2, a0 = 0, and A0 = 100I. Finally, the hierarchical prior on the12switching coefficients is specified as:
βh1k ∼ N (β̄1k , 1)(18)
β̄1k ∼ N (β̄0 , ν0 )where β̄0 = 0 and ν0 = 10.

4.3

Computation

Applying MCMC methods to our high dimensional choice model presents significant computational challenges. MCMC is a time consuming technique and the model scales exponentially in the number of alternatives and households. We overcome these challenges
by employing parallel computing, which allocates the sampling procedure for the set ofhousehold-level parameters to a set of 144 cores of CPU. The common parameters in the
distribution of heterogeneity can be updated in the usual fashion (e.g., Gibbs sampling).
This approach drastically reduces computational time from more than several months to
only a couple of days.

4.4

Estimation Results

Table 2 reports measures of in-sample and predictive model fit. In-sample fit is evaluated using the log marginal density (LMD) and Bayesian deviance information criterion(DIC). The LMD statistic is calculated using the Newton-Raftery algorithm (Newton &Raftery, 1994). The DIC is a statistic used for model comparison that explicitly penalizes
model complexity (Spiegelhalter et al., 2002). Predictive fit is evaluated using root-meansquared-error (RMSE). We use the last observation from each panelist and compute
v
u
H X
m
u 1 X
t
RM SE =
(xj,Th +1 − x̂j,Th +1 )2
Hm h=1 j=1

13

(19)

where x̂j,Th +1 is the predicted demand for individual h at time Th + 1. Demand forecasts
are generated by maximizing the utility function in (1) subject to the budget constraint
p0h,Th +1 xh,Th +1 ≤ Eh,Th +1 , where ph,Th +1 and Eh,Th +1 are fixed at average price and expenditure levels during the in-sample period.
Table 2: Model Fit
Carbonated Beveragein-sample
out-of-sample
Model
LMD
DIC
RMSE
Static -1090.049 10914.347
3.098
NDF
-850.912 10366.264
3.155
SNDF
-876.193
9969.135
2.593
SSDF1 -809.822 8911.165
1.980
SSDF2 -1012.713 9438.858
1.653
SSDF3 -866.639
9561.690
2.135

Yogurtin-sample
out-of-sample
LMD
DIC
RMSE
-859.523
8210.251
6.042-844.1308193.423
5.965-792.1947952.334
5.551-586.123 6851.133
3.351-670.514
7124.513
3.415-620.1077095.019
3.005

Across both data sets, we find that allowing for dynamics in baseline preferences provides an improvement in in-sample and predictive fit over the static model of Hasegawa etal. (2012). Our proposed suite of models that add a switching structure based on satiation
dynamics further improves model fit. Specifically, the SSDF1 specification provides thebest in-sample fit to the data. This suggests that any gains in flexibility offered by relating
preference dynamics to both satiation and past preference (models SSDF2 and SSDF3)
do not outweigh the costs of estimating more parameters. Moreover, the predictive fit formodel SSDF1 is only outperformed by other dynamic switching models. This is evidencein support of accommodating this discrete switching behavior in our data.
Estimates of parameters in model SSDF1 are provided in Appendix C. Specifically,tables C.1 and C.2 provide estimates of baseline preference and satiation parameters forthe carbonated beverage data, and tables C.3 and C.4 do the same for the yogurt data.
Across both data sets, we find that estimates of baseline preferences are roughly proportional to purchase shares, which helps validate our results. Table 3 reports the estimatesof β̄11 and β̄12 , which represent the effects of previous satiation levels on preference. In
particular, these estimates indicate the average effect across households on the direction14

of change with respect to previous satiation. We find that the preference vector of an
average consumer tends to rotate clockwise as previous satiation levels increase for bothcategories.
Table 3: Switching Equation Estimates

β̄11
β̄12

Carbonated Beverage
Mean SD

YogurtMean SD

0.275 (1.512)-0.201 (1.321)

0.351 (0.958)-0.119 (0.101)

Figure 2 illustrates the heterogeneity of preference change across both data sets. We
measure preference change for household h by computing the proportion of times theswitching equation in (8) is turned on over the course of R iterations and Th choices.
R Th
1 1 XX∗(r)
I(fht−1 ≥ 0).
kh =R Th r=1 t=2(20)

Here we call kh ∈ (0, 1) a propensity score for preference change, where large values indicate frequent change and small values indicate stable preferences. We find the distributionof propensity scores to be very different between the two product categories. In the carbonated beverage category, most households either exhibit extremely stable or extremely
dynamic preferences. In the yogurt category, the majority of households exhibit changing
preferences.
Figure 3 shows histograms of estimated coefficients on the switching equation. The left
and right figures plot estimates of the first and second preference directions, respectively.
We find the tails of the distribution to be much longer in the yogurt data, with a leftskew in the second preference direction. The patterns of rotation of preference vector
are heterogeneous, with some households have different signs implying moves in different
directions. There are also a significant number of households who have estimates very
close to zero, implying no change on one or both dimensions.

15

-Yogurt
Data(b)
Yogurt(a) Carbonated Beverage

600
200

400

Frequency

500 100000Frequency

2000

800

-Beverage Data-

0.0

0.2

0.4

0.6

0.8

1.0

0.0

0.2

0.4

0.6

0.8

1.0

Figure 2: Distributions of heterogeneity for the individual propensity score of preferencechange.
2

0

100

300

Frequency

200
100
0

Frequency

300

1 (a) Carbonated Beverages

-2

-1

0

1

2

3

-3

-2

beta1

-1

0

1

2

beta2

(b) Yogurt

2

100

200

Frequency

200
100

0

0

50

Frequency

300

300

1

-15

-10

-5

0

5

10

15

-30

beta1

-20

-10

0

10

beta2

Figure 3: Distributions of heterogeneity for the coefficients of switching equations.

