Consumer Preferences in Food Packaging: Cub Models and Conjoint Analysis
Consumer Preferences in Food Packaging: Cub Models and Conjoint Analysis
Consumer Preferences in Food Packaging: Cub Models and Conjoint Analysis
1
Department of Land Use and Territorial Systems, University of Padova, Legnaro, Italy,
rosa.arboretti@unipd.it
2
Department of Management and Engineering, University of Padova, Vicenza, Italy,
bordignon.paolo@alice.it
Packaging features have been shown to be of great importance for the consumer final choice
of fresh products (Connolly and Davidson, 1996; Silayoi and Speece, 2007). Packaging is an
extrinsic attribute, which consumers tend to rely on, when relevant intrinsic attributes of the
product are not available. Thus, packaging is constantly developing to meet changing and
challenging consumer demands. In the current literature, studies on the influences of
packaging features on consumer preferences are mainly related to classical preference
evaluation methods like conjoint analysis (CA). Starting from a real case study in this field,
along with Conjoint Analysis, we apply CUB models (Iannario and Piccolo, 2010) as a useful
tool to evaluate preferences. CUB models can grasp some psychological characteristics of
consumers related to the “feeling” towards packaging attributes and related to an inherently
“uncertainty” that affects the consumers’ choices. Both psychological characteristics “feeling”
and “uncertainty” can be linked to relevant subject’s information. The aim of our paper is
twofold. At first we detect preferred packaging attributes of fresh food by means of CA, then
we apply CUB models to some relevant attributes from the CA study. Results show that
attributes like packaging material and size/shape of packaging are the most important
attributes and that biodegradable packaging, reclosable trays/bags and long “best by” date
are also valuable features for consumers.
Methodology
Conjoint Analysis and CUB models are very different approaches both aimed at evaluating
preferences. In a typical CA application, attribute levels are experimentally combined and an
orthogonal plan is usually applied in order to lower the number of profiles. CA estimates the
utilities of the levels and the relative importance of the attributes by appropriate estimate
methods (Green & Srinivasan, 1978).
CUB models have been developed in order to explain the choice process of an item. “Feeling”
and “uncertainty” are supposed to be latent variables involved in the choice process of an
item (Iannario & Piccolo, 2012). D’Elia and Piccolo (2005) present the model as a valuable
method for evaluating preferences, describing the probability structure of the model. Many
years later, after several successful applications of CUB models, Iannario and Piccolo (2012)
and Iannario (2014) present a detailed description of the CUB models along with the main
extensions.
The random variable Y is fully explained by:
m − 1
(1 − ξ ) ξ m− y + (1 − π ) ,
y −1 1
Pr(Y = y ) = π y = 1, 2,..., m .
y − 1 m
A shifted binomial distribution is intended to mimic the choice behaviour of a rate y among m
according to the feeling of respondents, while a discrete uniform distribution is aimed at
describing the maximum expression of the uncertainty component surrounding any choices.
The random variable Y is distributed as a mixture of shifted binomial and discrete uniform
distributions with 1-π, π є (0,1], a direct measure of uncertainty and ξ є [0,1] a measure of
feeling according to the measurement scale coding (Iannario, 2014). CUB model has been
shown to be very flexible and parsimonious assuming very different shapes thanks to only
two parameters π and ξ (Piccolo, 2003a; D’Elia & Piccolo, 2005). This flexibility allows
CUB models explain different choice behaviours. We referred to D’Elia (2003) and Piccolo
(2003b) for maximum likelihood parameter estimation by an E-M algorithm.
The feeling latent variable has been considered a psychological component involved in the
choice process. The final choice is the result of psychological aspects like the
agreement/disagreement toward the item, socio-cultural aspects, the knowledge of the item,
past experiences and so on. On the other side uncertainty takes into consideration the inherent
indecision accompanying any human choice and it can be referred to a tendency to joke or
fake, to have a confusing idea of the evaluated object, a bias involving
questions/questionnaires, a way of collecting data and so on (Corduas et al., 2009; Iannario &
Piccolo, 2012; Iannario, 2014).
Among the several extensions that have been developed (Iannario, 2014), we are considering
the introduction of covariates for explaining feeling and uncertainty parameters. A formal
description of CUB model with covariates (D’Elia, 2003; Piccolo, 2003b) shows that thanks
to the logistic functions
1 1
πi = − β0 − β1xi 1 −K− β p xip
= − β0 − xi β
1+ e 1+ e
and
1 1
ξi = −γ 0 −γ1wi 1 −K−γ q wiq
= − γ 0 − wi γ ,
1+ e 1+ e
parameters πi and ξi can be fully explained by covariate vectors xi=(1,xi1,…,xip) and
wi=(1,wi1,…,wiq). In such a framework, the model extension
m − 1 yi −1 m − yi 1
Pr(Yi = yi ) = π i (1 − ξi ) ξ i + (1 − π i ) , y = 1, 2,..., m
yi − 1 m
describes the probability distribution of the random variable Y for the i-th subject conditioned
to relevant covariates. Piccolo and D’Elia (2008) show that subjects’/objects’ covariates were
relevant to describe different patterns of smoked salmon evaluations according to gender, age
and country of origin of respondents and according to salt content, lightness and intensity of
red of smoked salmons.
