Hierarchical linear modeling - minimum number of observations per group?

tess2

New Member
#1
I'm looking at the relationship between income and scores on an instrument. Income is estimated by ZIP code. To account for nesting (i.e., people within the same ZIP code sharing an income), I've run a mixed model with ZIP as the random effect. There's a mean of 1.9 observations per ZIP. Is this too low to use a mixed model? Is there a minimum number of observations per group that's statistically sound?
 

hlsmith

Not a robit
#2
I am sure there are better people out there to answer this question, more knowledgeable, but yeah that seems like too few. To put it in perspective how much more variability can be explained by controlling for the second level. Do you think they have random intercepts and slopes? So with the levels you get averages at group level, so at times probably an average of 1 and 2 people.

A quick thing you can likely do is run the model with and without controlling for groupings and see if it makes any difference, controlling for groups also probably sucks up degrees of freedom.
 

tess2

New Member
#3
I am sure there are better people out there to answer this question, more knowledgeable, but yeah that seems like too few. To put it in perspective how much more variability can be explained by controlling for the second level. Do you think they have random intercepts and slopes? So with the levels you get averages at group level, so at times probably an average of 1 and 2 people.

A quick thing you can likely do is run the model with and without controlling for groupings and see if it makes any difference, controlling for groups also probably sucks up degrees of freedom.
Thanks for the response. It doesn't make much difference (results are still significant), but it does seem the grouping approach is slightly more conservative. I could change incomes to by county (as opposed to by ZIP), which increases observations per group to about 5. Thoughts?
 

hlsmith

Not a robit
#4
I feel there is a formal test to examine if controlling for groupings explains a greater amount of variability, if it doesn't you can use fixed effects with robust standard errors.