16

5Implications

In this section, we investigate two possible implications of our model of preference dynamics. First, we discuss the impact of dynamics on the value of product assortments
and compare the compensating values implied by the dynamic factor model to those froma traditional static model. The results indicate that varieties are more highly valued withthe proposed dynamic model, implying that consumer highly value wide assortments. We
also examine the dynamics of preference change by considering three households withdifferent preference patterns that either exhibit frequent changes over time, moderately
frequent change, and non-changing preferences. We then consider how estimates for individual consumers are related to observed purchase behavior and switching structures.
The dynamic joint space maps are depicted.

5.1

Compensating Values

Compensating value (CV ) is measured by first computing the maximum attainable utility
from the observed choices using our utility model.

Vht (pht , Eht |θ h ) = max U (xht |θ h ) such that p0ht xht = Eht
xht

(21)

The posterior mean of parameters θ h = (ψ h , γ h , β h ) and the observed values of pht andEht are inserted into (21) to obtain xht and Vht for each household h and choice occasion t.
We also calculate maximum attainable utility under the case of product i being removed
from the choice set.

(i)

Vht (pht , Eht |θ h ) = max U (xht |θ h ) such that p0ht xht = Eht and xiht = 0.
xht

17

(22)

(i)

(i)

We then find the value CVht such that Vht and Vht are equal.
(i)

(i)

Vht (pht , Eht ) = Vht (pht , Eht + CVht )(23)

The set of CV estimates are provided in Appendix D. We report the median of the
distribution of heterogeneity, as near-zero estimates of the satiation parameter can leadto large compensating values and a right-skewed distribution. We also report estimates
(i)
(i) P
of CV as a share of budget, denoted P CVh = CVh / t Eht . Table D.1 and Table D.2
compare CV and PCV estimates for the static model and proposed dynamic model. Bothtables indicate significantly larger values of CV and PCV for dynamic model. This meansthat the value of product assortments in the store is underestimated by static model, andthe variety of products are supported by dynamism of consumer preference through theirexperience.

5.2

Preference Dynamics

Figure 4 plots preference directions for three households from each data set. The top
panel corresponds to the carbonated beverage category and the bottom corresponds to theyogurt category. Below each plot of preference directions, we provide the set of household
estimates of the preference switching model parameters. For the sake of brevity, we will
limit our discussion to the carbonated beverage data.
Figure 4a shows that the preference direction associated with the purchase occasions ofhousehold #314. The associated purchase records indicate positive demand across manyvarieties, the satiation score (fht ) remains at a high level, and the switching mechanism
works such that the coordinates in the attributed space move all the time. This consumer
can be characterized as a variety seeker. The satiation level affects both coordinates
positively, and this impact is much greater for the first dimension.
In contrast, Figure 4c provides the map and parameter estimates for household #66,