For the sake of completion, we briefly describe some important CUB model extensions.
Iannario (2012) and Iannario (2014) introduce some CUB model extensions in order to catch
specific choice behaviors. A shelter choice is considered an over-selected grade in order to
simplify the evaluation task. Such a behavior can be responsible for an upward choice of a
specific grade or rank and Iannario (2012) shows that a proper CUB model can capture the
shelter effect and help to improve model fitting.
Iannario (2014) discusses about extra-variability that could be ascribed to an inter-personal
way of selecting among grades that is a variability of personal feeling. A Beta-binomial
random variable has been considered to be involved in the overdispersion effect and the
CUBE (convex Combination of a Uniform and a shifted BEta-binomial random variable)
model has been described by Iannario (2014).
Useful fitting measures for CUB models are based on estimated and observed probabilities
and on log-likelihood. A dissimilarity index has been developed in order to measure the
absolute distance between estimated and observed probabilities (Corduas et al., 2009;
Iannario, 2009). The normalized dissimilarity index
m
Diss = 0.5∑ f y − p y (θ )
y =1
represents the percentage of respondents that should change their choice in order to reach a
perfect fitting. It can be considered a satisfactory fitting when Diss ≤ 0.1 (Iannario, 2009). The
dissimilarity index approach cannot be extended to the CUB model with covariates and it
should be noticed the application of Likelihood Ratio Test (LRT) in order to compare log-
likelihoods of nested models (Piccolo, 2003b; Corduas et al., 2009; Iannario, 2009).
We are considering a CUB (0, 0) with the parameter vector θ’=(π, ξ) and a nested model CUB
(p, q) with the parameter vector θ’’=(βi, γj), i=1,…,p+1, j=1,…,q+1. The log-likelihood
deviance is derived as LRT = −2 ( l (θ ′ ) − l (θ ′′ ) ) and it is distributed as a χ2 with degree of
freedom equal to the difference of the parameter number (D’Elia & Piccolo, 2008; Iannario &
Piccolo, 2009).
The basic idea of our proposal (figure 1) is to deepen the conjoint analysis results by applying
CUB models to those product profiles described by attribute levels that have been evaluated
as most relevant.
Procedures
The case study involved a firm that produces the raw material for food packaging purposes.
The main scope of the research was to collect consumer preferences for food packaging in
order to carry out insightful analysis. Once defined attribute levels (table 1), two experimental
designs were drawn. Each experimental design was drawn to define the product concepts on
which the conjoint analysis study was based. Each conjoint analysis has considered product
concepts that were described by four out of five attributes. We excluded “disposal” as an
attribute in the conjoint analysis called “cook-able”, the opposite occurred when we excluded
“cook-able packaging” as attribute. A fractional factorial design using an orthogonal plan was
adopted to reduce the number of level combinations.
Disposal Cook-able pkg Size Shape Shelf life
Figure 2 Attribute importance of cook-able version (left panel) and disposal version (right panel).
Consumers gave more importance to both cook-able pkg and disposal than other attributes.
We hypothesize that this trend could be a bias due to the interviewing procedures. In fact
consumers were asked to state if they paid more attention to the possibility to cook food
inside the packaging or if they paid more attention to the packaging material (recyclable or
not). The shape and the size of packaging were also important attributes.
At the same time we describe a summary of the part-worth utilities for each version of the
CA. Utilities are shown in bar plots in order to have an overview of the levels with the highest
utility.
Results show that the levels with the highest utility were the cook-able packaging by oven and
the biodegradable packaging.
Figure 4 Level utilities for size attribute: cook-able and disposal versions in left and right panel respectively.
Split packs and long shelf life are the levels with the highest utility in both CA versions.
Figure 4 shows that single pack and family pack have negative utilities while figure 5 shows
that a long shelf life has very positive utility with respect to short shelf life. Long shelf life
was defined to be two weeks while short shelf life was set at one week. Finally “shape” shows
a slightly different pattern of level utilities.
Figure 5 Level utilities for shelf life attribute: cook-able and disposal versions in left and right panel respectively.
The levels for “shape” with the highest utility are cover-reclosable trays and zip lock-
reclosable bags. The pattern shown in figure 6 stresses the importance of a bag or a tray that
can be closed after that it has been opened.
