Top-down models, such as Latent Class and Random or Mixed Multinomial Logit (MMNL) Model, which are widely used to study preferences heterogeneity, may relax some preferences assumptions (McFadden & Train, 2000). While Latent Class models do not assume normal preferences distribution across the whole survey, this assumption has to be accomplished only within behavioural groups. Mixed MNL models relax the preferences correlation assumption, however they have to make assumptions about the type of distribution for the preferences (normal, lognormal, triangular and uniform) (Huber & Train, 2001).

The main difference between top-down and bottom-up models is that the first group of models estimates the average preference of a (sub)group of respondents, while a single individual is the basic unit of analysis for the second model. Bottom-up models are estimated directly by Individual Utility Functions (IUF), i.e., one utility function per single respondent. IUF do not need any theoretical assumptions about preferences distribution and correlation among individuals because each individual preference is estimated independently of each other. Thus, it avoids the problem of mischaracterising mean/variance heterogeneity: the empirical distribution of the true heterogeneity is available (Flynn, 2010).

Despite the theoretical advantages, bottom-up models need a greater amount of preference information per respondent. This information is obtained through multiple responses choice task. An extreme case of IUF estimation is presented by Pihlens & Louviere (2004). They carry out a choice experiment to evaluate choice errors of a single subject to different colours stimulus. Subjects answer 100 replications (choice sets) of paired comparisons. Their experiment is cognitive exhaustive (answer quality decrease) and it deals with preferences from only one person. Choice experiments with many replications would be economically non-viable for those studies that take into account preferences of many people, because surveys would need a long time to be answered. Louviere et al. (2008) suggest asking more questions about each choice set, instead of asking more choice sets to each person. It is less exhaustive but provides enough information to estimate IUF. Their method assembles the best-worst choice task, the optimal experimental design and the estimation process (see below).

Except choice experiments for laboratory in psychology, it is rare to find choice modelling studies with bottom-up models (Ebling et al., 2010). In addition to the estimation simplicity, Frischknecht (2011) and Louviere (2011) present some reasons to use bottom-up models. According to them, bottom-up models allow making estimations with few observations (small samples population), and are a proper way to aggregate individuals decisions, valuing which attributes actually matter in the decision process, testing how much uncertainty exists in each individual response, checking the top-down models assumptions, and studying unobserved variability between and within individuals.

This paper describes how consumers make their purchase decision with respect to late season peaches attributes-levels and values preferences variability among consumers.

Best-worst choice task was proposed by Louviere & Woodworth (1990) as a multiple choice extension of Thurstone’s method of paired comparisons. Finn & Louviere (1992) applied it the first time to overcome rating scale bias. This characteristic was very important in studies as Cohen & Neira (2004) and de-Magistris et al. (2014). Even though this choice task was proposed more than 20 years ago, it was formalised recently. Marley & Louviere (2005) formalised the best-worst choice experiment for choices among things (Case 1) (in most studies, those things are attributes of products or services), while Marley et al. (2008) formalised it for choices within profiles (Case 2) and Marley & Pihlens (2012) for choices among profiles (Case 3). This work deals with choices among profiles.

In general, best-worst choice task consumers are asked to make statements about the best and the worst alternatives, among three or more available alternatives, only once or more times in each choice set. This choice task makes a good use of respondents’ ability to identify extreme options. Hence, individual answers present less variability with best-worst tasks than ranking the alternatives of a choice set from the best to the worst alternatives. Lower variability in the answers has direct effects on diminishing the Confidence Interval (CI). Hence parameters become more accurate and it is possible to make more precise inferences about consumers’ preference. Sufficient information to model a single respondent preference, with Bottom-up models, is given from full ranking of alternatives with the best – worst task (Louviere, 2011).

It is necessary to make the experimental design after knowing which variables will be incorporated in the choice experiment (in our case, with a best-worst choice experiment, the variables are attributes-levels) and how preferences will be measured through the empirical model. The number of alternatives in each set and the number of choices are chosen based on the number of levels of each attribute and the empirical model. The number of choice sets is calculated based on the combination among attribute-levels (levels of attributes), but frequently it is too large to be answered in a survey. Thus, it is usual to adopt fractional factorial design, which is less exhaustive to be answered although it may lose statistical properties.

