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An Assessment of When, Where and Under What Conditions In-Store
Sampling is Most Effective
Sandeep R. Chandukala a , Jeffrey P. Dotson b,∗ , Qing Liu ca Singapore Management University, Singapore
b Brigham Young University, United Statesc University of Wisconsin-Madison, United States

Abstract
In-store product sampling is a commonly used promotional technique designed to give prospective consumers an opportunity to experiencea product prior to purchase. While prior research has documented a positive relationship between short-term sales and perceptual measures of
the customer shopping experience, little is known about the long-term impact of sampling or factors that moderate its success. In this paper, wedevelop an empirical approach that allows us to study the short-term and long-term effects of in-store sampling on both own and competitive
products. We apply our approach to six store-level scanner data sets across four different product categories and show that in-store samplinghas both an immediate (short-term) and sustained (long-term) impact on sales. We also show that the impact of sampling on sales is moderated
by the characteristics of the store conducting the event, and that repeated sampling for a single product leads to a multiplicative increase in its
long-term sales performance. We find that, unlike many types of in-store promotion, sampling results in a category expansion effect as opposed toa pure substitution effect. We contrast the immediate and long-term sales patterns for in-store sampling to those of product displays and discuss
managerially relevant differences. Finally, we demonstrate incremental profit implications and store selection scenarios for different incremental
costs of conducting the in-store events using constrained optimizations.
© 2017 New York University. Published by Elsevier Inc. All rights reserved.
Keywords: In-store sampling; Marketing mix modeling; Retail strategy

Introduction
Manufacturers regularly engage in in-store promotions thatinvolve the distribution of free product samples. This is a common practice in the grocery industry where manufacturers seek
to distinguish their products from a myriad of competitors.
According to a VSS Communications Industry Forecast, marketers spent $2.21 billion dollars on product sampling in 2009.
In February 2009, Walmart launched a weekly program called“Bright Ideas” that aims to make product sampling and demonstrations an integral part of a customer’s in-store experience(Industry Insights 2009). Furthermore, a recent article describes
how food product sampling is again on the rise with companies
taking advantage of options like SamplingLab (Heneghan 2015).

∗ Corresponding author.

These announcements have generated significant interest among
both manufacturers and retailers alike in determining how to
optimally execute and measure the success of these events.
Sampling provides consumers with an evocative, visceralexperience that allows them to touch, taste and smell the product,thus appealing to both hedonic and utilitarian values. As a result,the impact of product sampling on sales has been shown to belarger than that of other forms of marketing activity like advertising Mcguinness et al. 1992(Mcguinness, Gendall, and Mathew
1992). Manufacturers prefer in-store sampling events to pricebased promotions like couponing, temporary price reductions(TPR) or rebates, as they add value to a product by encouraging
trial without reducing margins or altering consumer expectationsof price (Simpson 2006). Retailers also benefit from the use ofin-store sampling as it enhances the consumer shopping experience, thus encouraging both increased sales and store loyalty(Dong-Mo 2003; Sprott and Shimp 2004)

addresses:
sandeepc@smu.edu.sg(S.R.
Chandukala),E-mailjeff.dotson@byu.edu (J.P. Dotson), qliu@bus.wisc.edu (Q. Liu).
http://dx.doi.org/10.1016/j.jretai.2017.07.002
0022-4359/© 2017 New York University. Published by Elsevier Inc. All rights reserved.

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In contrast to at-home sampling promotions where freesamples are delivered to consumer households, in-store sampling promotions occur at point-of-purchase and have uniquecharacteristics that require studies of their own (Heilman,
Lakishyk, and Radas 2011). Past research on product trial has
primarily focused on at-home sampling (Bawa and Shoemaker
2004; Gadenk and Neslin 1999; Rothschild and Gaidis 1981).
Research on in-store sampling is more limited (Heilman et al.
2011; Lammers 1991). Although it has been demonstrated thatin-store sampling has a positive impact on short-term sales, it
is unclear how this effect will evolve over time. In addition,
research is needed that addresses several critical aspects of instore sampling promotions.
First, in-store sampling events can be conducted a single
time to introduce consumers to a product, or they can be run
repeatedly for the same product to reinforce perceptions of thepositive benefits of the product. As such, it is important tounderstand the impact (both immediate and carryover) of sampling and how this effect differs for events that are run once
versus multiple times. Second, manufacturers and retailers use
other types of promotions like in-store displays that are similar in nature, that is, products placed at a secondary locationin addition to their primary location. Unlike in-store sampling
events, in-store displays do not provide shoppers with the opportunity to ‘experience’ the product. It would be of interest toboth manufacturers and retailers to understand how sampling
events compare to other forms of non-price promotions likein-store display. Specifically, it would be useful to know if instore sampling produces a bigger immediate lift in sales thanin-store displays, and how the carryover effects differ for thetwo types of promotion. Further, it would be useful to know how
these effects differ for events that are run once versus multiple
times.
Finally, a common goal of in-store sampling is to encouragetrial of a new or existing product with the intent of converting the consumer to the product, thus leading to repurchase in
the future. Ideally, retailers would like to see repeat purchasesin the same store, thus allowing them to grow the category
sales. Although manufacturers benefit from sales of their products irrespective of outlet, in the case of new products theirinterests are also closely aligned with those of the retailers.
They would like to establish the prominence of a particular
SKU in a given retail location. This is the direct result of
current category management practice where assortment decisions are largely based upon sales rankings for both own andcompetitive stores. If the manufacturer can demonstrate that a
product is successful in Retailer A it will increase the probability of Retailer B adopting the product into its assortment,
thus increasing its sales potential. Thus, it is imperative tounderstand the store characteristics and the competitive structure that are conducive to the success of an in-store sampling
event.
We approach these research questions by developing a modelthat allows us to capture both the short-term and carryover
impact of in-store sampling. Specifically, we build a salesresponse model that (i) incorporates non-geometric decay incarryover effects through the use of a gamma distribution. This

