Traditionally, the structure of higher-order data in genotype-by-environment interaction requires simplification to use bilinear reduction models. Flexible multiway reduction models have been claimed to be more informative, as they allow exploration of individual trends and account for the covariance among data modes. In complex latent traits, such as acclimation response of grapevine (Vitis sp.), these methods may offer increased insight into plant adaptive processes. In a growth chamber study, data from seven phenotypic traits at 11 photoperiodic times in the presence of two temperatures of 30 accessions were analyzed. The four-way interaction among these data modes was isolated and further examined through bilinear singular value decomposition (SVD) and multiway Tucker decomposition models. A similar set of three latent process traits were identified regardless of model used. The Tucker decomposition model led to more concise clustering of wild-type accessions, was more interpretable, as trends could be evaluated separately, and had less indication of overfitting; therefore, the multiway method was preferred over the standard SVD bilinear method in the investigation of high-order interaction in acclimation response. This methodology may offer insight into other complex traits, such as phenolic development, drought tolerance, and horizontal disease resistance to improve breeding efforts as other individual mechanisms used by the organism are separated, quantified, and compared rather than the culmination of events as an end-product.