In a nested design, it is the combinations of the levels of the factors that is important.
y ~ 1 + (1|A/B/C)
y ~ 1 + (1|A) + (1|A:B) + (1|A:B:C)
So, you need to apply the rule of thumb to the levels of
A, the levels of the interaction
A:B and the levels of the interaction
A:B:C. In the example you give,
A has 4 levels,
A:B has 12 levels and
A:B:C has 72 levels.
It is debatable whether 4 levels is sufficient, and at the end of the day, pragmatism is probably the best approach:
- Does the data support that random structure? That is, does the model converge and is it non-singular ?
- Are the random effects plausibly normally distributed ?
- Does the model fit adequately ?