Following classical ANOVA, I thought it important to have replication at each level. Maybe this is not essential for mixed models? 
 
Here's my model: Y~1+(1|SUBJECT/OCCASION) 
 
Each subject was tested on multiple occasions.I want to evaluate the variance between-subjects and variance between-occasions (within-subjects). 
 
I have data for 105 subjects. Occasions per subject ranges from 1 to 4. Repeated measurements of the response Y per occasion range from 1 to 5. 
 
Originally, I thought to restrict the modelling to subjects tested on at least 2 occasions and with at least 2 Y data per occasion. Here are the numbers of "levels" in this reduced dataset: 
 
> model=lmer(Y~1+(1|SUBJECT/OCCASION), data=reduced) 
> # subjects 
> length(ranef(model, standard=TRUE)[[2]][, 1]) 
[1] 57 
> # occasions 
> length(ranef(model, standard=TRUE)[[1]][, 1]) 
[1] 138 
> # Y measurements 
> length(resid(model)) 
[1] 353 
 
And here's what I get with the full dataset: 
 
> model=lmer(Y~1+(1|SUBJECT/OCCASION), data=full) 
> length(ranef(model, standard=TRUE)[[2]][, 1]) 
[1] 105 
> length(ranef(model, standard=TRUE)[[1]][, 1]) 
[1] 196 
> length(resid(model)) 
[1] 471 
 
There are 3 different potential issues in the full dataset affecting 48/105 of the subjects: 
1) No replication (i.e. subjects measured on 1 occasion and once). 
2) No replication of occasions (i.e. subjects measured multiple times but on 1 occasion). 
3) No replication of measurements on some occasions (i.e. subjects measured on multiple occasions but sometimes with only 1 measurement per occasion). 
 
I do not want to ignore potentially informative data and the precision for random effect results seems to improve with the full dataset. 
 
I welcome some guidance on how I should proceed. Perhaps some of the issues 1), 2), 3) are allowable and some are not? 
 
Stephen.

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