allows us to study not just the immediate effect of in-store sampling but also the shape of its carryover effect; (ii) explicitly
accounts for potential endogenous store selection for in-store
sampling events; (iii) incorporates the impact of conducting
single versus multiple events; (iv) accounts for serial autocorrelation and incorporates store characteristics to learn about
competitive and environmental effects that moderate the effectof sampling.
We apply our model to six different data sets containing products from four distinct product categories. We use the results ofour model to empirically contrast the effects of in-store sampling
to an empirical generalization of the effect of in-store displays.
This latter effect is constructed using our model specification(to facilitate an apples-to-apples comparison of effect sizes) andscanner data for similar types of products. We also demonstrate
the differences in effect size and decay for products with single
versus multiple in-store sampling events.
Our study provides insight about the short-term and longterm impact of in-store sampling events on sales. We findthat in-store sampling events have both an immediate (shortterm) and carryover (long-term) effect. This is true in all sixof our data sets, thus increasing our confidence in the generalizability of this finding. As expected, the magnitude of theshort-term effect is larger than that of the long-term effect. We
also find that the short-term effect of in-store sampling vary
for different types of products. The effects of sampling arealso heterogeneously distributed across stores of varying characteristics. For example, we find that the impact of in-store
sampling is more localized and stores with smaller assortment of products have more to gain than stores with larger
assortments. In terms of the benefit of conducting a single
versus multiple events, we find that the immediate effect of
repeated sampling is lower, but that the effect lasts for a much
longer period of time. Furthermore, our comparison of in-store
sampling events with in-store displays provides important implications for the retailer in terms of the magnitude and decayof sampling effects compared to display effects. Finally, wedemonstrate using constrained optimizations that incremental
profits can be increased when selecting a subset of the storescompared to a given benchmark scenario. We also find theincremental cost threshold at which sampling event will not
be profitable for the manufacturer. Additionally, we also showthat if manufacturers have a predetermined incremental profit
goal it can be achieved by conducting the sampling event at amuch smaller set of stores based on variations in incremental
costs.
The remainder of this paper is organized as follows: We begin
by reviewing the literature on product sampling and identify
key features of the process that should be formally included
in our model. We use this theory to develop a general modelof in-store sampling and discuss our approach to estimation andinference. We then describe the data used for our empirical application. Results obtained from this analysis are then discussed.
We conclude the paper with a discussion of the key managerial
implications of our research, as well as limitations and potential
extensions.

Please cite this article in press as: Chandukala, Sandeep R., et al, An Assessment of When, Where and Under What Conditions In-Store Samplingis Most Effective, Journal of Retailing (xxx, 2017), http://dx.doi.org/10.1016/j.jretai.2017.07.002

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Theoretical Motivation
As a result of an increasingly competitive operating environment, manufacturers must expend considerable effort to add
value to the consumer shopping experience in order to increase
sales and differentiate themselves from their competition. Instore product sampling has emerged as an effective marketingvehicle that manufacturers can use to introduce their products to
consumers in an efficient (utilitarian) and enjoyable (hedonic)
way (Peattie and Peattie 1993). Prior research has demonstrated
that in-store sampling events lead to an increase in short-termsales (Lammers 1991; Shi, Cheung, and Prendergast 2005),
where the increase can result from brand switching, producttrial, purchase acceleration or stockpiling (Houben 2007). In
this paper we do not investigate the different routes throughwhich sales increase, but rather treat any increase in product sales(through in-store sampling) as the manufacturer’s motivational
driver for conducting these events. Similarly, a retailer’s motivation for in-store sampling could be one of increasing either
the entire category sales or increasing store traffic.
From a theoretical perspective, in-store sampling of new
products is considered to be more effective than other promotional tools in building brand awareness, loyalty, expanding
category participation and encouraging brand switching (Jain,
Mahajan, and Muller 1995). One of the primary theoreticalexplanations for its effectiveness is that it provides consumers
with direct product experience. Prior research has demonstrated
that experience is a highly engaging mode of learning because it
is both vivid and intentional (Fazio and Zanna 1978; Hoch 2002).
Direct product experience is self-selected and self-generated andcan therefore have a lasting advantage in terms of recall (Hoch2002), as contrasted to learning that occurs without experience.
Product knowledge gained through experiential modes of learning like product trial lead to the development of strongly heldbrand beliefs and attitudes that will have a stronger correlation
with future product usage (Fazio and Zanna 1978; Smith andSwinyard 1988).
In addition to experiencing the product, most sampling events
involve direct contact with a sales person that can provide
additional information about the product (i.e., calorie content,
complimentary products, price differences relative to competitors). This, in combination with the information obtained fromproduct experience, results in less uncertainty about productquality which aids in the formation of consumer preferences(Levin and Gaeth 1988) and has greater influence on subsequent attitudes and behavior as compared to advertising andother promotions (Kempf and Smith 1998). For example, Wrightand Lynch (1995) demonstrate that attention paid to experiential attributes is higher during product trial than when the same
information is provided through an advertising message.
The theoretical appeal of experiential promotional activities
like in-store sampling has been bolstered by a rapidly expanding
literature on sensory marketing. Research in this area has shownthat odor related memory is more emotionally effective than cues
presented visually or verbally (Herz and Schooler 2002) and persists over long periods of time (Engen, Kusima, and Eimas 1973;

3

Zucco 2003). Krishna (2012) shows that engaging consumers
through subconscious triggers that appeal to the basic senses ismore effective than traditional advertising messages. Elder andKrishna (2010) demonstrate that sensory simulation that emphasizes multiple sensations (i.e., taste, smell and touch) results
in better perceptions of taste than simply emphasizing taste inisolation. Taken collectively, this research is highly relevant toin-store sampling as it provides consumers with a multi-sensory
experience that evokes multiple modes of learning.
In addition to its sensory and experiential aspects, productsampling is also attractive from the perspective of reciprocity(Gouldner 1960). It is well known that upon receipt of a gift or
unrequested service consumers feel socially obliged to respondin kind. In the context of sampling, this suggests that consumers
may feel indebted to the store or sponsoring company when they
accept a free trial (Laochumnanvanit and Bednall 2005). This
could lead to a variety of positive outcomes, including immediatepurchase, repeat purchase, and increased loyalty to the brand or
store or both.
Finally, research on advertising has extensively discussed theissue of single versus multiple exposures to advertising messages. The common logic suggesting that single exposure could
create awareness whereas real effectiveness requires consumers
to be exposed to the ad multiple times (Vakratsas and Ambler1999). Given the aforementioned benefits of in-store sampling,
the common dilemma faced by manufacturers and retailers alikeis understanding the benefits of single versus multiple productsampling. Does a single in-store sampling event create enoughawareness and are there benefits to conducting the event multiple times? Additionally, how do the immediate and long-term
effects differ for single versus multiple events?
In sum, these theories strongly suggest that in-store samplingshould have both a short-term and carryover impact on consumerpurchase behavior. While the sensory aspect of in-store sampling
likely gives consumers immediate hedonic benefits, the information obtained at the event and from experiential learning provides
utilitarian benefits that can influence not only current but future
product purchase (Jones, Arnold, and Reynolds 2006). In thispaper we show empirical evidence that in-store sampling indeed
provides short-term lift that is larger than in-store product display (i.e., placing the product in a second position in the store)
and is also more effective than display when conducted multiple
times. In addition, we find substantive differences between various products in terms of the relative importance of short-termand carryover effects. Further, we demonstrate the cumulative
impact and benefit of conducting these events multiple times.
Our study focuses on three unique and important aspects
for understanding in-store sampling events. First, we investigate
both the short-term and carryover effects of in-store sampling.
While manufacturers and retailers are particularly interested
in understanding if in-store sampling events can provide sustained sales lift and thus be more than just a short-term tactic,
there has been little research on the carryover and dissipationof the impact of non-price promotions such as in-store sampling events. This is in contrast to price promotions, where there
has been abundant research on both the short and long-term
impacts (e.g., Blattberg and Neslin 1989; Gupta 1988; Lewis

