Preference mapping using quantile regression

13 September 2018
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ASA 2018 - Statistics and the Assessment, Control and Scenarios of Risks. Applications to Food, Social and Health, Economic and Environmental Fields
Pescara, 12-14 September
Convegno dell’Associazione Italiana per la Statistica Applicata
Conference webpage

The peculiarity of Quantile Regression (QR) is to provide an estimate of conditional quantiles of the dependent variable rather than of conditional mean. The interpretation of the parameters estimated by QR follows that of any other linear model: the rate of change of some quantiles of the dependent variable distribution per unit change in the value of some predictor.

In preference mapping we generally aim at finding linear relations between acceptance data and sensory data. This information can be used for several purposes including improving or optimizing existing products. For each consumer we assume that the preference increases/decreases linearly for each sensory attribute. Preference mapping derives a multidimensional representation of products and consumers according to preference patterns.

Using QR in preference mapping, we assume the same model but for different conditional quantiles not only for the conditional mean. For example, we could find that a consumer like sweetness and our conclusion with LS would be that the consumer’s preference on average will increase as the degree of sweetness increases. Using QR we explore the whole distribution of the dependent variable, that is of the consumer preference. For example, we might find that the preference for the lower quantiles is less affected by sweetness, that is, for the less preferred products an increase in sweetness would have less effect. This clearly applies to all consumers, and therefore it is necessary to arrive at plots similar to the classic loading plots that allow to extract this information in a simple way. For this purpose, we present a particular graphical rep- resentation that combines the results of the classic approach based on the least squares with the results of the QR. A case study on consumer preferences for fruit juices will show the potential of the proposed approach.

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