My knowledge of the standard model is very limited so please let me spell out my assumptions first (and please let me know when I have mangled concepts, terminology or I am plainly just out of my depth).
My assumptions are:
We don't currently have an underlying theory for these parameters, we obtain their values experimentally, not theoretically.
The table below lists 19 certain parameters ( I am aware there are more), and my assumption is that, if we ever developed an underlying theory and experimentally verified it, say for one mass, then we have a good chance of explaining the other masses through extensions to that theory.
But being lucky enough to be able to explain the mass based parameters would not get us far in explaining say, electric charge.
So my question is, of these parameters, how many are in totally independent groups, or by definition alone, are they all independent?