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2004; Mela, Gupta, and Lehmann 1997; Pauwels, Hanssens,
and Siddarth 2001; Raghubir, Inman, and Grande 2004; Van
Heerde, Gupta, and Wittink 2003). Given the need for and lackof research on in-store sampling we aim to provide a framework to better understand the sales-sampling event relationship.
Second, across various data sets for different products and different categories, we demonstrate the impact of in-store samplingfrom both the manufacturer and retailer standpoint. Finally, we
compare and contrast the impact of single and multiple in-store
sampling events with single and multiple in-store displays.

For model sparsity, Aribarg and Arora (2008) recommended setting κ parameter equal to 2 and estimating the β parameter ofthe gamma function.
Note that with the gamma density specification of λmjst , wehave ι λmjst dι = 1, and thus the parameter τ mjs in Eq. (1) can beinterpreted as the total sales increase of product j in store s dueto this mth sampling event. To examine how the sales increase isaffected by the presence of previous sampling events and time
lapsed between the events, τ mjs can be further modeled as

Model Development

where Cmjs include variables such as whether there was at least
one previous in-store sampling event and the number of weeks
since the last event, and γ is the vector of parameters that capture the effects of the these variables. Note that γ can only be
identified if there are multiple sampling events and there areenough variations in the Cmjs variables. In the case of one single
sampling event or when there are not enough variations in Cmjs
(for example, all stores had previous sampling events), we set
τ mjs =τ 0js .
To account for the potential endogenous selection of stores
where in-store sampling events are conducted, we model the
probability that in-store sampling occurs in store s as a logit
function of the expected magnitude of sales lift from the event.
That is,We propose a general model that captures the impact of
in-store sampling on sales, while accounting for the potential
endogenous selection of stores where the in-store sampling
events are conducted. We also account for possible intertemporal and cross-brand dependencies. This model assumes
that we observe repeated (over-time) observations of store-levelsales for a collection of one or more products, where at least
one product was promoted through the use of in-store sampling.
The proposed model uses a flexible specification that captures
the cumulative impact of repeated sampling events, the decayof sampling effects over time and potential spill-over effects ofown-brand sampling to competitive brands.
Specifically, we model sales, yjst for product j in store s attime-period t as:
yjst = xjst ηjs +(1)
τmjs λmjst Imjst + εjstmwhere xjst denotes a vector with 1 in the first element and acollection of control variables that can influence sales such as
price, seasonality, trend, and so forth. Due to the discrete natureof in-store sampling, we follow Aribarg and Arora (2008) andcapture the effect of the mth in-store sampling event throughτ mjs λmjst Imjst .
The parameter τ mjs captures the magnitude of sales increase
due to the in-store sampling event and the parameter λmjst allows
this effect to change over time. Imjst is an indicator variable that
denotes the presence of an in-store sampling event. It assumes
the value of 1 on the week of the sampling event and retains
that value throughout the following 52 weeks. This allows thesales lift from in-store sampling to last beyond a single week but
not beyond one year after the event. The shape of the carryover
effect is modeled through a flexible gamma density distribution,that is, λmjst is expressed as:κ −1

λmjst =je
ιmjst

−ιmjst βj−1κΓ (κj )βj j(2)where ιmjst is an index that is equal to 1 during the week of
the in-store sampling event, 2 during the week following theevent, and so on. The gamma density distribution accommodates many different shapes of carryover effects, including themonotonically decreasing exponential decay function when theκ parameter equals 1 and the more flexible Erlang-2 decay function that allows for both a monotonic or non-monotonic shape.

τmjs = τ0js + Cmjs γ

Prob(maxt Imjst = 1) =(3)

exp(α1j + α2j ∗ τ0js )1 + exp(α1j + α2j ∗ τ0js )(4)For a given product j, if α2 > 0, then there is endogenous store
selection where those stores with higher expected sales lift tend
to be selected for in-store sampling promotions. On the other
hand, if α2 = 0, then all stores have equal chances of getting instore sampling promotions and thus there is no endogenous store
selection.
Next, to account for heterogeneity of effects across stores,
we complete the hierarchy in the model by allowing thestore-specific parameters ηs and τ 0s to vary by covariates
Zs such as store characteristics, that is, let η∗s = (ηs , τ0s ) =(η1 s, . . ., ηJ s, τ01s , . . ., τ0Js ), andη∗s ∼Multivariate Normal(Zs δ, Dη∗ ).

(5)Finally, we account for inter-temporal dependence andacross-brand dependence through the following specification of
the unobserved errors εjt for each store s in Eq. (1):εjt = φj εjt−1 + νjt .

(6)

The cross-brand dependence is captured through the covariance matrix Σ where vector νt = (ν1t , . . ., νJt ) ∼ Multivariate
Normal(0, Σ). The inter-temporal dependence is modeled by
the stationary VAR(1) process (Chib and Greenberg 1995) wherethe vector φj captures serial correlations between brand j at timet and all brands at time t-1. The matrix Φ = (φ1 , . . ., φJ ) is apositive definite J × J matrix with characteristic roots inside theunit circle.
In summary, the model provides a flexible specification that
captures not only the overall effect of sampling events on sales,

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Table 1
Descriptive statistics – manufacturer (univariate) data.

Avg. unit sales
Avg. price
ACV (in 1,000,000s)# Competitors# Weeks before sampling# Weeks after sampling# Total stores# Stores – sampling

Data set 1
Mean (std. dev.)

Data set 2
Mean (std. dev.)

Data set 3
Mean (std. dev.)

Data set 4
Mean (std. dev.)

Data set 5
Mean (std. dev.)