Efficient experimental designs are characterised by four properties: level balance, orthogonality, minimum overlap and utility balance (Huber & Zwerina, 1996). Level balance deals with the number of times that each attribute-level appears within choice sets and across them. Balanced design is obtained when all attributes-levels have to be presented the same number of times. Orthogonal design is when attributes-levels vary independently across alternatives and choice sets. Trade-offs in each choice situation is optimised as well as the amount of preference information by minimising asymptotic errors.

An efficient design minimises the variance-covariance estimator, i.e., it maximises the amount of information the design conveys to identify marginal utilities. The information matrix to design under the conditional logit assumption is given by the matrix of second derivatives of the log-likelihood functions. A suitable algorithm would search, through different arrangements of attributes and levels, an optimal solution according to some criteria.

There are many criteria to measure the design efficiency. Actually, the right criterion has to be chosen in accordance with the study objective. Scarpa & Rose (2008) suggest using the D-error criterion if the desire is to perform a model that minimises the standard errors and covariance of estimated parameters. Bliemer & Rose (2011) find that experimental designs based on the D-error criteria instead of the orthogonal design produce estimated parameters with lower standard errors and sample size requirements decrease. In part, this difference is explained by the generation of dominant alternatives, which is greater in orthogonal design than in D-error. Louviere et al. (2008) recommend using D-optimal (D-error of 100%) in their bottom-up model.

No biased estimators are obtained if expected parameters converge to real values and efficient parameters as those that have the minimum variance. Attributes levels are combined to get non biased and efficient parameters, following suggestions of Street et al. (2005) and Street & Burgess (2007). Their strategies to construct a statistically efficient experiment design are based on modular mathematic, which starts with an Orthogonal Main Effect Plan (http://www2.research.att.com/~njas/oadir/) and then there is a generation of choice sets’ options based on the first selected profiles.

There are many definitions of food quality. Basically, it can be defined by two points of view: objective quality or perceived quality. Perceived quality is based on the consumers’ perspective. It is defined as a subjective individual evaluation encompassing the total characteristics of a product that satisfy the consumers’ needs. Nelson (1970) proposed to distinguish among many types of product quality attributes based on the ease with which they can be communicated to consumers. Search attributes can be verified at the time of the purchase (e.g., fruit size or colour); experience attribute can be assessed only after the purchase has taken place (for example, taste or convenience); and credence attributes cannot be objectively verified and are based on trust (for example, healthiness or method of production).

In our case, four late season peaches attributes (peaches origin, type of packaging, peach size and price) have been selected and three levels have also been considered for each attribute as a result of a literature review, a focus group, personal interviews to fruit and vegetable managers in supermarkets, and local supermarket monitoring (Table 1).

The empirical model1 (Eq. [1]), takes only main effects into account and it is an additive function of the alternative j. Peaches “from Calanda area without PDO” is coded as the reference-level for peaches origin. The marginal utility between the reference-level of peaches origin and peaches “from Calanda area with PDO”, estimated by β_1,q, shows how much consumer q values the PDO Calanda brand. If consumer q prefers a certified peach over a non-certified peach (both produced in the Calanda area), this parameter will take a positive value. However, if the consumer is indifferent between these two attribute-levels (his/her utility does not increase or decrease), the estimated parameter will be statistically equal to zero. The value of β_2,q assess to what extent consumer q appreciates the Calanda production area, but without any guaranty of quality associated to the PDO brand.

Louviere et al. (2008) approach generates artificial observations to increase the information amount. Thus, if there are three alternatives in each choice set and all alternatives are ordered by the Best-Worst task, estimations without artificial observations consider that consumer q makes one choice between six available alternatives (MaxDiff approach) or two choices, one among three and another between two available alternatives (Sequential Best-Worst approach). With artificial observations, the estimation process considers that consumer q makes three choices in each choice set (all alternatives are chosen) and each choice is made among three available alternatives.

In the survey, every individual made multiple choices and ranked all alternatives of the choice sets (via the best-worst choice task). Then, according to the alternative rank position, individual preferences are calculated with Linear Probability Models (LPMs), such as Multinomial Logit Model (MNL), or Weighted Least Square (WLS) regression models (Louviere et al., 2008). MNL models also deal with a great amount of information because they take into account not only the alternatives that are chosen in the choice set, but the strength of competition within each set (Orme, 2009). The MNL function is weighted according to the probability of the chosen alternative, as shown in Louviere & Woodworth (1983).