18

Carbonated Beverage Data(a) Frequent Change
#314
0.5

-1.0

1.0

-0.5

2

0
-2
-4

0.5

C17

C28 C16
18

C7

C29
-4

4

-2

0

2

4

C19

C19

fht
-0.6370.551-0.002
0.389
0.718
1.095
1.337
1.878
0.960
0.568
1.203
0.734

4

C9
C2 C10C26
3 C22
C11 C20 C30 C1C18
C3
C8 C24
C6
C25
C5
C4

C29
0

1.0

4

0.0
-0.5
-1.0

-4

-2

0

C9
C2C10
C26
C22
3
11C11 C20 C30 C1
C18
C3
C8
C24
C6
82
C25
C5
C17
C4
4
C28 C16
C7
9
51

C15
9
C21
5

C27 C23

2

2

0.5

6
C15
C21
10
7

C27 C23

-2

1.0

2
C13

1.0

4

C13

-4

0.5

C14

C14

t
1
2
3
4
5
6
7
8
9
10
11
12

0.0
C12

C12

0.0

0.0

-0.5

-0.5

(c) Little Change
#66

-1.0

-1.0

(b) Occasional Change
#122

ght1
0.480
2.563
2.752
-0.470
0.118
0.811
0.325
3.154
-0.3951.895-1.641
3.002

ght2-1.222-0.1440.227-0.319-0.5341.169
0.260-0.388-0.5031.619
0.043-1.292

kht
1.000
0.808
0.756
0.798
0.870
0.988
0.894
0.733
0.835
0.999
0.989
0.788

t
1
2
3
4
5
6
7
8
9

fht
-1.121
0.409-0.0060.233-0.618-1.043-0.670-1.185
0.525

ght1
1.078
0.123
-1.395
1.787
1.964
1.485
-0.289
1.380
1.065

ght2
-1.569
1.682
0.281
0.586
1.141
1.290
1.716
-1.872
0.952

kht
1.000
0.740
0.923
0.972
0.886
0.460
0.431
0.526
0.970

t
1
2
3
4
5
6
7
8

fht
-2.491-3.567-4.267-5.172-5.692-4.727-5.066-4.577

ght1
2.987
2.149
0.457
0.803
0.546
-1.084
0.160
1.372

ght2
-0.275-1.7160.168-2.743-0.2660.015
2.499-0.653

kht
1.000
0.331
0.080
0.031
0.133
0.013
0.001
0.001

Yogurt Data(e) Occasional Change
#18

1.0

fht
1.872
2.477
2.211
2.289
2.182
2.214

-0.5

0.0

ght1
0.122
-0.018-0.331-0.1190.129-0.418

0.5

1.0

ght2
0.381
-0.123-0.0240.065
0.066-0.037

-1.5

kht
1.000
0.928
0.828
0.946
0.866
0.919

t
1
2
3
4
5
6
7
8
9
10

1.0

-1.0

fht
0.034
0.373
0.502
1.219
-0.272
0.139
0.038
0.028
0.573
0.434

-0.5

0.0

ght1
0.400
0.800
0.353
-0.158-0.175-0.321
0.177-0.350-0.096-0.167

Y20
1

0.5

1.0

ght2
-0.024-0.121-0.130
0.215
0.145
0.101
-0.0100.194
0.015-0.016

1.0
0.5
0.0

Y1

Y13

-1.5

1.5

kht
1.000
0.742
0.821
0.459
0.974
0.491
0.465
0.653
0.643
0.846

Y3
Y27
Y26
Y24
Y33
Y14
Y31
Y6
Y34
Y29
Y5
Y9
Y4
Y15
Y35
Y22
Y25
Y8
Y19
Y7
Y10
Y30
Y21 Y12Y23
Y11 Y17
Y16
Y18

-0.5

0.5
0.0

Y1 1
2
3

-0.5

Y3
Y27
Y26
Y24
Y33
Y14
Y31
Y6
Y34
Y29
Y5
Y9
Y4
Y15
Y35
Y22
Y25
Y8
Y19
Y7
Y10
Y30
Y12
Y21
Y23
Y11 Y17
Y16
Y18

Y2
Y32

-1.0

Y20

Y32

Y13

1.5

0.5

-1.5

9

0.5

0.5

5

-1.5

-1.0

0.0

1.0

1.0

1.0

2

-1.5

-1.5

t
1
2
3
4
5
6

-1.0

Y13

8

0.0

Y1

-0.5

Y28

Y2

-0.5

Y3
Y27
Y26
Y24
Y33
Y14
Y31
Y6
Y34
Y29
Y5
Y9
Y4
Y15
Y35
Y22
Y25
Y8
Y19
Y7
Y10
Y30
Y12
Y21
Y23
Y17
Y11
Y16
Y18

-1.0

Y20

5

-1.0

1.0

-1.0

-0.5

3

0.5

Y32

-0.5

0.0

0.5

4

0.5

Y28

0.0

1.0

1
Y2

0.0

1.5

1.0

Y28

-0.5

1.5

-1.0

0.0

0.5

-0.5

0.0

-1.0

-0.5

1.5

-1.0

(f) Little Change
#15

-1.0

(d) Frequent Change
#251

t
1
2
3
4
5
6

fht
-1.729-1.284-1.711-1.073-1.721-1.502

-1.0

-0.5

ght1
-1.997-1.663-2.226-1.814-1.712-1.658

0.0

0.5

ght2
-1.292-1.485-1.205-1.373-1.527-1.321

1.0

1.5

kht
1.000
0.041
0.263
0.123
0.180
0.169

Figure 4: Preference directions for three households are plotted from each data set. The
top panel corresponds to carbonated beverage bottom corresponds to yogurt. We also
provide the set of household estimates of the preference switching model parameters.
19which exhibits no preference changes. For instance, in the data we observe this householdto purchase caffeine free Diet Coke or Diet Pepsi in 73% shopping trips. The satiation level
negatively and positively affects the first and second coordinates to change, respectively,
and it is much greater for the first coordinate. Together, these figures demonstrate theflexibility of the proposed dynamic model for studying preferences.

6

Concluding Remarks

In this paper we develop a model of dynamic variety seeking that relates preference changes
to brand satiation. Two dynamic factor models are developed for baseline and satiation
parameters in a direct utility model of horizontal variety that are integrated so that
preference can change abruptly when the satiation factor score exceeds a threshold level.
We find strong empirical support for our model in two datasets, and provide evidence thatwide product assortments are undervalued when dynamic preference changes are ignored.
Our model is motivated by theories of adoption and change similar to McAlister (1982)
and McAlister and Pessemier (1982), who proposed a framework for relating satiation
to preference. The presence of different operating regimes also has a long history in themarketing and psychology literature (e.g., Coombs & Avrunin, 1977).
We compare our model to six alternative specifications, including a static model implying that preference does not change at all, a dynamic model without a switching structure
on preference change, and dynamic models with switching structures. The models in thelast category are composed of non-parametric local linear trend, parametric regression,and their hybrid models. When applied to two household panel data sets, both measuresof model fit support the model with a switching structure and parametric regression.
The empirical applications demonstrate that abrupt preference changes are common,as the majority of consumers are found to change their preferences over the course of
their purchase history. Our results indicate that the standard modeling assumption of20

static preferences may not always hold, particularly in light of the large increase in model
fit for our proposed dynamic models. We find that consumers with wider varieties ofpurchases tend to change their preferences more often – that is, through periodic shifts inpreference as described by the model. This finding is consistent with consumers having
well defined tastes that vary through time, as opposed to broad tastes for which many
brands will suffice. Our results are consistent with emerging evidence of binge behavior,or “clumpliness” in consumer demand that is not consistent with the notion of stablepreferences (Zhang et al., 2015).
Future research is needed to understand the context of purchase and consumption.
Our results indicate that the unit of analysis for heterogeneity is not the respondent, butinstead the respondent at a specific purchase occasion who is influenced by their pastdecisions and other factors. Additional work is needed to identify and integrate thesefactors and past events into models of consumer decision making that allow marketers toanticipate shifts in preference. We believe that the temporal study of satiation, and othertriggers of preference change, is a fruitful area for future research.

21

A

Product Descriptions
Table A.1: Product Descriptions – Carbonated Beverage
C1
C2
C3
C4
C5
C6
C7
C8
C9
C10
C11
C12
C13
C14
C15
C16
C17
C18
C19
C20
C21
C22
C23
C24
C25
C26
C27
C28
C29
C30

Variety
Pepsi
Diet Pepsi
Mountain Dew
Pepsi CF
Diet Pepsi CF
Wild Cherry Pepsi
Schweppes
Coke CF
SpriteDiet Coke
Diet Sprite
Diet Coke CF
Cherry Coke
Coke
Barqs
A&W
7Up
Diet 7Up
Mug
PL Cola
PL Cream Soda
PL Cherry
PL Fruit Punch Soda
PL Ginger Ale
PL Grape
PL Lemon Lime
PL Orange
PL Diet Ginger Ale
PL Diet Orange
PL Root Beer
TOTAL

Incidence
788
429
214
193
285
126
195
242
673
783
270
536
98
1631
145
41
151
134
172
754
379
91
105
483
299
261
882
357
286
318
11321

Quantity
1460
773
288
316
480
149
242
407
860
1391
411
1044
124
2950
163
51
193
172
193
1050
456
100
125
584
352
282
1130
447
405
480
17078