10.83(7.88)
3.88(1.01)
33.83(8.96)
6.89(3.29)
15
13
39
23

3.41
(4.00)
3.20(0.16)
24.70(8.88)
9.43(4.69)
8
10
83
83

3.66
(3.80)
3.19(0.16)
24.70(8.88)
9.43(4.69)
8
10
83
83

8.46
(6.46)
3.65(0.35)
19.02(5.06)
9.26(5.91)
21
31
157
157

8.05
(5.89)
3.69(0.34)
20.30(6.51)
13.55(5.78)
21
31
223
223

but also the shape and decay of the effect of sampling overtime. Additionally, it captures spill-over effects of own-brandsampling to competitive brands and accounts for the possibility of temporal dependence and endogenous selection of storesfor sampling events. We estimate the model using hierarchical
Bayesian methods. A variety of simulations studies were conducted to validate the efficacy of this approach. Full details of
the estimation routine appear in the appendix.

Data Description
In this section, we describe in detail the various data sets that
we use. As a general note, we found that it was very difficult to
get access to this type of data as it requires a fusion of scanner
data from IRI or Nielsen and data on sampling events that must
be provided by a retailer or third-party provider. When data arecollected from the manufacturer’s standpoint, it does not usually
have information on competitor sales or pricing, which makes
it difficult to investigate competition effects. On the other hand,data collected for the retailer does, but retailers are reluctant todivulge this information.
For this project, we were able to obtain six different scanner
data sets to demonstrate the consistency and robustness of ourfindings. The six data sets include four different product categories. Five of these data sets were provided by manufacturers(referred to hereafter as the manufacturer or univariate data) andan additional data set was provided by a retailer (referred tohereafter as the retailer or multivariate data). The manufacturer(univariate) data each contain only one instance of an in-store
sampling event during the observed time series, while in theretailer (multivariate) data we observe multiple in-store sampling events. The primary reason for using multiple data sets is
to demonstrate the generalizability of our findings across different products and categories. Multiple data sets also allow us to
examine how the effect of sampling across brands and productcategories differs for multiple and single sampling events, andhow these effects are attenuated by store characteristics. Detailsof each of these data sets and corresponding summary statistics
and time series plots appear below.

Manufacturer (Univariate) Data
A total of five data sets were obtained from manufacturers
and contain data with varied lengths of post-sampling observations (from 9 to 31 weeks) for five different products and threedifferent product categories. The number of stores conducting
the events also varied from 23 to 223. The data sets that we use
to test our model come from scanner data for different products
during 2009 and 2010. No promotional activity (i.e., feature ordisplay) was conducted for these SKUs during the observed time
period. This helps us investigate the true impact of in-store sampling and is an inherent advantage of the different data sets that
we use.
Data set 1: The product for data set 1 is a single SKU in theDiet/Health snacks category. Although this product was released
by a well known national brand, it is not a simple line extension and is therefore new to the market. As it is a consumable,
shelf-stable snack product, it is ideal for use in in-store sampling
demonstrations. Collectively, our data include information for
28 weeks about the number of units sold, price of each unit
(which incorporates price discounts) and store characteristics(ACV and number of competitors for each store). The store characteristics were provided by a national syndicated data source
provider that is widely used in the grocery industry. We also haveinformation about the exact day of the in-store sampling event at
each store. The first column in Table 1 provides the descriptive
statistics for the data set. Table 2 provides the correlation matrix
and Fig. 1 provides the plot for the average sales across all stores.
The manufacturer conducted the in-store sampling event in 23of the total 39 stores.
Data sets 2 and 3: The products for data sets 2 and 3 are
two different SKUs in the frozen snacks categories. Unlike data
Table 2
Correlation matrix – dataset 1.

Units
Price
ACV
# Competitors

Units

Price

ACV

−0.14
0.31
0.02

0.03
0.00

−0.03

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Fig. 1. Average weekly sales for the univariate datasets.
Table 3
Correlation matrix – dataset 2.
Units
Units
Price
ACV
# Competitors

−0.29
0.17
0.04

Table 4
Correlation matrix – dataset 3.
Price

−0.03
−0.05

ACV

0.12

set 1, which involves a new product introduction, products indata sets 2 and 3, released by a well-known national brand, areexisting products and are therefore not new to the market. Thisdata includes information for 18 weeks about the number of units
sold, price of each unit (which incorporates price discounts) andstore characteristics (ACV and number of competitors for eachstore). The second and third columns in Table 1 provide thedescriptive statistics for the data sets. Tables 3 and 4 provide thecorrelation matrices, and the middle two charts in Fig. 1 provides
the plot of average sales across all stores for the two products.
We find that the manufacturer conducted the in-store sampling
event in all of the 83 stores.
Data sets 4 and 5: The products for data sets 4 and 5 are twodifferent SKUs in the snacks categories in a large coffee shop
chain while data sets 1, 2 and 3 are from two different large
grocery retailer chains. Unlike products in data sets 1 through

Units
Price
ACV
# Competitors

Units

Price

ACV

−0.30
0.14
0.01

−0.04
−0.08

0.12

Units

Price

ACV

−0.17
0.33
0.16

−0.01
−0.04

−0.01

Table 5
Correlation matrix – dataset 4.

Units
Price
ACV
# Competitors

3 (which are shelf stable products), the products in data sets
4 and 5 are consumable frozen novelty products. Collectively,
this data include information for 52 weeks about the number ofunits sold, price of each unit (which incorporates price discounts)
and store characteristics (ACV and number of competitors foreach store). The fourth and fifth columns in Table 1 provide thedescriptive statistics for these data sets. Tables 5 and 6 provide

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7Fig. 2. Plot of retailer (multivariate) data.
Table 6
Correlation matrix – dataset 5.
Units

Table 7
Descriptive statistics - retailer (multivariate) data.
ACV

Variable

Mean

Std. dev.

−0.03

Competitor brandAvg. sales (oz)Avg price (per oz)
Avg discount (per oz)

3,182.56
0.33
0.007

2,196.87
0.01
0.002

Focal brandAvg. sales (oz)Avg price (per oz)
Avg discount (per oz)

5,568.13
0.23
0.001

3,746.52
0.02
0.004

the correlation matrices, and the last two charts in Fig. 1 provide
the plot for the average sales across all stores. We find that the
manufacturer conducted the in-store sampling event in all of the
157 and 223 stores for data set 4 and 5, respectively.