Theoretically, let S be a complete set of choice situations, each choice situation has J alternatives, and each alternative is described by a (k × 1) vector of explanatory variables x_sj. For a single consumer q the conventional likelihood function in multinomial logistic regressions is given by Eq. [2]. In this equation the dependent variable y_qsj is a dummy variable equal to 1 (one) when alternative j is chosen in the choice set s by consumer q and equal to 0 (zero) otherwise. The function is maximised with respect to the betas (β’_qk).

Data were collected from a survey conducted in a medium-sized Spanish town, Zaragoza, during the late peaches season in October 2008. All respondents were PDO Calanda peaches consumers. They were identified when it was asked them if they had bought PDO Calanda peaches in the last two years. Sample size was set at 316 PDO Calanda consumers of peaches who were visiting two hypermarkets. As there were about 650,000 citizens in Zaragoza in 2008, its population can be considered infinite and assuming a confidence level of 95.5%, k=2 and p=0.5, this sample size results in a sampling error of ±5.6% in Zaragoza (Trespalacios et al., 2005). The sampled consumers’ profile is similar to the actual population. Consumers’ socio-demographics characteristics are shown in Table 2.

Consumers’ ages were calculated from their birthdates and are grouped in five age classes. These age classes have the same range than the statistical information from Aragon. In 2008, the average age of the Aragonese population was 42.9 years old and the average age for PDO Calanda peaches consumers was 46.5 years old.

The percentage of women (59.2%) on the survey was higher than for the Aragon population (50.1%). This difference can be desired because it reflects the real percentage of women buying peaches in the market. According to Cerdeño (2006) women are to a great extent responsible of fruits and vegetables purchase in Spain.

On average, sampled consumers have higher education level than the average population of Aragon. The percentage of consumers attending college is 31.3% and elementary school is 27.5% while in Aragon those percentages are 24.4% and 34.1%, respectively.

In order to represent the preference of 316 consumers, 316 IUFs, each one with 8 parameters, were estimated. In total, 2,528 parameters were calculated. Each estimated parameter represents how much utility improves or diminishes when a consumer exchange an attribute-level (the attribute-level of reference) to another. The average values of these estimated parameters are shown in the Table 3.

Consumers have strong preference for peaches from Calanda area and peaches with PDO Calanda. On average, utility increases when consumer exchange peaches from other area without PDO Calanda recognition to peaches from Calanda area, but without PDO Calanda. Exchanging peaches from Calanda area without PDO to other peaches from the same area with PDO increases also utility. Marginal utility from origins’ levels have the highest values when compared with other marginal utility. These strong preferences may be explained by the proximity between the city of Zaragoza and Calanda area and by the great PDO Calanda reputation. Espejel et al. (2007) studied the case of preferences for air-cured ham, Alfonso et al. (2001) evaluated the preferences for lamb meat and Espejel & Fandos (2008) studied the preferences for olive oil, and they also found strong preferences for other local PDOs in the city of Zaragoza.

Peaches sold in normal packaging provide higher utility than peaches traded in active packaging or in bulk. Although receiving natural treatment with Syzygium aromaticum oil, consumers dislike peaches in active packaging because it is associated with a longer shelf-life, which loses freshness and is less natural. However, consumers are more willingness-to-pay for convenient products. For example, Baselice et al. (2014) found that consumers renounce to fresh-cut products in comparison to longer shelf-life products. Convenience explains why consumers prefer peaches in natural packaging instead in bulk. One example of the inconvenience is that consumers spend more time purchasing peaches in bulk than in normal packaging. Bulk peaches must be weighed and consumers have to take queues in the market.

Usually, greater peach size is better. Results show that the largest size (380 g/fruit) is preferable to medium size (250 g) and medium size is preferable to the smallest size (160 g). Why larger fruit is preferable? According to Bruhn (1995) a lot of consumers believe that large peaches are sweeter than small ones because small fruits are perceived as harvested too early. In our case, at the interview, many consumers declared that largest size peaches represent abundance while the smallest size denotes poorness. This result highlights the importance of the PDO Calanda Regulatory Council policy, which determines a minimum size for the product. Normally, larger peaches have higher price in the market.

During the survey period, peach price was sold around 2.5 €/kg. Consumer behaviour did not run away from the classical economic theory prediction regarding prices. The increase in price causes disutility among consumers. The highest disutility was observed when price was increased from 2.5 to 3.5 €/kg.

