D'Elia and Piccolo (2005) have recently proposed a mixture distribution, named CUB, for ordinal data which has proved to be effective in numerous real applications arising in various fields such as social analysis, medicine and marketing. The CUB model provides the probability distribution of the random variable generating ordinal data induced from judgments or evaluations that groups of respondents express on given items.The use of such a mixture distribution for modelling ratings is justified by the following consideration: the judgment that a subject expresses is the result of two components, uncertainty and selectiveness. The first one is well represented by the fact that the rather, who is requested to assign a score on a discrete scale to a certain item, tends to hesitate before providing the answer since he/she has to force his/her mental construct about liking/disliking into a numerical value. The uncertainty is represented by a Uniform distribution which assigns to each possible score the same probability. The parameter π determines the role of uncertainty in the final judgment: the lower the weight (1−π) the smaller the contribution of the Uniform distribution in the mixture.The parameter ξ, instead, characterizes the shifted Binomial distribution which may assume different shapes. Depending on the meaning of the highest score (positive or negative judgment), this parameter denotes the strength of 'liking' (or 'disliking') that the rather feels for the item (selectiveness/awareness).In this sense, the CUB model is very flexible because it provides a continuum of alternative theoretical distributions to represent the subjects' ratings.In a further extension of the model the influence of external factors in the final judgement is considered (Piccolo and D'Elia, 2008). In particular, two relations, which connect the model parameters to significant covariates (which, for instance, may represent features of judges) by means of a logistic link function, are added to (1). The possibility of relating the parameters of CUB models to covariates makes the formulation interesting for practical applications. As a matter of fact, this relationship allows for the interpretation of the latent factors (uncertainty and selectiveness), acting in the process of forming a judgement, with respect to specific characteristics of interviewees (such as socio-demographic variables, consumer tastes, etc.). CUB model was applied to a case study related to fair-trade coffee. A sample of 224 fair-trade coffee consumers were interviewed at stores after purchasing at least one box of coffee. With this data-set, CUB model split consumers, according to their preferences, in two different segments: one showing high price elasticity, and one with a low price elasticity. CUB model allowed, also, to characterize these two segments in great details.

Valuing consumers' preferences with the CUB model: a case study on fair-trade coffee / Cicia, Giovanni; Corduas, Marcella; DEL GIUDICE, Teresa; Piccolo, Domenico. - (2009). (Intervento presentato al convegno 3rd International European Forum on System Dynamics and Innovation in Food Network tenutosi a Igls/Innsbruck, Austria nel 16-20 Febbraio 2009).

### Valuing consumers' preferences with the CUB model: a case study on fair-trade coffee

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*CICIA, GIOVANNI;CORDUAS, MARCELLA;DEL GIUDICE, TERESA;PICCOLO, DOMENICO*

##### 2009

#### Abstract

D'Elia and Piccolo (2005) have recently proposed a mixture distribution, named CUB, for ordinal data which has proved to be effective in numerous real applications arising in various fields such as social analysis, medicine and marketing. The CUB model provides the probability distribution of the random variable generating ordinal data induced from judgments or evaluations that groups of respondents express on given items.The use of such a mixture distribution for modelling ratings is justified by the following consideration: the judgment that a subject expresses is the result of two components, uncertainty and selectiveness. The first one is well represented by the fact that the rather, who is requested to assign a score on a discrete scale to a certain item, tends to hesitate before providing the answer since he/she has to force his/her mental construct about liking/disliking into a numerical value. The uncertainty is represented by a Uniform distribution which assigns to each possible score the same probability. The parameter π determines the role of uncertainty in the final judgment: the lower the weight (1−π) the smaller the contribution of the Uniform distribution in the mixture.The parameter ξ, instead, characterizes the shifted Binomial distribution which may assume different shapes. Depending on the meaning of the highest score (positive or negative judgment), this parameter denotes the strength of 'liking' (or 'disliking') that the rather feels for the item (selectiveness/awareness).In this sense, the CUB model is very flexible because it provides a continuum of alternative theoretical distributions to represent the subjects' ratings.In a further extension of the model the influence of external factors in the final judgement is considered (Piccolo and D'Elia, 2008). In particular, two relations, which connect the model parameters to significant covariates (which, for instance, may represent features of judges) by means of a logistic link function, are added to (1). The possibility of relating the parameters of CUB models to covariates makes the formulation interesting for practical applications. As a matter of fact, this relationship allows for the interpretation of the latent factors (uncertainty and selectiveness), acting in the process of forming a judgement, with respect to specific characteristics of interviewees (such as socio-demographic variables, consumer tastes, etc.). CUB model was applied to a case study related to fair-trade coffee. A sample of 224 fair-trade coffee consumers were interviewed at stores after purchasing at least one box of coffee. With this data-set, CUB model split consumers, according to their preferences, in two different segments: one showing high price elasticity, and one with a low price elasticity. CUB model allowed, also, to characterize these two segments in great details.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.