I have a variable (call it 'group') that I would like to treat as a random effect in a logistic regression. However, the number of groups is small (9 groups, larger than the recommended absolute minimum of 5 but not by much), and the sample size in each group is small and unbalanced (one group <10 observations, four groups 30-40 observations, two groups 70-90 observations, two groups 100+ observations). (I am primarily interested in the effects of the other predictors in the regression, not 'group').
I notice that if I treat 'group' as a fixed effect rather than as a random effect, it has only a minor impact on the results - standard errors of the predictors I care about are slightly smaller, and their coefficients are slightly closer to zero, when 'group' is treated as a random rather than a fixed effect, but effectively the same results.
Which predictors come out significant are also the same regardless of whether I treat 'group' as a fixed or random effect, but they change if I exclude 'group' from the model altogether.
So my question is: In a situation where initial considerations suggest that a variable should be treated as a random effect, but there are small + unbalanced group sizes as in my example (for a smallish but acceptable number of groups), and the researcher is interested in the betas of the significant predictors: is it advisable to 'back off' to a model that treats the group variable as a fixed effect, or perhaps even to a model that does not include the group variable at all?
If not, what caveats should be included with the interpretation of the random effects model (i.e., would it be accurate to state that standard errors are likely to be underestimated, and may be closer to those of a model that does not include the group variable)?