All the applications so far in the literature have been focused on either MVT or UVT. In other words, a strict MVT applies to the situations of truly multivariate nature while a purely UVT is adopted to the conventional AN(C)OVA or GLM. However, if we treat the components from ESM as simultaneous response variables, the presence of one or more within-subject factors (e.g., two task conditions in the experimental data of this paper) necessitates a partial MVT. Here we demonstrate a strategy to formulate partial MVT with the construction of L and R using a template of two-way within-subject ANOVA with factors A and B of a and b levels respectively. Suppose that we want to model the levels of factor A as a simultaneous response variables (e.g., components or effect estimates from ESM) while factor B is considered as an explanatory variable (e.g., conditions). MVT for the effect of B can be achieved through the following specifications in (A1), L=Iq,R=Ia⊗R(B).