J. Mojet (1), A.A.M. Poelman (1) and N.M. Faber (2)
1 CICS-Wageningen UR,
2 Chemometry Consultancy, Ede
In the standard implementation of external preference mapping, consumer preferences are fitted as polynomial functions of the first two principal components (PCs) of the sensory data. This implementation is known to suffer from two major weaknesses, namely
- the relatively small number of consumers that can be significantly fitted, and
- the often limited utility of the elliptical and quadratic models.
Therefore, we previously explored the possibility of including higher-numbered PCs while restricting the model choice to the simplest polynomial function, i.e. the (linear) vector model [1]. To determine the number of PCs to keep in the fit, we proposed a heuristic decision rule [1]. Here, we present a novel randomization test as a formal alternative.
Randomization tests are extremely useful for this type of modelling since only weak assumptions are made about the data. Moreover, they are entirely data-driven, hence user-friendly. As a test statistic, we opted for the improvement of consumer fit when adding a PC. It is shown that the heuristic rule can easily lead to over-optimistic results for consumer fit. The randomization test is applied in e.g. the preference mapping of apples and the improvement with respect to method used in the previous publication [1] will be presented to support our recommendation to apply the novel randomization test for the estimation of principal components in external preference mapping.
[1] N.M. Faber, J. Mojet and A.M.M. Poelman, Simple improvement of consumer fit in external preference mapping, Food Quality and Preference, 14 (2003) 455-461.