Notes: CF = Caffeine Free, PL = Private Label

22

Corner Solutions
428 (0.54)
221 (0.52)
63 (0.29)
96 (0.50)
148 (0.52)
49 (0.39)
87 (0.45)
109 (0.45)
170 (0.25)
366 (0.47)
100 (0.37)
289 (0.54)
17 (0.17)
872 (0.53)
46 (0.32)
37 (0.90)64 (0.42)
71 (0.53)
69 (0.40)
354 (0.47)
134 (0.35)
25 (0.27)
20 (0.19)
196 (0.41)
81 (0.27)
74 (0.28)
396 (0.45)
223 (0.62)
80 (0.28)
117 (0.37)5002 (0.44)

Interior Solutions
360 (0.46)
208 (0.48)
151 (0.71)
97 (0.50)
137 (0.48)
77 (0.61)
108 (0.55)
133 (0.55)
503 (0.75)
417 (0.53)
170 (0.63)
247 (0.46)
81 (0.83)
759 (0.47)
99 (0.68)
4 (0.10)87 (0.58)
63 (0.47)
103 (0.60)
400 (0.53)
245 (0.65)
66 (0.73)
85 (0.81)
287 (0.59)
218 (0.73)
187 (0.72)
486 (0.55)
134 (0.38)
206 (0.72)
201 (0.63)6319 (0.56)

Table A.2: Product Descriptions – Yogurt
Y1
Y2
Y3
Y4
Y5
Y6
Y7
Y8
Y9
Y10
Y11
Y12
Y13
Y14
Y15
Y16
Y17
Y18
Y19
Y20
Y21
Y22
Y23
Y24
Y25
Y26
Y27
Y28
Y29
Y30
Y31
Y32
Y33
Y34
Y35

Variety
Yoplait Original Strawberry
Yoplait Original Mountain BerryYoplait Original Mixed BerryYoplait Original Key Lime Pie
Yoplait Original French Vanilla
Yoplait Light Blackberry
Yoplait Light Vanilla
Yoplait Light Red Raspberry
Yoplait Light Blueberry
Yoplait Light Peach
Dannon FOTB Strawberry
Dannon FOTB Blueberry
Dannon FOTB Peach
Dannon FOTB Mixed BerryColombo Classic Blackberry
Stonyfield Farm Vanilla
Stonyfield Farm Strawberry
Stonyfield Farm Peach
Stonyfield Farm Raspberry
Stonyfield Farm Blueberry
Dannon FOTB Raspberry
Dannon LNF Strawberry Banana
Dannon LNF Blueberry
Dannon LNF Raspberry
Dannon LNF Strawberry
Dannon LNF Vanilla
Colombo Classic Vanilla
Colombo Classic Blueberry
Colombo Classic Peach
Colombo Classic Strawberry
PL Blueberry
PL Cherry
PL Peach
PL Raspberry
PL Strawberry
TOTAL

Incidence
383
392
432
383
330
327
260
285
318
269
147
228
121
170
351
122
156
188
197
201
145
302
462
414
319
402
358
503
387
453
453
462
423
386
484
11213

Quantity
680
819
886
824
744
604
714
491
656
482
232
457
239
295
619
247
218
302
339
395
247
522
790
700
537
1014
974
1223
763
866
975
982
697
674
1004
22211

Corner Solutions
90 (0.23)
80 (0.20)
111 (0.26)
145 (0.38)
116 (0.35)
26 (0.08)
64 (0.25)
25 (0.09)
31 (0.10)
20 (0.07)
12 (0.08)
50 (0.22)
26 (0.21)
29 (0.17)
76 (0.22)
29 (0.24)
13 (0.08)
18 (0.10)
21 (0.11)
32 (0.16)
21 (0.14)
46 (0.15)
102 (0.22)
81 (0.20)
59 (0.18)
177 (0.44)
134 (0.37)
138 (0.27)
64 (0.17)
77 (0.17)
55 (0.12)
87 (0.19)
41 (0.10)
39 (0.10)60 (0.12)2195 (0.20)

Notes: FOTB = Fruit on the Bottom, LNF = Light & Fit, PL = Private Label

23

Interior Solutions
293 (0.77)
312 (0.80)
321 (0.74)
238 (0.62)
214 (0.65)
301 (0.92)
196 (0.75)
260 (0.91)
287 (0.90)
249 (0.93)
135 (0.92)
178 (0.78)
95 (0.79)
141 (0.83)
275 (0.78)
93 (0.76)
143 (0.92)
170 (0.90)
176 (0.89)
169 (0.84)
124 (0.86)
256 (0.85)
360 (0.78)
333 (0.80)
260 (0.82)
225 (0.56)
224 (0.63)
365 (0.73)
323 (0.83)
376 (0.83)
398 (0.88)
375 (0.81)
382 (0.90)
347 (0.90)424 (0.88)9018 (0.80)

B

MCMC Algorithms

Below we describe our approach from sampling from each parameter’s full conditional
distribution.
1. ψ ∗ht |xht , γ ∗ht , b, g ht , Vp(ψ ∗ht |xht , γ ∗ht , b, g ht , V )


1
−1/2
0 −1
∝ det |V |exp − (ψ ht − bg ht ) V (ψ ht − bg ht )×Lht (ψ ht )
2

(B.1)

The term Lht (ψ ht ) is the likelihood function for consumer h = 1, . . . , H at purchasetime t = 1, . . . , Th , where the likelihood function is composed of a combination ofdensity and mass, arising from the interior and corner solutions, respectively, andis defined for experimental data as
Z gn +1

Z gm

1

L = φ(g1 , . . . , gn1 )|J| ×

···
−∞

−∞

f (εgn1 , . . . , εm )dεgn1 · · · dεm(B.2)

where the probability mass function can be evaluated in closed-form due to EV(0,1)
errors. We sample from this posterior using a Metropolis-Hastings algorithm using
random-walk proposals of the form∗(r)∗(r−1)

ψ ht = ψ ht

+ λψ , λψ ∼ N (0, k · I)

(B.3)

where k was chosen to be 0.5.
2. γ ∗ht |xht , ψ ∗ht , a, fht , Σp(γ ∗ht |xht , ψ ∗ht , a, fht , Σ)


