Estimation for the three-mode GMANOVA model with unobserved design matrices

Abstract When data are collected from n individuals for m items over p time points, the data can be stored as three-mode data of size $$n \times m \times p$$ . In order to analyze such three-mode data, the three-mode generalized multivariate analysis of variance (3mGMANOVA) model can be applied. Although this model has been shown to be useful, the available algorithms for its implementation assume that both a between-individuals design matrix and a between-items design matrix should be set prior to the analysis. This limits the model’s practical application. In this study, we propose estimation methods for the 3mGMANOVA model that accommodate various conditions related to the availability of between-individuals and between-items design matrices. In addition, the similarities and differences between the 3mGMANOVA model and three-mode principal component analysis model, also known as the Tucker 3 model, are illustrated, using real data.