AbstractOne of the problems in analyzing sensory profiling data is to handle the systematic individual differences in the assessments from different panelists. It is unavoidable that different persons have, at least to a certain degree, different perceptions of the samples as well as a different understanding of the attributes or of the scales used for quantifying the assessments. Hence, any model attempting to describe sensory profiling data needs to deal with individual differences; either implicitly or explicitly. In this paper, a unifying family of models is proposed based on (i) the assumption that latent variables are appropriate for sensory data, and (ii) that individual differences occur. Based on how individual differences occur, various mathematical models can be constructed, all aiming at modeling simultaneously the sample‐specific variation and the panelist‐specific variation. The model family includes Principal Component Analysis (PCA) and PARAllel FACtor analysis (PARAFAC). The paper can be viewed as extending the latent variable approach commonly based on PCA to multi‐way models that specifically take certain panelist‐variations into account. The proposed model family is focused on analyzing data from quantitative descriptive analysis with fixed vocabulary, but it also provides a foundation upon which comparisons, extensions and further developments can be made. An example is given which shows that even for well‐working data, models handling individual differences can shed important light on differences between the quality of the data from individual panelists. Copyright © 2007 John Wiley & Sons, Ltd.