1 ∗
0 −1
∗
−1/2
×Lht (γ ∗ht )∝ det |Σ|exp − (γ ht − afht ) V (γ ht − af ght )
2

24

(B.4)

We again use a random-walk Metropolis-Hastings algorithm:∗(r)∗(r−1)

γ ht = γ ht

+ λγ , λγ ∼ N (0, k 0 · I)

(B.5)

where k 0 was chosen to be 0.5.
3. a|γ ∗ht , fht , ΣUnder the assumption of uncorrelated ak ’s, we define f h = (fh1 , . . . , fhTh )0 to be a Th P
dimensional vector and let f = (f 01 , . . . , f 0H )0 be a ( h Th )-dimensional vector. We
define γ hk and γ̄ k in an analogous fashion. Then, the posterior can be derived froma normal regression equation with coefficient parameter vector γ̄ k and explanatory
matrix f . That is,ak |γ ∗ht , fht , Σ ∼ N (âk , Ak )

(B.6)

−1 0
−1 0
−1
where Ak = (A−1and âk = Ak (A−10 + σk f f )0 a0 + σk f γ̄ k ). The identification

condition is considered when k ≤ 1.
4. b|ψ ∗ht , g ht , V
As in step (3), we define g h = (g h1 , . . . , g hTh )0 to be a Th ×2 matrix, g = (g 01 , . . . , g 0H )0P∗∗, . . . , ψhTh j )0 a Th -dimensional vector, and ψ̄ j =a ( h Th ) × 2 matrix, ψ ∗hj = (ψh1jP00(ψ ∗1j , . . . , ψ ∗Hj )0 a ( h Th )-dimensional vector. Just as before,
bj |ψ ∗ht , g ht , V ∼ N (b̂j , Bj )(B.7)

where Bj = (B0−1 + vj−1 g 0 g)−1 and b̂j = Bj (B0−1 b0 + vj−1 g 0 ψ̄ j ). The identification
condition is considered when j ≤ 2.
5. fht , g ht |γ ∗ht , ψ ∗ht , Σ, V
We reformulate the measurement equation as25

γ ∗ht
ψ ∗ht






     
 

a 0
fht
εht
εht
Σ 0
=
+
,
∼ N 0,
0 b
g ht
δ ht
δ ht
0 V

(B.8)

as well as the system equation as



fht
g ht




=

1

−Kht β h10(1 − Kht )I    
 

fht−1
νht
νht
1 0
+
,
∼ N 0,
g ht−1
ω ht
ω ht
0 Kht
(B.9)

∗
≥ rh ). We use Carter and Kohn (1994)
where β h1 = (βh11 , βh12 )0 and Kht = I(fht−1

for a time-varying coefficient in the state space model described above.
6. SSDF1: β 1 = (β11 , β12 )0 |fht , g ht , β̄ 10

βh1k ∼ N (β̂h1k , (f ∗h f h + 1)−1 k = 1, 2∗0∗0(B.10)∗

where β̂h1k = (f̃ h f̃ h + 1)−1 (f̃ h g̃ hk + β̄1k ) and f̃ h = −f̃ h and f̃ h and g̃ hk are thedata matrix and vector, respectively, collected in the case of fht−1 ≥ rh . If f̃ h =(i.e., Kht = 0 for all t), the posterior is βh1k ∼ N (β̄1k , 1) by homogeneity.
7. SSDF1: β̄ 1 = (β̄11 , β¯12 )0 |β 11 , . . . , β H1 , vβ0β̄1k ∼ N (β̂1k , (H + vβ0 )−1 k = 1, 2
where β̂h1k = (H + vβ0 )−1 ((B.11)−1h βhk + vβ0 β0 ).

P

8. SSDF3: β h1 = (βh11 , βh12 )0 , β h2 = (βh21 , βh22 )0 |fht , g ht , β̄ 1 , β̄ 2
The parameters β h1 , β h2 , β̄ 1 , and β̄ 2 are sampled according to the MCMC procedureof the standard hierarchical Bayesian regression model shown above.

β hk ∼ N (β̄ k , I)

26

(B.12)

We use the data f̃ h and g̃ hk when fht−1 ≥ rh . If f̃ h = (i.e., Kht = 0 for all t), theposterior is β hk ∼ N (β̄ k , I).

27

C

Estimation Results
Table C.1: Baseline Preference Estimates – Carbonated Beverage

Pepsi
Diet Pepsi
Mountain Dew
Pepsi CF
Diet Pepsi CF
Wild Cherry Pepsi
Schweppes
Coke CF
SpriteDiet Coke
Diet Sprite
Diet Coke CF
Cherry Coke
Coke
Barqs
A&W
7Up
Diet 7Up
Mug
PL Cola
PL Cream Soda
PL Cherry
PL Fruit Punch Soda
PL Ginger Ale
PL Grape
PL Lemon Lime
PL Orange
PL Diet Ginger Ale
PL Diet Orange
PL Root Beerψ∗
Mean SD
0.365 (0.091)
0.107 (0.086)-0.023 (0.081)-0.360 (0.102)-0.071 (0.130)-0.226 (0.079)-0.012 (0.099)-0.038 (0.099)
0.388 (0.099)
0.683 (0.091)-0.038 (0.138)
0.089 (0.156)-0.310 (0.129)
1.721 (0.098)-0.170 (0.103)-0.275 (0.109)-0.027 (0.101)-0.168 (0.109)-0.314 (0.095)
0.279 (0.113)-0.107 (0.097)-0.415 (0.078)-0.445 (0.082)
0.053 (0.131)-0.124 (0.130)-0.260 (0.107)
0.460 (0.120)-0.259 (0.101)-0.440 (0.113)
- -

b
Mean
1.000
0.883
1.000
1.247 -0.146
0.173 -1.459-1.503 -0.851-0.662 -0.383
5.996 -2.523-0.400 -0.257-1.768
1.021
1.832
1.015
-3.036
0.225
0.184
5.463
0.608
3.435
-2.421
4.769
2.708
2.589
3.671 -2.079
4.876 -1.272
1.591 -0.034-1.146 -7.595-1.256
0.071
2.553
2.370
-2.5520.535-0.2122.345
0.759 -0.295
1.589 -0.507
1.028
0.759
-1.5842.307
2.307 -2.258
0.357 -4.447-

