I think its more likely that there are four categories of the shards, assuming there are categories at all (which i think is likely, considering how much Brandon likes to subdivide). Adonalsium is believed to be balanced, with none of its components having been originally more powerful than the others. dividing the sixteen pieces of Adonalsium into three compartments would leave the universe fundamentally unbalanced, with either the physical, mental, or spiritual facets containing one more shard than the other two.
In Mistborn, there are four categories of allomantic metals- physical, mental, temporal, and enhancement. I believe the shards of Adonalsium may reflect this pattern- sixteen shards divided into subsets of four, which are divided into four shards apiece.
Not to say that a three-group system is completely unfeasable. However, if it were to occur, I think it would follow closer to the pattern of the three metallic arts; five positive shards, five negative shards, and six neutral shards. Positive being Shards like Honor, Endowment, and Preservation; Negative being shards with greater potential for misuse, such as Odium and Ruin. Neutral shards could really go either way- things like Devotion, seeing as a person can be devoted to good things, like charity work, or bad things, like torturing puppies.
Thoughts?