# Can I run generalized linear mixed models using lme4 on very small sample sizes?

I am analyzing data (size/survival) of two groups of fish (Group1, Group2) mixed together in tanks with two different environmental variables applied at two levels to the tanks, e.g. +Predator/-Predator, Low-food/High-food, for a combined total of 4 treatments. There are 2 tanks per treatment and 50 fish per group in each tank to start. Survival and size of fish were measured after 30d in the tank. The way I'd planned on analyzing this was with generalized linear mixed models using the lmer4 package, so that the variables (e.g. size) were modelled as:

lmer (variable ~ FishGroup * PredatorPresence * FoodLevel + (1|Tank/FishGroup)) followed by ANOVA analysis.

However, due to the n=2 tanks the calculated standard deviation on the model predicted values is 0. Is there any way to run this sort of test on an n=2, or a way to do an appropriate analysis on the individual fish rather than the tanks (at least for size). Thanks.

• I would try variable ~ FishGroup * PredatorPresence * FoodLevel + Tank+ (1|Tank:FishGroup) as a start; see here for some of the answers about what to do with zero-variance estimates ... – Ben Bolker Apr 22 '16 at 3:19