For example, in three-dimensional panel data, the dependent variable of a model is observed along three indices, such as Yijt, i =1,...,N, j =1,...,M, and t = 1,...,T,.
How to group the dimensions three-dimensional Panels?
Could you tell us what do you mean by 'group? and what are the three dimensions?
If they were say occasion (t) nested within individuals (i) with countries (j) I would fit a three-level multilevel model to isolate the patterns at each level net of the patterns at the other levels, but I am only guessing at what you want.