EPM is a hybrid method with two distinct steps. The first is to obtain the ‘external axes’, often these are the 1st two principal component dimensions of a PCA computed on sensory panel mean scores. This constitutes the product map to which consumer liking data is projected using response surface regression analysis. A separate regression model is computed for each consumer, where their liking scores (Z), are regressed onto the product coordinates (X & Y). The software offers a choice of the regression model used which may be one of the following options:
Vector : Z = aX + bY + c
Elliptic : Z = aX + bY + cX2
+ dY2 + e
Quadratic : Z = aX + bY + cX2
+ dY2 + eXY + f
In the early days of the EPM method users would try to interpret the estimated parameters in one of the models above, however this is a complex task as there is a separate set of estimates for each consumer and for the 2 models with curvature there is the possibility of either maxima or minima. These days it is more usual to summarize all these models with a contour plot, Danzart (1998) and Danzart et al. (2004). The product map is divided into a n x n grid, and for each cell in the grid the number of consumers whose models exceed a threshold liking value is counted. A coloured contour plot is then used to highlight areas where these counts are highest, as these are the same areas where the greatest number of consumers are predicted to be accepting of a product.
The main graphical outputs are shown below. The first two plots are the PCA product scores and variables loadings plots for the first two dimensions; these are only generated if the user chooses the ‘pre-transformation’=PCA option. The third plot shows the external preference map itself, which clearly shows that ‘Daily Delight’ bread is well placed in the darkest red region, while the ‘Sliced Right’ bread is poorly liked as it is in the darkest blue region. All three plots were generated using the example breads data set, using a correlation PCA on all attributes, the elliptical model option, and a grid size of 100.