Notes: CF = Caffeine Free, PL = Private Label

28

SD(0.025) (0.028) (0.038)(0.031) (0.032)(0.049) (0.028)(0.028) (0.038)(0.027) (0.029)(0.027) (0.035)(0.032) (0.027)(0.028) (0.028)(0.027) (0.029)(0.022) (0.032)(0.024) (0.025)(0.031) (0.037)(0.023) (0.034)(0.028) (0.032)(0.025) (0.032)(0.021) (0.031)(0.031) (0.029)(0.025) (0.035)(0.028) (0.025)(0.023) (0.038)(0.025) (0.026)(0.026) (0.033)(0.034) (0.023)(0.028) (0.029)(0.031) (0.035)(0.029) (0.032)(0.027) (0.044)
-

V
Mean
0.391
0.901
0.730
0.550
0.071
0.966
0.715
0.662
0.848
0.446
0.550
0.542
0.726
0.546
0.455
0.984
0.177
0.417
1.240
0.430
1.331
0.320
0.774
0.097
0.755
0.642
0.374
1.070
0.349
-

SD
(0.259)(0.166)(0.271)(0.231)(0.354)(0.394)(0.298)(0.245)(0.333)(0.162)(0.138)(0.228)(0.247)(0.323)(0.167)(0.402)(0.366)(0.224)(0.341)(0.250)(0.097)(0.239)(0.198)(0.290)(0.350)(0.401)(0.368)(0.440)(0.269)-

Table C.2: Satiation Estimates – Carbonated Beverage

Pepsi
Diet Pepsi
Mountain Dew
Pepsi CF
Diet Pepsi CF
Wild Cherry Pepsi
Schweppes
Coke CF
SpriteDiet Coke
Diet Sprite
Diet Coke CF
Cherry Coke
Coke
Barqs
A&W
7Up
Diet 7Up
Mug
PL Cola
PL Cream Soda
PL Cherry
PL Fruit Punch Soda
PL Ginger Ale
PL Grape
PL Lemon Lime
PL Orange
PL Diet Ginger Ale
PL Diet Orange
PL Root Beer

Mean
0.643
0.747
0.213
0.295
0.003
-0.4440.100
0.238-0.531
0.657
0.504
0.270
0.188
-0.5430.087
0.444-0.520-0.1680.676-0.6600.083-0.842-0.2610.125-0.241
0.249-0.028-0.131
0.216
0.047

γ∗
SD
(0.243)(0.477)(0.455)(0.299)(0.297)(0.351)(0.290)(0.285)(0.393)(0.249)(0.491)(0.261)(0.244)(0.215)(0.238)(0.424)(0.448)(0.412)(0.249)(0.557)(0.394)(0.295)(0.379)(0.281)(0.424)(0.302)(0.370)(0.160)(0.453)(0.422)

a
Mean
1.000
0.605
0.014
0.075
0.390
-0.203-0.007-0.032-0.010-0.001-0.0540.041-0.106-0.147-0.3640.102
0.253-0.101
0.336
0.328
0.134
-0.416-0.3800.190-0.1060.180-0.056-0.4560.192
0.387

Notes: CF = Caffeine Free, PL = Private Label

29

SD(0.033)(0.034)(0.032)(0.021)(0.031)(0.026)(0.044)(0.029)(0.028)(0.031)(0.030)(0.033)(0.023)(0.032)(0.030)(0.029)(0.035)(0.028)(0.029)(0.036)(0.025)(0.034)(0.030)(0.025)(0.023)(0.030)(0.025)(0.033)(0.029)

Mean
1.484
0.934
0.552
0.695
0.493
0.661
0.913
0.546
0.926
0.309
0.957
0.159
0.646
0.626
0.536
0.429
0.618
1.235
1.000
0.548
0.430
0.632
0.272
0.090
0.704
0.953
0.929
0.789
0.339
0.763

Σ
SD
(0.144)(0.103)(0.057)(0.112)(0.134)(0.043)(0.081)(0.139)(0.130)(0.064)(0.154)(0.116)(0.091)(0.074)(0.120)(0.089)(0.036)(0.053)(0.257)(0.139)(0.150)(0.197)(0.107)(0.045)(0.159)(0.083)(0.034)(0.097)(0.130)(0.116)

Table C.3: Baseline Preference Estimates – Yogurt

Yoplait Original Strawberry
Yoplait Original Mountain BerryYoplait Original Mixed BerryYoplait Original Key Lime Pie
Yoplait Original French Vanilla
Yoplait Light Blackberry
Yoplait Light Vanilla
Yoplait Light Red Raspberry
Yoplait Light Blueberry
Yoplait Light Peach
Dannon FOTB Strawberry
Dannon FOTB Blueberry
Dannon FOTB Peach
Dannon FOTB Mixed BerryColombo Classic Blackberry
Stonyfield Farm Vanilla
Stonyfield Farm Strawberry
Stonyfield Farm Peach
Stonyfield Farm Raspberry
Stonyfield Farm Blueberry
Dannon FOTB Raspberry
Dannon LNF Strawberry Banana
Dannon LNF Blueberry
Dannon LNF Raspberry
Dannon LNF Strawberry
Dannon LNF Vanilla
Colombo Classic Vanilla
Colombo Classic Blueberry
Colombo Classic Peach
Colombo Classic Strawberry
PL Blueberry
PL Cherry
PL Peach
PL Raspberry
PL Strawberryψ∗
Mean SD
0.279 (0.108)
0.139 (0.089)
0.163 (0.151)
0.093 (0.131)
0.071 (0.032)
0.031 (0.181)-0.109 (0.071)
0.016 (0.113)
0.017 (0.162)-0.158 (0.018)-0.240 (0.051)-0.052 (0.131)-0.393 (0.079)-0.272 (0.158)
0.074 (0.110)-0.390 (0.112)-0.211 (0.086)-0.323 (0.182)-0.180 (0.077)-0.301 (0.166)-0.304 (0.187)-0.012 (0.175)
0.294 (0.082)
0.146 (0.107)-0.023 (0.118)
0.142 (0.185)
0.165 (0.100)
0.416 (0.142)
0.238 (0.147)
0.252 (0.171)
0.122 (0.092)
0.235 (0.027)
0.107 (0.200)
0.095 (0.169)
- -

