(in plain text) Replication in nested structure, how much?

Following classical ANOVA, I thought it important to have replication at each level. Maybe this is not essential for mixed models? 
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Here's my model: Y~1+(1|SUBJECT/OCCASION) 
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Each subject was tested on multiple occasions.I want to evaluate the variance within-subjects and variance within-occasions. 
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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. 
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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 the reduced dataset: 
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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 
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And here's what I get with the full dataset: 
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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 
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There are some 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). 
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I do not want to ignore potentially informative data and the precision for random effect results seems to improve with the full dataset. 
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I welcome some guidance on how I should proceed. Perhaps some of the issues 1), 2), 3) are allowable and some are not? 
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Stephen.