Exploring complex interactions in designed data using GEMANOVA. Color changes in fresh beef during storage

Data from a severely reduced experimental design are investigated in order to obtain detailed information on important factors affecting the changes in quality of meat during storage under different conditions. It is possible to model the response, meat color, using traditional ANOVA (analysis of variance) techniques, but the exploratory and explanatory value of this model is somewhat restricted owing to the number of factors and the fact that several interactions exist. For those reasons, it is not possible to visualize the model in a simple way and therefore not possible to have a clear overview of the total variation in the data. Using a recently suggested alternative to traditional analysis of variance, GEMANOVA (generalized multiplicative ANOVA), it is possible to analyze the data effectively and obtain a more interpretable solution that enables a simple overview of the whole sampling domain. Whereas traditional analysis of variance typically seeks a model with main effects and as few and simple interactions and cross-products as possible, the GEMANOVA model seeks to describe the data primarily by means of higher-order interactions, albeit in a straightforward way. The two approaches are thus complementary. It is shown that the GEMANOVA model is simple to interpret, primarily because the GEMANOVA structure is in agreement with the nature of the data. It is shown that the GEMANOVA model used is mathematically unique, which leads to attractive simplified ways of interpreting the model. The results presented are the first published results where the GEMANOVA model is not simply equivalent to an ordinary PARAFAC model, thus taking full advantage of the additional structural power of GEMANOVA. A new algorithm for fitting the GEMANOVA model is developed and is available from the authors. Copyright (C) 2002 John Wiley Sons, Ltd.