Store characteristics
ACV
Number of competitors# Total stores# Stores – sampling

2,373.34
1.45
73
73

289.85
0.28––

Retailer (Multivariate) Data

Data characteristics# Weeks before first sampling event# Weeks after first sampling event# Weeks after last sampling event

47
57
11

–
–
–

Units
Price
ACV
# Competitors

−0.15
0.31
0.08

Price

−0.02
−0.02

We obtained one data set from a large grocery chain store in
the eastern United States. The product category includes only
two major brands. We obtained the scanner data for sales, priceand promotion information for both brands in the category tounderstand the total category-level impact of in-store samplingof one of the brands during 2013 and 2014. No promotional
activity (i.e., feature or display) was conducted for these SKUs
during the period we observe in our data. Again, this helps us
investigate the true impact of in-store sampling and is an inherent
advantage of this data set.
Only one of the brands (focal brand) conducted in-store sampling during the two years of data that we obtained, there were
8 sampling events for the same SKU of the focal brand. Collectively, our data include information for 104 weeks about the
number of units sold, price of each unit, price discounts and store
characteristics (ACV and number of competitors for each store).
The store characteristics were provided by a national syndicateddata source provider widely used in the grocery industry. We also
have information about the exact days of all the in-store sampling
events at each store. Table 7 provides the descriptive statistics forthis data set. Table 8 provides the correlation matrix (with prefix
C. and F. referring to competitor and focal brand respectively)
and Fig. 2 provides the plot for the average sales for both the
focal and competitor brand (and the category) across all stores.
We find that the in-store sampling events were conducted in allof the 73 stores.

Results
For ease of comparison across different data sets, we used
standardized log sales for the dependent variable in the model.
Similarly, we used standardized log price for the control variable
and standardized ACV and number of competitors for the store
characteristics. Table 9 provides the posterior estimates and the
95% credible intervals (in parenthesis) for all five manufacturer(univariate) data sets. To ensure convergence we ran our estimation routine for 100,000 draws, keeping every 100th draw andusing the last 750 draws to compute the posterior estimates.
We find a consistent pattern in the results across the different data sets. We find that the immediate impact of samplingis positive and significant, while the magnitude of the impact
differs across various products. We also find that, as expected,
price has a negative and significant impact on unit sales. We findthat store ACV has a negative and significant interaction effectwith sampling (−0.91) for data set 5, indicating that smaller
stores probably benefit more from sampling than larger stores(i.e., stores with a smaller assortment of products have more togain from in-store sampling than stores with a larger assortmentof products). This is an interesting finding and we observe thisto be the case with the retailer (multivariate) data as well.
In terms of sampling endogeneity we find that it is not significant (α2 ) for data set 1, which is the only data set where

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Table 8Correlation matrix – retailer (multivariate) data.

C. Units
F. Units
C. Price
F. Price
C. Disc
F. Disc.
ACV# Competitors

C. Units

F. Units

C. Price

F. Price

C. Disc

F. Disc.

ACV

0.66
−0.38
−0.04
−0.12
−0.10
0.67
−0.27

−0.41
0.42
−0.20
−0.01
0.51
−0.20

−0.31
0.16
0.05
−0.21
0.08

−0.12
0.27
−0.03
0.01

0.45
−0.10
0.07

−0.10
0.06

−0.36

Table 9Manufacturer (univariate) data results.

Intercept
Time trend
Price
Sampling
Sampling interactions
ACV# Competitors
Sampling endogeneity
α1
α2Gamma decay
βError autocorrelationφData set 1
Estimates

Data set 2
Estimates

Data set 3
Estimates

Data set 4
Estimates

Data set 5
Estimates−0.15[−0.4,0.01]
0.02[−0.1,0.1]−0.28[−0.43,−0.13]
2.61[1.58,4.0]−0.36[−0.5,0.23]
0.02[−0.03,0.07]−0.34[−0.42,−0.26]
4.66[4.32,4.99]−0.41[−0.55,−0.28]
0.03[−0.03,0.08]−0.38[−0.46,−0.30]
4.43[4.06,4.79]

0.12[0.01,0.24]−0.01[−0.03,0.02]−0.15[−0.19,−0.12]
7.89[5.23,18.7]

0.001[−0.09,0.08]−0.001[−0.02,0.02]−0.13[−0.16,−0.10]
16.31[8.73,29.16]

0.1[−0.9,1.0]
0.14[−0.74,0.98]−0.22[−0.55,0.12]
0.11[−0.22,0.44]

0.19[−0.11,0.53]
0.28[−0.03,0.62]−0.19[−0.89,0.20]−0.27[−1.01,0.14]−0.91[−2.21,−0.21]−0.34[−1.32,0.29]−3.18[−5.47,−1.64]−1.31[−3.92,0.32]

–
–
–
–

–
–
–
–

–
–
–
–

–
–
–
–

0.95
[0.58,1.47]

0.58[0.52,0.64]

0.65[0.58,0.72]

0.24[0.18,0.30]

0.18[0.16,0.23]

0.37[0.31,0.43]

0.08[0.01,0.15]

0.13[0.05,0.20]

0.12[0.10,0.15]

0.11[0.09,0.13]

sampling was conducted in a subset of the stores. In all otherdata sets, sampling was conducted in all stores. All the β shapeparameters in Table 9 are less than one, indicating that the peakeffect is attained during the first week and the joint impact of
the shape and lift indicate the dissipation occurs fairly quickly
across all data sets. Fig. 3 provides the lift and shape variationfor each of the data sets.
We find that the dissipation of the sampling effect lasts anywhere from 2 weeks to 8 weeks across the different data sets.
This is similar to the pattern for feature advertising observed
by Aribarg and Arora (2008). We also find that the number ofcompetitors does not have a significant interaction effect within-store sampling. This indicates the localized impact of in-store
sampling (i.e., since sampling is usually conducted inside a store
with customers from competing stores having very little knowledge of these events), it is possible that in-store sampling is not
impacted by the number of competitor stores in the vicinity. We

find a significant positive serial correlation between the sales attime t and sales at time t − 1 (φ parameter in Table 9).
Table 10 provides the parameter estimates for the model estimated using the retailer (multivariate) data. We observe that,across the two brands, in-store sampling for the focal brand has
a large significant positive impact on unit sales and a small positive impact on the competitor brand (0.32). This demonstrates
the category benefits of in-store sampling (i.e., in-store sampling has a positive spillover effect on competitor brand in the
category). This is especially useful for retail managers because,
unlike price promotions that lead to brand switching, sampling
events could be considered as quality events that lead to category
expansion. With regard to the interaction of in-store samplingand store characteristics, using Table 11, we find that store ACV
has a negative (−1.96) and significant interaction effect withsampling, indicating that smaller stores probably benefit morefrom sampling than larger stores (i.e., stores with a smaller

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Table 10Retailer (multivariate) data results.