b
Mean
1.000
0.326
1.000
-0.001
0.325
0.088
0.034
0.039
0.043
0.037
0.074
-0.056 -0.070-0.009 -0.023
0.019
0.039
0.071 -0.111-0.329 -0.348-0.068 -0.157-0.889 -1.221
0.062
0.085
0.216
0.010
-0.591 -0.509
0.018 -0.283-0.540 -0.673
0.249 -0.033-1.057 -0.676-0.576 -0.221-0.070 -0.013
0.388 -0.271
0.283
0.115
0.005 -0.012-0.089
0.152
0.027
0.167
0.143
1.310
-0.091
0.057
0.276 -0.123-0.004
0.073
0.134
0.609
0.065
0.100
0.066
0.065
-

SD
(0.019) (0.029) (0.032)(0.025) (0.004)(0.017) (0.018)(0.032) (0.046)(0.032) (0.023)(0.027) (0.039)(0.033) (0.025)(0.007) (0.031)(0.007) (0.022)(0.034) (0.019)(0.012) (0.033)(0.023) (0.025)(0.029) (0.018)(0.026) (0.027)(0.033) (0.033)(0.029) (0.023)(0.014) (0.021)(0.036) (0.016)(0.019) (0.012)(0.029) (0.057)(0.024) (0.024)(0.035) (0.032)(0.035) (0.027)(0.030) (0.026)(0.028) (0.038)(0.030) (0.042)(0.035) (0.021)(0.034) (0.018)(0.029) (0.020)(0.029) (0.006)(0.042) (0.016)(0.039) (0.039)-

Notes: FOTB = Fruit on the Bottom, LNF = Light & Fit, PL = Private Label

30

V
Mean
0.211
0.300
0.134
0.093
0.338
0.255
0.471
0.333
0.411
0.528
0.195
0.191
0.356
0.295
0.244
0.169
0.255
0.359
0.254
0.397
0.355
0.238
0.199
0.246
0.274
0.240
0.541
0.089
0.275
0.226
0.158
0.333
0.410
0.240
-

SD
(0.188)(0.360)(0.373)(0.318)(0.226)(0.286)(0.364)(0.181)(0.066)(0.317)(0.113)(0.141)(0.213)(0.131)(0.050)(0.118)(0.280)(0.352)(0.281)(0.209)(0.227)(0.175)(0.244)(0.068)(0.077)(0.047)(0.017)(0.442)(0.089)(0.289)(0.218)(0.138)(0.225)(0.288)-

Table C.4: Satiation Estimates – Yogurt

Yoplait Original Strawberry
Yoplait Original Mountain BerryYoplait Original Mixed BerryYoplait Original Key Lime Pie
Yoplait Original French Vanilla
Yoplait Light Blackberry
Yoplait Light Vanilla
Yoplait Light Red Raspberry
Yoplait Light Blueberry
Yoplait Light Peach
Dannon FOTB Strawberry
Dannon FOTB Blueberry
Dannon FOTB Peach
Dannon FOTB Mixed BerryColombo Classic Blackberry
Stonyfield Farm Vanilla
Stonyfield Farm Strawberry
Stonyfield Farm Peach
Stonyfield Farm Raspberry
Stonyfield Farm Blueberry
Dannon FOTB Raspberry
Dannon LNF Strawberry Banana
Dannon LNF Blueberry
Dannon LNF Raspberry
Dannon LNF Strawberry
Dannon LNF Vanilla
Colombo Classic Vanilla
Colombo Classic Blueberry
Colombo Classic Peach
Colombo Classic Strawberry
PL Blueberry
PL Cherry
PL Peach
PL Raspberry
PL Strawberryγ∗
Mean SD-0.015 (0.613)-0.072 (0.821)-0.160 (1.051)
0.469 (0.385)
0.246 (1.477)
0.218 (1.748)
0.956 (2.289)-2.585 (1.430)
0.459 (0.952)-1.250 (1.936)-0.360 (1.017)
0.009 (1.223)
2.453 (1.100)
0.085 (1.208)
0.014 (1.945)
0.734 (0.527)-0.332 (1.336)
0.582 (0.728)-0.051 (2.153)-0.997 (1.160)
0.457 (2.200)
1.633 (0.505)-0.052 (0.487)-0.239 (1.223)-0.134 (1.205)
0.635 (0.613)
3.073 (0.675)-0.026 (1.442)-0.789 (1.314)
0.732 (1.609)
0.025 (1.166)
0.058 (1.220)
0.251 (1.353)
0.955 (0.312)-0.091 (0.709)

a
Mean
1.000
-0.077-0.160
0.078
0.012
0.050
0.096
0.008
-0.056-0.251-0.0220.015-0.2040.079
0.156-0.1660.085-0.069
0.329
0.002
0.299
0.045
0.076
-0.020-0.122-0.0550.096
0.310-0.4520.173-0.2530.002-0.006
0.011
0.301

SD
(0.034)(0.010)(0.005)(0.014)(0.002)(0.014)(0.016)(0.004)(0.020)(0.023)(0.015)(0.002)(0.001)(0.013)(0.017)(0.010)(0.017)(0.015)(0.018)(0.014)(0.025)(0.023)(0.007)(0.010)(0.016)(0.010)(0.008)(0.025)(0.007)(0.020)(0.014)(0.010)(0.019)(0.003)

Mean
0.720
0.652
0.709
0.917
0.369
0.447
0.799
1.088
0.826
0.194
0.841
0.719
0.468
0.784
0.509
0.811
0.698
0.731
1.416
0.426
0.483
0.753
0.647
0.629
0.172
0.166
0.659
0.701
1.084
0.308
0.358
0.826
1.435
1.021
0.428