Estimating consumers preferences of the entire sample using MNL models provides consistent estimations only if preferences (represented by estimated parameters of each attribute-level) across consumers are normally distributed (Louviere et al., 2000). Thus, Kurtosis, Skewness, Kolmogorov-Sminov, Shapiro-Wilk statistics and statistical significance, which are used to value more objectively how well preferences distributions performed as normal distributions, are calculated for every parameter distribution (Table 3).

Neither estimated parameter is normally distributed. In this case, if a top-down model was estimated, results have been seriously biased, with misleading inferences and conclusions (Fiebig et al., 2010).

The estimated parameters (marginal utilities) distributions of peaches “from Calanda area with PDO” and “from other areas without PDO” are less dispersed around the mean than any other estimated variable and more spread than in a normal distribution because their Kurtosis statistics are -0.913 and -0.704, respectively. Estimated parameters (marginal utilities) of both origins levels are not distributed asymmetrically. The estimated parameters of attribute-level “from Calanda area with PDO” tend to be right tail distributed while the estimated parameters of attribute-level “from other area without PDO” have the opposite tendency.

Bulk peach utilities are more centred on the average value (-0.01) than any other variable, which means that most consumers show similar preference about this packaging type. Regarding the preference asymmetry, “active packaging” has -1.001 Skewness (left-skewed), meaning that there are more consumers with smaller marginal utility values than the average. This asymmetry is also checked for preference distribution of estimated parameters such as “from Calanda area with PDO”, “high price” and “smallest size” peaches. On the other hand, there are more betas with higher values than the average utility (Skewness > 0) for “bulk”, “largest size”, “from other areas without PDO” and “low price” peaches.

Preferences (estimated parameters) have to be uncorrelated to obtain consistent estimations with MNL models (top-down models) (Louviere et al., 2000). Table 4 shows the correlation among all consumers’ preferences towards late season peaches attributes-levels. The highest correlations are observed among marginal utilities of attribute-levels from the same attribute and present negative values. Thus, top-down models would have provided wrong conclusions. For origins levels, it means that there are two tendencies for preferences ordering. One includes those people who like peaches with the PDO Calanda brand and also like peaches produced in the Calanda area and the second preference tendency shows that those people who like peaches not produced in Calanda area also dislike the PDO Calanda brand.

The negative correlation among packaging levels marginal utilities means that those who prefer normal packaging over bulk also like active packaging or those who prefer bulk peaches instead of normal packaging also refuse active packaging.

In our case, both basic conditions required in MNL models (normal distribution and uncorrelated preferences) were not accomplished. Thus, bottom-up models provide consistent estimated parameters as well as consistent conclusions. Next section deals with the consumers preferences description based on bottom-up model estimations. Some statistical inferences have to be imposed.

Statistical inferences about estimated parameters are undertaken to deal with consumers’ indifference towards late season peaches attributes-levels. In the case of IUF calculated with the bottom-up model, it is possible to identify which levels – from the same attribute – have the same utilities for each consumer by making statistical inferences on each estimated parameter.

In this case, the null hypothesis checks if the marginal utility is statistically equal to zero (H₀: β = 0) and the alternative hypothesis checks if the marginal utility is different from zero (H₁: β ≠ 0). Statistical significance levels of 1%, 5% and 10% are considered (often measured by p-values) on empirical studies. Thus, if the null hypothesis is refused at 1% of statistical significance, it means that the estimated parameter is different from zero with a probability of 99%. In consequence, when one IUF estimated parameter of individual q is refused to be zero at 1% of p-value, it means that consumer q prefers one attribute–level instead of the attribute–level of reference with 99% of accuracy. The null hypothesis is accepted when consumer q is indifferent between those attribute–levels with the same accurateness.

Each IUF has 8 betas or parameters to be estimated (Eq. [1]). Figure 1 shows the consumers’ preference through changes at different statistical significance of estimated parameters. At 40% of p-value, 39, 164, 68, 27, 10 and 3 IUFs have 1, 2, 3, 4, 5 and 6, respectively, parameters statistically different from zero. At this p-value, consumers’ preferences complexity can be taken into account, nevertheless accuracy is low. There is a 40% probability of making error type I (refusing the true hypothesis). The accuracy at this significance level is too small.