Intercept
Trend (weeks 59–104)
Price ownPrice crossDiscount
Sampling

Competitor brand

Focal brand−0.15[−0.35,0.03]−0.03[−0.13,0.07]−0.08[−0.16,−0.01]−0.11[−0.19,−0.02]
0.02[−0.07,0.10]
0.32[0.23,0.40]−0.53[−0.70,−0.37]
0.26[0.15,0.39]
0.001[−0.10,0.10]−0.007[−0.07,0.06]
0.02[−0.04,0.07]
16.22[14.86,17.39]

9peak impact of in-store sampling is observed in the week of thesampling and then dissipates over time, ranging from 2 weeks
to 8 weeks after the sampling event. We do find that there issome heterogeneity for the different products in terms of thedissipation time and the peak (or lift). We find that data set 2
has the greatest immediate lift in sales, while data set 1 has thelongest carryover effect.
For multiple events, we find that the there is a sustained lift
followed by a gradual dissipation that lasts much longer (in thevicinity of 48 weeks). It is evident from Fig. 3, that there isconsiderable difference in the impact of single and multiple
sampling events. We further investigate these differences andcompare it with another extensively used promotion in retailindustry (i.e., in-store displays) in the following section.
Discussion and Conclusion

Table 11Additional sampling model parameter estimates.
Sampling interactions
ACV# Competitors
Gamma decay
βError autocorrelation
φ11
φ22Comparing the Effects of Sampling Versus In-Store Display−1.96[−3.0,−0.93]−0.45[−1.45,0.58]
12.40[11.77,12.97]
0.28[0.11,0.44]
0.27[0.10,0.43]

assortment of products have more to gain from in-store sampling than stores with a larger assortment of products). Given
the presence of multiple in-store sampling events we find that the
focal brand reaches its peak (β = 12.40) and the dissipation takes
much longer (i.e., more than 45 weeks), unlike single sampling
events where the dissipation is quick. Thus, one of the benefitsof conducting the sampling event multiple times is a sustained
lift that dissipates slowly.
Fig. 3 provides the lift and shape variation patterns for both
single and multiple event data (i.e., univariate and multivariatedata). These plots were created using the estimated β parameters
for the Gamma decay function for each data set in conjunction
with the estimated τ parameters that capture the magnitude of
the sampling effect. For single events, the results show that the

To help frame the effects described above, Fig. 4 provides
a comparison of the estimated decay curves for the sampling
events observed in our data (for both single and multiple sampling events) and an empirical generalization of the effect of
in-store display. When a product is on “display” it is stocked
in a secondary location in the grocery store, in addition to its
primary location on the shelf in its category. Common typesof displays include end-caps, free-standing displays, and clipstrips. Display is used frequently as a form of promotion and iscommonly included as a variable provided in IRI and Nielsen’sscanner data sets. We chose display as a point of contrast to sampling as in-store sampling can be viewed as a form of display as
the product being sampled is given a secondary location in thestore on the day of the sampling event.
We contrast the results of our model to the average effect of
display by constructing an empirical generalization of display
effects. This is accomplished by fitting our proposed model toscanner data where we substitute display for sampling. Specifically, we used data from six categories in the academic IRI dataset (Bronnenberg, Kruger, and Mela 2008), including Spaghetti
Sauce, Frozen Pizza, Mayonnaise, Salty Snacks, Sugar Substitutes, Peanut Butter and Hot Dogs. We selected a collectionof shelf-stable, frozen and refrigerated products to enhance thegeneralizability of this result and ensure that it is similar to thecategories of in-store sampling products used.
In order to facilitate as fair a comparison as possible, we use
the following procedure. We begin by first importing 52 weeks

Fig. 3. Estimated shape of the decay curve for stores with single versus multiple sampling events.

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Fig. 4. A comparison of sampling versus display decay curves.

of data for a given category. We then select a single SKU (starting with the top-selling item in the category) and search overall stores in the data to identify the subset of stores that only
conducted one display during the 52 week time period in question. We then clean the data so the structure was identical to thatof our proposed model (i.e., standardized log sales, standardized log price, time trend, etc.) and estimate the model saving
the coefficients of interest. This process is then repeated for the
10 SKUs in the category and for each of the categories listed
above. We compute a representative display effect by taking aweighted (by observations) average of the parameters of interest.
This process is repeated for stores with multiple display events
to build an empirical generalization of display effects for multiple events. The results of this analysis appear in Fig. 4. The
left panel shows the average decay curve for sampling events
versus display for a single event/display. The right panel shows
the same decay curves for stores with multiple events/displays.
For stores with single events, there are a couple of featuresof the curve that are worth noting. First, the magnitude of theimmediate impact of sampling is much larger than that of display. On average, running a sampling event yields an immediate(week-of) increase in log sales of close to 2. For display events
this immediate effect is about 1. Second, the carryover effectof in-store sampling is more sustained. Taken collectively, we
can infer that the total effect of sampling, as measured by anincremental lift in sales, is much larger than that of in-store
display.
The right panel of Fig. 4 shows the decay curves for stores
where there were multiple in-store sampling and/or display
events executed throughout the year. The decay curve for multiple displays is almost identical to that of stores with a single
display. The carryover effect of display dissipates after 2 weeks.
The immediate effect of a display in stores with multiple displays is about 0.65 versus 1 for stores with a single display. Thissuggests that there are diminishing returns to repeated display
activity, or that the immediate impact of display decreases asconsumers are exposed to a greater number of displays. Further,
the pattern of decay is markedly different for sampling versus
display. In the case of the former, we observe that the effect of asampling event is sustained over many weeks. We do recognizethat we would need additional data to generalize the impact ofmultiple sampling events. Nevertheless, it is interesting to findthese differences across single and multiple events that can beinvestigated by future research with the availability of more data.

