GEMANOVA model

The following example provides an illustration of some of the interpretational advantages of the GEMANOVA model but also illustrate that the inferential power of such models is still largely lacking. 

In establishing the GEMANOVA model, it is necessary to determine which effects to include. This is done by first evaluating different alternatives to a one-component five-way PARAFAC model. From cross-validation results, it is determined that an adequate and simple GEMANOVA model for these data, is given by... 

Figure 10.66. Results of leave-one-out cross-validation using the GEMANOVA model in Equation (10.13).

Figure 10.67. Parameters from multiplicative effect in GEMANOVA model. The estimated response at specified levels of the four factors equal the product of the corresponding effects plus the muscle term, which varies between 31 and 33.

Multiplicative multilinear models can be used for modeling ANOVA data. Such multilinear models can be interesting, for example, in situations where traditional ANOVA interactions are not possible to estimate. In these situations GEMANOVA can be a feasible alternative especially if a comparably simple model can be developed. As opposed to traditional ANOVA models, GEMANOVA models suffer from less developed hypothesis testing and often the modeling is based on a more exploratory approach than in ANOVA. 

On the contrary, when applying the GEMANOVA model the interactions are modelled as one higher-order multiplicative effect, resulting in the eqn 9.5... 

The resulting GEMANOVA model for the data in Table 9.2 can be written as equation 9.6, sinee the effect of the 02-level is insignificant in the interval between 40-80% O2 (Bro and Jakobsen 2002). The interaction term Day Temp Light c02 describes deviations from the a -value on day 0 in a very simple way, and interpretation of the model parameters can be performed from Fig. 9.2. 

The GEMANOVA model confirms the results from Jakobsen and Bertelsen (2000) by emphasising the importance of keeping a low storage temperature and showing no effect of O2 level in the interval between approximately 40-80%. However, the interpretation of the model is much more simple, since the effect... 

The complexity of the interactions/squared terms in eqn 9.3 called for further search for adequate models. A novel approach called GEMANOVA (Generalized Multiplicative ANOVA) was therefore used in Bro and Jakobsen... 

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