# Random intercepts model - one measurement per subject

I have repeated measurements on several hundred subjects. I plan to fit a random intercepts model. Most subjects have 3 to 4 measurements but about 20% only have one measurement.

For the subjects with one measurement, should they share the same intercept or should they each have their own intercept as well? I'm not sure if there is enough information for the latter.

I plan on doing the modelling in BUGS where I can control the intercepts for each subject.

I have not used BUGS but I believe that conceptually you should allow an random intercept for all of your subjects. Having said that, I believe you will find that there is very little difference in the model fits whether you include or exclude the single-observation groups (assuming you are not using a glmm where in that case issues of over-dispersion come into play). Heteroscedasticity between subjects might be an issue but you will probably be unable to present subject-specific variances but other than that you should be OK.
About the quantity of missing information: 20% missing observations seems still fair enough to allow ML fitting. If you want to be really sure that the missing data do not cause any problem, you could use a multiple imputation (MI) model before estimation of the multilevel model. Also multiple imputation will assume data are MAR, but the Bayesian nature of the method may be easier to accomodate in BUGS. An alternative in R is the package mice.