Most empirical studies assume a statistical accuracy of 10% of p-value. At this p-value, the analysis has an acceptable accuracy and 210 consumers (66.5% of total consumers) are not indifferent among all attributes-levels. The differentiation between attributes-levels allows describing the different consumers’ preference structure. At 10% of p-value, there are 140 IUFs with one parameter statistically different from zero and 70 IUFs have 2 estimated parameters statistically different from zero. When an IUF had 2 estimated parameters statistically different from zero, they were from different levels from a same attribute. The remaining 106 IUF had all estimated parameters statistically equal to zero, i.e., they were indifferent among all attribute-levels over the reference-levels. Preferences description may be done with estimated parameters’ details, as shown in Table 5.

According to the results, there are 88 IUFs with β₁ > 0 and all other betas are statically equal to zero. It is represented in the Table 5 by: U_{with DOP Calanda} > U_{from Calanda area without DOP} = U_{from other area without PDO}. It means that peaches from Calanda area with PDO Calanda provide higher utility than (i.e., they are preferable to) peaches from Calanda area without PDO Calanda (reference-level) to 88 consumers. At same time peaches from other area without PDO provide same utility than peaches from Calanda area without PDO, i.e., consumers are indifferent between peaches produced in Calanda area or not. These 88 consumers are also indifferent among all other attribute-levels. In summary, they only have a strong preference toward PDO Calanda peach brand.

Similarly, there are 15 consumers with a strong preference for the production area. They prefer peaches from Calanda area without PDO over peaches from other area without PDO and they are indifferent among all other attributes-levels. Other 48 consumers have a strong preference for the production area as well as for the PDO Calanda brand. They want peaches produced in Calanda area with the PDO Calanda. In total, 151 (88+15+48) consumers, who were not indifferent with any attribute-level of origin, were grouped in the Origin Sensitive Group. In addition to this group consumers were grouped in the Packaging Sensitive Group, Size Sensitive Group and Price Sensitive Group.

The Packaging Sensitive Group has 13 consumers (4.1% of total). A Packing Sensitive Consumer has more (or less) utility when exchanging a peach in bulk and/or a peach conditioned in active packaging for another peach conditioned in normal packaging and he/she is indifferent among all other attributes-levels. Within this group, 6 consumers dislike peaches prepared in active packaging (U_bulk = U_{normal packaging} > U_{active packaging}) while 2 consumers like it (U_bulk = U_{normal packaging} < U_{active packaging}). Active packaging preserves peaches 12 days more than the normal one, but some consumers dislike it because the product may lose freshness and normal looking. On the other hand, there are other consumers that value the convenience of the storage.

Peach size is very important for 13 consumers (4.1% of total). They belong to the Size Sensitive Group. In total, 6 consumers effectively reject the smallest peaches (U_smallest < U_medium = U_largest), 4 consumers simply want the largest peaches (U_smallest = U_medium < U_largest) and 3 consumers like the largest peaches and they avoid buying the smallest (U_smallest < U_medium < U_largest). It states that there is a small market segment in which is viable for growers to produce medium (250 g/peach) and large (380 g/peach) size peaches. In relation to plum and nectarine, Sterling Rice Group (SRG, 2005) observed that larger peaches are more acceptable by consumers. They also found that peach size impact more positively on purchasing when they are between tennis ball and softball size. Normally, larger peaches have higher market price.

Price Sensitive Group is the second largest group, with 33 consumers (10.4% of all consumers). A great part of those consumers (14 people) behave such as the Classical Economic Theory predicts, lower price always increase utility. In table 5, it is shown by the following expression: U_1.5€/kg > U_2.5€/kg > U_3.5€/kg. Within Price Sensitive Group exist 9 consumers that refuse the highest price for peaches, but they are indifferent between peaches sold at 2.5 and 1.5€/kg (U_1.5€/kg = U_2.5€/kg > U_3.5€/kg). For them, the fair price is around 2.5€/kg and when price is higher they feel explored. For other 3 consumers, late season peaches only matter if they are sold for 1.5€/kg (U_1.5€/kg > U_2.5€/kg = U_3.5€/kg). They are indifferent between 2.5 and 3.5€/kg probably because 2.5€/kg is the reservation price. Price was also used as a quality cue for 7 (1 + 4 + 2) consumers (2.2% of consumers). Price, as an extrinsic quality attribute, gains more importance than intrinsic attributes in purchasing situations when it is difficult to evaluate quality by experience and credence attributes (Zeithaml, 1988). In our case, an experience attribute is the PDO Calanda peaches taste and a credence attribute is the PDO Calanda peaches production system.