Linear Mixed model, number of observations per group

Question

I am trying to fit a mixed model with about 45 groups, about 10 of the groups have just one observation and about 10 groups have more than 5 observations. The total number of observations is around 170. Should I be concerned about the estimates? Is there merit in just removing the groups with one observations or somehow merging them with the other ones? Are there techniques for that?

Answer 1

This sample size is rather small for Linear Mixed Model. Hox (2002) quotes Kreft's (1996) rules of thumb for minimal sample size:

• 30/30 - minimum 30 groups with 30 observations per group
• 50/20 - minimum 50 groups with 20 observations per group
• 100/10 - minimum 100 groups with 10 observations per group

Ten observations per group is minimal sample size that is often mentioned. The general problem is that 1 or even 5 is a very small sample for a group. Also your general sample size of 170 is rather small for estimating as complicated model as multilevel model. The smaller the sample, the more biased your results can get.

As an alternative, you can use Bayesian estimation, since it often works well even with small sample sizes. However, with this approach you could end up with estimates being drawn purely from prior distribution.

You can find more information on preferable sample sizes and power analysis for multilevel modeling in those two books:

• Snijders, T.A.B. & Bosker, R.J. (2012). Multilevel Analysis: An Introduction to Basic and Advanced Multilevel Modeling. London: Sage Publishers.
• Hox, J. (2010). Multilevel Analysis: Techniques and Applications. New York: Routledge.