Hierachical Random Mixed effect sizes

Question

When using a mixed effect model the rule of thumb seems to be that you need at least 5 levels to use a random factor . Is this still True when you have a hieachical model. i.e A - 4 level factor B - 3 level factor C - 6 level factor

with a formula of

y~1+(1|A/B/C)

Will the first 2 levels just cause issues?

Answer 1

In a nested design, it is the combinations of the levels of the factors that is important.

y ~ 1 + (1|A/B/C)

expands to

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:

1. Does the data support that random structure? That is, does the model converge and is it non-singular ?
2. Are the random effects plausibly normally distributed ?
3. Does the model fit adequately ?