Figure 6 Level utilities for shape attribute: cook-able and disposal versions in left and right panel respectively.
Based on the levels with the highest utility,
utility we have selected and grouped the profiles and we
have run CUB models without and with covariates. Parameter π,, parameter ξ and dissimilarity
indexes are shown in tables 2 and 3 for both versions of CA. The variable
vari “All” is
representing all cards with at least one attribute level that has been estimated with the highest
utility.
Variable π ξ Diss. Log likelihood
1 Cook-able pkg: oven 0.576 (0.051) 0.342 (0.016) 0.0489 -792.351
3 Shelf life: long 0.451 (0.037) 0.257 (0.014) 0.0756 -1620.434
4 Shape: bag with zip lock 0.309 (0.052) 0.221 (0.028) 0.0619 -826.835
5 Size: split packs 0.546 (0.066) 0.121 (0.019) 0.0857 -301.8470
6 All 0.418 (0.031) 0.286 (0.013) 0.0533 -2448.948
Table 2 Pai and Csi estimates (standard error), dissimilarity indexes and log likelihood for cook-able
cook version of CA.
Figure 7 Observed relative frequencies (dots) and fitted probabilities (circles) of CUB models for cook-able
cook version of CA.
Figure 8 Observed relative frequencies (dots) and fitted probabilities (circles) of CUB models for disposal version
vers of CA.
In order to have a comprehensive overview of the uncertainty and the feeling dimensions,
dimensions we
placed each of those attribute levels into space (figure 9). The CUB model gives two
parameters for each attribute level so that we can determine points
point into a two-dimensional
two
space.
The feeling for “split packs” is very high and also for “biodegradable”.
le”. The attribute level
with the higher uncertainty is the tray reclosable by cover. Then we have applied a CUB
model with covariates for each group of cards.
cards
Covariates Coding
Gender 0= male;1= female
Nationality 0= Italy;1= Austria
Age Continuous variable
1= elementary; 2= intermediate;
Educational level
3= high school; 4= graduate
1= <800; 2= 800-1700;
Income (monthly in Euros)
3= 1800-2900; 4= >2900
Table 4 Covariates for CUB model.
The covariates (table 4) have been introduced once at a time and useful descriptions (from
tables 5 to table 8) show which of them and how they affect CUB-model parameters. In
particular we reported π or ξ estimates, the effect estimates (β or γ) of covariates that we can
use to estimate parameter π or ξ and we reported also the log-likelihood in order to have
sufficient data to compare nested models.
Log
Variable π or β0 π covariate β1 ξ or γ0 ξ covariate γ1
likelihood
0.449 -0.861 -0.323
- - Gender -1618.10
(0.037) (0.114) (0.149)
Shelf life: long
0.466 -0.149 Educational -0.371
- - -1610.121
(0.036) (0.212) level (0.083)
0.310 -0.833 -0.620
- - Gender -824.8445
Shape: bag with (0.051) (0.232) (0.302)
zip lock -2.432 0.933 0.220
Income - - -824.5315
(0.971) (0.482) (0.0260)
0.566 -2.947 0.024
- - Age -299.6697
(0.064) (0.499) (0.011)
0.607 -0.146 Educational -0.635
Size: split packs - - -295.8138
(0.067) (0.488) level (0.182)
-2.354 Educational 0.956 0.110
- - -295.5072
(0.857) level (0.296) (0.017)
0.111 -0.627 0.292
Gender - - -2446.353
(0.220) (0.272) (0.013)
-1.168 0.484 0.283
Income - - -2446.366
(0.411) (0.215) (0.013)
All
0.417 -0.703 -0.359
- - Gender -2444.622
(0.031) (0.091) (0.122)
0.429 -0.286 Educational -0.250
- - -2442.787
(0.031) (0.188) level (0.072)
Table 5 Parameter estimates (standard error) and log-likelihood of CUB models with covariates (cook-able version of CA).
Table 5 and table 7 show CUB (1, 0) with a significant covariate for π and CUB (0,1) with a
significant covariate for ξ. Each line in table 5 and table 7 presents the CUB model with a
significant covariate.
Each line in tables 6 and 8 show which covariates were significant for a CUB model with
more than one covariate. The first line of table 8 presents results of a CUB (1, 1) for
“disposal”: nationality and age were significant for explaining parameters π and ξ
respectively. The first line of table 6 shows a CUB (0, 2) for “long shelf life” (cook-able
version of CA): gender and educational level were both significant for explaining parameter ξ.
The LRT was also significant (χ31.618, 2, p-value < 0.000001).