Notes: FOTB = Fruit on the Bottom, LNF = Light & Fit, PL = Private Label

31

Σ
SD
(0.442)(0.314)(0.271)(0.302)(0.498)(0.481)(0.481)(0.355)(0.362)(0.418)(0.210)(0.218)(0.300)(0.363)(0.346)(0.400)(0.333)(0.363)(0.445)(0.411)(0.163)(0.413)(0.257)(0.384)(0.384)(0.646)(0.598)(0.222)(0.337)(0.328)(0.362)(0.423)(0.309)(0.421)(0.339)D

Compensating Value Estimates
Table D.1: Compensating Value – Carbonated Beverage

Pepsi
Diet Pepsi
Mountain Dew
Pepsi CF
Diet Pepsi CF
Wild Cherry Pepsi
Schweppes
Coke CF
SpriteDiet Coke
Diet Sprite
Diet Coke CF
Cherry Coke
Coke
Barqs
A&W
7Up
Diet 7Up
Mug
PL Cola
PL Cream Soda
PL Cherry
PL Fruit Punch Soda
PL Ginger Ale
PL Grape
PL Lemon Lime
PL Orange
PL Diet Ginger Ale
PL Diet Orange
PL Root Beer

StaticCV
PCV
0.0195 0.0005
0.0160 0.0003
0.0162 0.0003
0.0172 0.0003
0.0161 0.0003
0.0137 0.0003
0.0149 0.0003
0.0148 0.0003
0.0155 0.0002
0.0197 0.0003
0.0151 0.0003
0.0170 0.0003
0.0182 0.0003
0.0184 0.0003
0.0143 0.0004
0.0161 0.0003
0.0152 0.0003
0.0169 0.0003
0.0166 0.0003
0.0160 0.0003
0.0160 0.0003
0.0163 0.0003
0.0178 0.0003
0.0170 0.0003
0.0160 0.0003
0.0151 0.0003
0.0171 0.0003
0.0194 0.0004
0.0150 0.0003
0.0155 0.0003

SSDF1
CV
PCV
20.2509 0.3491
5.0299 0.1465
3.9403 0.1134
3.7450 0.1036
5.3870 0.1380
6.6039 0.1830
8.4965 0.2112
11.7279 0.2525
8.0336 0.1667
8.7617 0.2237
14.3698 0.2753
16.9473 0.2852
14.4814 0.2754
17.0918 0.3034
23.3214 0.4352
12.3346 0.2435
9.7593 0.2274
8.2013 0.1628
11.1629 0.2563
18.5633 0.3717
12.4827 0.2908
12.1290 0.2267
7.0369 0.1979
7.2441 0.1984
7.5850 0.1952
8.3066 0.2016
10.1558 0.2423
17.8160 0.3501
15.8729 0.3277
14.4087 0.2485

Notes: (1) CF = Caffeine Free, PL = Private Label; (2)The table reports posterior medians.

32

Table D.2: Compensating Value – Yogurt

Yoplait Original Strawberry
Yoplait Original Mountain BerryYoplait Original Mixed BerryYoplait Original Key Lime Pie
Yoplait Original French Vanilla
Yoplait Light Blackberry
Yoplait Light Vanilla
Yoplait Light Red Raspberry
Yoplait Light Blueberry
Yoplait Light Peach
Dannon FOTB Strawberry
Dannon FOTB Blueberry
Dannon FOTB Peach
Dannon FOTB Mixed BerryColombo Classic Blackberry
Stonyfield Farm Vanilla
Stonyfield Farm Strawberry
Stonyfield Farm Peach
Stonyfield Farm Raspberry
Stonyfield Farm Blueberry
Dannon FOTB Raspberry
Dannon LNF Strawberry Banana
Dannon LNF Blueberry
Dannon LNF Raspberry
Dannon LNF Strawberry
Dannon LNF Vanilla
Colombo Classic Vanilla
Colombo Classic Blueberry
Colombo Classic Peach
Colombo Classic Strawberry
PL Blueberry
PL Cherry
PL Peach
PL Raspberry
PL Strawberry

StaticCV
PCV
0.5490 0.0230
0.5016 0.0208
0.4663 0.0175
0.5364 0.0218
0.5546 0.0186
0.4779 0.0197
0.4737 0.0206
0.4465 0.0209
0.5127 0.0205
0.4772 0.0167
0.3911 0.0183
0.5199 0.0212
0.4066 0.0164
0.4875 0.0185
0.4620 0.0228
0.4172 0.0173
0.4590 0.0161
0.4837 0.0189
0.4330 0.0206
0.4736 0.0222
0.5147 0.0147
0.3848 0.0178
0.5130 0.0202
0.5229 0.0215
0.3932 0.0175
0.4636 0.0208
0.6120 0.0195
0.5123 0.0153
0.5952 0.0242
0.5589 0.0247
0.5812 0.0215
0.5303 0.0181
0.4834 0.0150
0.5532 0.0225
0.4818 0.0139

SSDF1
CV
PCV
12.4628 0.7382
1.6155 0.1373
4.7407 0.2807
8.8176 0.5082
5.5190 0.2571
7.1409 0.3615
7.6276 0.4045
4.5683 0.1997
8.5746 0.4018
6.6978 0.2903
7.0690 0.3511
9.1290 0.6163
7.7693 0.4446
4.5784 0.2852
5.7094 0.3335
9.0676 0.7036
9.5513 0.5074
7.6548 0.4301
8.0039 0.4764
8.3628 0.5760
9.4719 0.5076
7.5411 0.3459
9.8317 0.5973
12.8920 0.6775
8.6497 0.5356
8.1320 0.3287
6.6391 0.3694
7.0741 0.3699
9.6205 0.5396
8.7918 0.4928
7.9742 0.4067
6.5377 0.3454
6.3499 0.3378
8.4701 0.5316
8.4998 0.5472

Notes: (1) FOTB = Fruit on the Bottom, LNF = Light & Fit,
PL = Private Label; (2) The table reports posterior medians.

33

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