Optimal Store Selection
In this section, we discuss managerial implications anddemonstrate how the findings from our model can help managers make better decisions regarding the selection of stores for
an in-store sampling event. Optimal store selection for discrete
promotions is a special case of the universal resource allocation problem faced by marketers. As such, it is a topic of highimportance as managers are constantly engaged in the processof trying to determine how to best allocate their finite budgets
across a multiplicity of potential activities. For the purpose of
the analysis, we focus on the first dataset in our study (the only
dataset where sampling was conducted in a subset of the stores,
i.e., 23 of the 39 stores) and assume that the cost of conducting
the in-store sampling event is the same for each store (which
is usually true in practice). We also obtained additional information that includes the latitude and longitude for each store
and the number of employees in each store (as a proxy forstore size). We treat the current store selection scheme as thebenchmark, and compare alternative selection schemes to thebenchmark. Ideally, managers want to see an increase in incremental profit due to the sampling event. Given the lack of specificcost information for in-store sampling we investigate optimal
store selection by: (i) maximizing incremental profit while constraining the number of stores with in-store sampling to be thesame as in the benchmark (ii) minimizing the number of stores
conducting the sampling event while still maintaining the same
incremental profit as in the benchmark scenario. In particular,
through this what-if analysis we plan to answer the following
questions:

1. Can incremental profits be increased? Given the constraintthat only a small number of stores (e.g., 23) can be selected
for the in-store sampling event, what is the best set of storesto maximize incremental profit? With the best set of stores atwhat cost threshold will sampling not be profitable anymore?
2. Can the number of stores conducting the event be minimized?
Given the constraint that incremental profit is similar to thecurrent benchmark profit, can the number of stores be fewer
than the number of stores in the benchmark scenario? If
this can be achieved what is the ideal number of stores fordifferent incremental cost assumptions?

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We compute incremental profit as the difference between
incremental revenue and incremental cost, where the incremental revenue is calculated as the overall impact of sampling foreach store multiplied by the average price of the product at eachstore. Since we do not have specific information on the incremental cost for in-store sampling, we start by assuming a low
cost scenario where the incremental cost is the same as the unit
price of the product.
The optimization results show that there is an 8.9% gain in
the incremental profit for the lower cost scenario compared tothe benchmark (from 940.35 to 1,024.08). To visually investigate the differences in the 23 stores that were selected aspart of the incremental profit maximization, we plot in Fig. 5
the set of stores based on the latitude and longitude of thestores. Additionally, the size of each circle in the figure represents the store size (number of employees). As can be seen
there are clear differences in the various stores that are selectedunder the goal of profit maximization as compared to the benchmark. We also find that, with the same set of stores obtainedby profit maximization (bottom panel Fig. 5), if the incremental cost of sampling event exceeded fifteen times the unit
price of the product then the sampling event would not be
profitable anymore for the manufacturer. We obtain this estimate by increasing the assumed cost of in-store sampling in
the what-if analysis and finding the break-even point beyond
which the sampling event would not be profitable. Thus, ourproposed methodology helps manufacturers decide what the
optimal stores should be and at what incremental cost thresholddoes the sampling event stop bringing in additional incremental
profits.
We also conducted a similar constrained optimization exercise as described previously, but, instead of maximizing profit
with a constrained number of sampling stores, we minimize
the number of stores conducting the sampling event while
restricting the incremental profit to be similar to the benchmark scenario. The primary reason for this optimization is toaccount for unobserved factors that only the manufacturer has
information about. For example, if the manufacturer has a predetermined incremental profit as a target, can this be achievedby using a fewer set of stores to conduct the sampling event(which will reduce overhead cost). We find that, as expected,
the optimal number of stores to be selected is dependent on
the assumed cost of in-store sampling. For higher costs suchas when it is ten times the average unit price of the sampling product, we find that the same incremental profit as thebenchmark can be obtained using just eleven stores as demonstrated in the top panel of Fig. 6. However, as the cost of
sampling lowers to about three times the unit price of the
product we find that the minimal number of stores required
to obtain the same incremental profit as the benchmark storesis 21 (bottom panel of Fig. 6). This is because as the costof sampling increases the incremental profit from the benchmark set of stores decreases and vice versa. Thus, as can be
expected, the cost of sampling plays an important role in the
choice of the store selection if the incremental profit goal ispredetermined. This exercise helps manufacturers decide on the11

optimal number of stores, location and size for conducting theevent.
In summary, these findings suggest that our proposed methodology can aid manufacturers in determining the threshold for
conducting in-store sampling events and also in the choice of
optimal number and location of stores. An interesting avenue
for future research would be to obtain more data on additional
store characteristics that can aid in store selection for conducting
sampling events.
Summary and Conclusion
The results of our analysis yield three key insights that should
be of interest to a managerial audience, particularly to category and brand managers. First, in-store sampling is a highly
effective form of quality promotion. In-store sampling generates both an immediate increase in sales and a sustained lift in
post-promotional sales. In contrast to the traditional price-based
promotions that are characterized by an increase in sales during
the week of price discount and a sharp decline in sales as pricereturns to its base level, we can conclude that in-store samplingis an effective tool that managers can use to build long-term sales
for a brand. Also, experiential events add value to a product without altering consumers’ expectations of price. We recommendthat in-store sampling should be used more frequently as brandand category managers seek to expand category penetration andsales.
Second, the relative success of an in-store sampling event
is likely influenced by product type. Our research shows thatthe long-term benefits and subsequently the total impact of asampling event tend to differ across product types. That said,
our results also show that sampling is a more effective formof promotion than other forms of non-price promotion that are
currently used in practice, like product display. Given cost information for both sampling and display, it would be useful tocontrast the ROI of these types of promotions.
Third, an interesting extension to our proposed modelingapproach would be to build a spatial model by obtaining
additional information on spatial locations and competitive
information for the stores conducting the sampling events. Furthermore, our current approach to address endogeneity only
investigates one source that is if stores with higher incremental sales were chosen to run the sampling events. However,
future research could investigate another form of endogeneitythat involves selection of stores with higher or lower base line
sales.
Fourth, analysis of the multivariate data suggests that in-store
sampling produces a category expansion effect. That is, execution of a sampling event by one brand leads to an increase insales for all brands in the category. This should be of interest
to category managers who are seeking to find ways to increase
total category profitability, and not the individual performanceof a single SKU or brand. Price-based promotions are ill-suited
to this task as they tend to encourage brand switching and stockpiling behavior. We encourage future research that continues
to expand this line of inquiry. Given access to a great numberof data sets and cost information, it would be useful to build an

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Fig. 5. A comparison of benchmark stores and stores selected by profit maximization.

empirical generalization of the effects of sampling. We view thispaper as a first step in that direction. Currently, we only investigate products that are consumed with a subsequent opportunity
to purchase. It would also be interesting to understand how thistranslates to different types of experiential events where there isa product demonstration (e.g., demonstration of the features ofa new durable product) without a tasting event followed by an
opportunity to buy. This could also be an interesting avenue for
future research.