Log
Variable π or β0 π covariate β1 ξ or γ0 ξ covariate γ1 and γ2
likelihood
-0.484
Gender
0.463 0.319 (0.147)
Shelf life: long - - -1604.625
(0.036) (0.255) Educational -0.442
level (0.087)
Shape: bag with -2.342 0.896 -0.937 -0.556
Income Gender -822.639
zip lock (0.915) (0.463) (0.209) (0.284)
-1.474 Educational 0.702 -0.626 Educational -0.463
Size: split packs -292.9269
(0.878) level (0.304) (0.570) level (0.190)
-0.525
Gender
0.272 -0.803 0.195 (0.123)
All Gender -2430.956
(0.213) (0.263) (0.215) Educational -0.329
level (0.075)
Table 6 Parameters (standard error) and log-likelihood of CUB models with more than one covariates applied to cook-able
CA cards.
From table 6, considering all attribute levels (the variable called “All”), the parameter π of
CUB model was significantly affected by gender and the parameter ξ was affected by gender
and educational level.
Log
Variable π or β0 π covariate β1 ξ or γ0 ξ covariate γ1
likelihood
0.372 -1.599 0.146
Nationality - - -1068.66
(0.201) (0.611) (0.015)
-1.491 Educational 0.595 0.144
- - -1067.423
Disposal: (0.509) level (0.174) (0.015)
biodegradable 0.515 -2.671 0.019
- - Age -1069.814
(0.047) (0.383) (0.007)
0.521 -0.705 Educational -0.403
- - -1069.253
(0.045) (0.353) level (0.138)
-1.853 Educational 0.395 0.199
- - -2061.719
(0.488) level (0.153) (0.018)
0.251 -0.573 0.192
Income - - -2063.067
(0.488) (0.282) (0.019)
Shelf life: long
0.319 -2.600 0.026
- - Age -2056.569
(0.035) (0.398) (0.007)
0.326 -2.059 0.361
- - Income -2062.043
(0.034) (0.295) (0.129)
Shape: tray with 0.241 -0.699 -2.301
- - Nationality -926.0493
cover (0.050) (0.158) (1.055)
-1.948 Educational 0.494 0.116
- - -665.8254
(0.700) level (0.216) (0.022)
0.364 -3.423 0.030
Size: split packs - - Age -663.9665
(0.048) (0.598) (0.010)
0.394 -0.311 Educational -0.558
- - -665.6478
(0.052) (0.785) level (0.276)
-1.900 Educational 0.411 0.222
- - -3439.968
(0.411) level (0.121) (0.014)
0.319 -2.076 0.017
All - - Age -3439.09
(0.027) (0.265) (0.005)
0.320 -1.843 0.298
- - Income -3443.031
(0.027) (0.245) (0.108)
Table 7 Parameter estimates (standard error) and log-likelihood of CUB models with covariates (disposal version of CA).
Log
Variable π or β0 π covariate β1 ξ or γ0 ξ covariate γ1 and γ2
likelihood
Disposal: 0.339 -1.564 -2.541 0.017
Nationality Age -1064.042
biodegradable (0.207) (0.590) (0.348) (0.006)
0.024
Age
0.323 -2.936 (0.007)
Shelf life: long - - -2054.960
(0.035) (0.433) 0.241
Income
(0.129)
-1.558 Educational 0.299 -1.822 0.013
All Age -3435.976
(0.366) level (0.121) (0.244) (0.005)
Table 8. Parameters (standard error) and log-likelihood of CUB models with more than one covariates applied to disposal
CA cards.
Tables 9 and 10 show directions of uncertainty (1-π) or feeling (1-ξ) when a significant
covariate is introduced. This way of representing effect direction is aimed at giving a tool to
easily discriminate patterns. Table 9 indicates that females have constantly higher feeling and
uncertainty than males.
(1-π) (1-ξ)
Variable π covariate ξ covariate
effect effect
Gender ↑
Shelf life: long - -
Educational level ↑
Shape: bag with zip lock - - Gender ↑
Age ↓
Size: split packs Educational level ↓
Educational level ↑
Gender ↑ Gender ↑
All
Income ↓ Educational level ↑
Table 9 Direction of the effect when covariates are introduced (cook-able version of CA).
Table 10 presents a slightly different pattern of covariates. Gender was not significant and
educational level was an important covariate that seemed to affect the uncertainty component.
(1-π) (1-ξ)
Variable π covariate ξ covariate
effect effect
Nationality ↑ Age ↓
Disposal: biodegradable
Educational level ↓ Educational level ↑
Educational level ↓ Age ↓
Shelf life: long
Income ↑ Income ↓
Shape: tray with cover - - Nationality ↑
Age ↓
Size: split packs Educational level ↓
Educational level ↑
Age ↓
All Educational level ↓
Income ↓
Table 10 Direction of the effect when covariates are introduced (disposal version of CA).
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