Preference mapping^{1} is referred to as a group of multivariate statistical techniques designed to develop a deeper understanding of consumer acceptance of goods. Results of such analyzes can be used to assist the product developer in selecting out of a set of prototypes, the product which may maximize consumer liking.

External preference mapping derives a multidimensional representation of products based on their sensory profile or a set of other external data such as instrumental measures of color, texture or flavor. This representation is usually obtained through Principle Component Analysis

PCA of a data matrix with products as rows and external data as variables or columns

^{2}. External mapping approaches are limited by the fact that the sensory space (i.e., multidimensional representation) is obtained from external data alone without prioritization of the attributes based on their importance to consumers. Jaeger et al.

^{3} point out that for external analysis to be successful, it is essential that the external stimulus space contains dimensions which pertain to preference.

The second step in the analysis is to fit the consumer data in the sensory space. To do this, some type of polynomial model is used to regress the hedonic scores given to the products onto the coordinates of the products in the sensory space. Four possible models (i.e, vector, circular, elliptical and quadratic) were originally described by Carroll^{1}. The models considered are special cases of the quadratic surface model which can be expressed as:

Where OL is overall liking (hedonic scores), PC_{i} are the product scores on the ith PC, a_{i}s and b_{i}s are regression coefficients for the ith PC linear and quadratic terms and c_{ij}s are regression coefficients for the interaction between ith and jth PCs.

## References

^{1 }Carroll, J.D. 1972. Individual differences and multidimensional scaling. In R.N. Shepard, A.K. Romney, and S.B. Nerlove (Eds) Multidimensional scaling: theory and applications in the behavioral sciences, Vol 1 (pp. 105-155). New York: Seminar Press.

^{2} Meullenet, J-F., Xiong. R. and Findlay, C. 2007. Multivariate and probabilistic analyses of sensory science problems. IFT Press. Blackwell Publishing, Ames, IA

^{3} Jaeger, S.R., I.N. Wakeling, H.J.H. MacFie. 2000. Behavioural extensions to preference mapping: the role of synthesis. Food Quality and Preference 11(2000) 349-359.

Martinez, C., M.J. Santa Cruz, G. Hough and M.J. Vega. 2002. Preference mapping of cracker type biscuits. Food Quality and Preference 13(2002) 535-544.