Appendix A. MCMC Algorithm for Model Estimation
The MMC algorithm builds upon that used in Aribarg andArora (2008). The unique steps are Steps 1 to 3 during which wetake into account of the possible endogenous selection of stores
where the in-store samplingSpecifically, events are conducted.
∗ = (x ,∗ = (x∗ , . . ., x∗ ),we first let
xjst
λ
I
)
,
x
jst
mjst
mjst
st
Jst
m
1st
and Wjst = ( m Cmjs λmjst Imjst ).
⎞∗ − x∗ φ
xjs2
s1 j
⎟
⎜
..
∗
⎟,
Xjs
=⎜
.
⎠
⎝
⎛



∗ − x∗
xjsT
sT −1 φj⎞
∗ − y∗ φ
y1s2
s1 1
⎟
⎜
⎞
..
⎟
⎜
.
⎟
⎜
⎟
⎟
⎜
∗ − y∗⎟,⎟ , Y ∗ = ⎜ yjst
φ
j
st−1
s
⎟
⎜
⎠
⎟
⎜
.
∗
⎟
⎜
..
XJs
⎠
⎝
∗ − y∗yJsT
φsT −1 J⎛⎛⎜
Xs∗ = ⎜
⎝

∗
X1s

..

.

∗ =y
∗
∗
∗
where yjst
jst − Wjst γ, yst = (y1st , . . ., yJst ).
The steps of the MCMC algorithm are as follows

Step 1 Draw vector η∗s = (ηs , τ0s ) using independent
Metropolis–Hastings (M-H) algorithm: draw a new value, from multivariate normal distributionof η∗s , that is, η∗news−1

MVN(as , As ), where As = [Xs∗ (Σ −1 ⊗ IT )Xs∗ + Dη−1
,
∗ ]
−1 ∗
∗
−1
∗
as = As [Xs (Σ ⊗ IT )Ys + Dη∗ η̄ ].
Accept
and
the
new
value
with
probability
that
equalsπ(Y |η∗new ,else)Prob(maxt Imjst =1|η∗new)s).
min(1, s s∗old∗oldπ(Ys |ηs,else)Prob(maxt Imjst =1|ηs)

Step 2 Draw αj = (α1j , α2j ) using random-walk M-H algorithm: let αnew
= αoldjj + small random normal variates,

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13

Fig. 6. Comparison for minimizing number of stores for different costs.

and accept the new value with probability that equalsmin(1,

Prob(maxt Imjst =1|α∗new)π(αnewjj )ssProb(maxt Imjst =1|α∗old)π(αoldjj )).

Step 3 Draw β using random-walk M-H algorithm: βnew = βold + small random normal variate, andaccept the new value with probability that equalsmin(1,s

π(Ys |βnew ,else)π(βnew )s

π(Ys |βold ,else)π(βold )).

Step 4 Generate Σ from Inverted Wishart(n, H) wheren = n0 + T, and H −1 = Ho−1 + (Y ∗ − X∗ η∗ − W ∗ γ) (Y ∗ −X∗ η∗ − W ∗ γ), and the prior for Σ is Inverted Wishart(n0 , H0 ).
Y* , X* , and W* are obtained by stacking up Ys∗ , Xs∗ , and Wjst
respectively.
Step 5 Generate Dη∗ from Inverted Wishart(g, G) where ∗ ∗g = g0 + S and G−1 = G−1s (ηs − Zs δ) (ηs − Zs δ). The
0 +prior for Dη∗ is Inverted Wishart(g0 , G0 ).
⎞⎛Wj12 − W11 φj
⎟
⎜
..
⎟
⎜
.
⎟
⎜
⎟
⎜
∗
⎜
W
−
W
φ
Step 6 Let Wjs = ⎜ jst
st−1 j ⎟⎟, where
⎟
⎜
..
⎟
⎜
⎠
⎝
.
WjST − WST −1 φj∗ to obtain W ∗ .
Wst = (W1st , . . ., WJst ). Stack up Wjss⎞∗∗ − y∗∗ φ
y1s2
s1 1
⎟
⎜
..
⎟
⎜
.
⎟
⎜
⎟
⎜
∗∗
∗∗
∗∗
∗ ∗
∗∗
⎜
Ys = ⎜ yjst − yst−1 φj ⎟⎟, where yjst = yjst − xjst ηjs .
⎟
⎜
..
⎟
⎜
.
⎠
⎝
∗∗
∗∗
yJsT − ysT −1 φJ
Draw γ from multivariate Normal distribution MVN(γ̄, Σγ ),
−1
Σγ = [ Ss=1 Ws∗ (Σ −1 ⊗ IT )Ws∗ + Dγ−1 ] ,
and
where

γ̄ = Σγ [ Ss=1 Ws∗ (Σ −1 ⊗ IT )Ys∗ ∗ +Dγ−1 γ0 ]. The prior of γ
is multivariate Normal (γ 0 , Dγ ).
Step 7 Generate δ from multivariate Normal distribution:

−1 −1
, and
δ∼MVN(δ̄, Σδ ), where Σδ = [ s Zs Dη−1
∗ Zs + D0 ]

−1 ∗
−1

δ̄ = s Σδ [Zs Dη∗ ηs + D0 δ̄0 ]. The prior of δ is multivariate
Normal (δ0 , D0 ).
∗ η∗ − w γ,
Step 8 Generate Φ – let ejst = yjst − xjst
jsjstest = (e1st , . . ., eJst ), Es = (es1 , . . ., esT−1 ) , and stack up Es toobtain E. Then, following Chib and Greenberg (1995), gen −1erate Φ from Φ ∼MATN( n Φ̄ , (E E) ⊗ Σ) × I(Φ), where−1Φ̄ = (E E) × ( s t=2 est−1 est ) and I(Φ) is an indicatorfunction that takes the value of 1 when all roots of Φ lie in theunit circle and 0 otherwise. Specifically, let Φ = Φ̄ + PTQ ,⎛Please cite this article in press as: Chandukala, Sandeep R., et al, An Assessment of When, Where and Under What Conditions In-Store Samplingis Most Effective, Journal of Retailing (xxx, 2017), http://dx.doi.org/10.1016/j.jretai.2017.07.002

+ModelARTICLE IN PRESSRETAIL-643; No. of Pages 14
14

S.R. Chandukala et al. / Journal of Retailing xxx (xxx, 2017) xxx–xxx

where P and Q are Choleski decompositions such that PP  =(E E)−1 and QQ = Σ, and T is a k × k matrix that consists of
independent standard normal variables. If all the roots of Φ areless than unity (the stationary condition) then Φ is accepted;
otherwise another T is drawn and the process repeats.
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Please cite this article in press as: Chandukala, Sandeep R., et al, An Assessment of When, Where and Under What Conditions In-Store Samplingis Most Effective, Journal of Retailing (xxx, 2017), http://dx.doi.org/10.1016/j.jretai.2017.07.002