Follow-up: Random & Crossed Random-Effects in Model Syntax in R (lme4) I'm following up on this question and this answer. The answer mentions that without having a clear study design, understanding whether the random-effects specified in an lmer() model syntax are CROSSED or NESTED is not possible.
Therefore, in this thread, I want to visually provide a couple of study designs as well as their suggested model syntax (from this blogpost) and learn how the model syntax may match up with the study design in terms of CROSSED or NESTED random-effects defined in them. In the following syntax, tx is a binary treatment indicator (0=control, 1=treatment).
DESIGN 1:
Imagine in a 3-wave, longitudinal study, two therapists both get to deliver the treatment and the control arms of the study to a different set of subjects.
The suggested lmer() model syntax is (Q: How does this model syntax match up with DESIGN 1?):
    lmer(y ~ time * tx +                      ## DON'T RUN
            (time | therapist:subjects) +
            (time * tx || therapist), 
             data = data)


DESIGN 2:
Imagine in a 3-wave, longitudinal study, two therapists both get to deliver ONLY the treatment arm of the study to different subjects. The control arm subjects will NOT meet any therapist at all.
The suggested lmer() model syntax is (Q: How does this model syntax match up with DESIGN 2?):
        lmer(y ~ time * tx +                         ## DON'T RUN         
                   (1 | therapist:subjects) +  
                   (0 + time | therapist:subjects) +
                   (0 + time:tx | therapist) + 
                   (0 + tx | therapist),
                   data = data)


 A: 
lmer(y ~ time * tx +                      ## DON'T RUN
         (time | therapist:subjects) +
         (time * tx || therapist), 
         data = data)

Q: does this model syntax match up with DESIGN 1 ?

Yes.
In this design, subjects are nested within therapists, so ( ... | therapist:subjects) + ( ... | therapist) matches with the design.
It is worth noting that since subjects are coded uniquely, therapist:subjects is the same as subjects

lmer(y ~ time * tx +                         ## DON'T RUN         
                  (1 | therapist:subjects) +  
                  (0 + time | therapist:subjects) +
                  (0 + time:tx | therapist) + 
                  (0 + tx | therapist),
                  data = data)

Q: does this model syntax match up with DESIGN 2 ?

No.
In this design, subjects are partially nested in therapists, however since therapist is missing from the control group, inclusion of therapist or therapist:subjects will result in the whole control group being dropped from the model, therefore unlike design 1, therapist:subjects is not same as subjects.  An appropriate model would be:
lmer(y ~ time * tx + (time * tx | subjects), data = data)

Alternatively, if a dummy therapist was added to the data, for the control group, then a model with the same random intercepts as that for design 1 would be appropriate. The proposed model for design 2 would not make sense in this case because it does not allow for variation attributable to therapist.
