[R-sig-ME] Narrative interpretation of a complex mixed model

[Timothy MacKenzie]

Dear community,

I have fit the mixed-effects model below. I was wondering if my narrative
interpretation of the random part of the model plus its residual modeling
is accurate?

-- Tim M

### Model:
lme(y ~ time*cal,
     random = list(participant = pdDiag(~cal+0)),
       data = data,
correlation = corCompSymm(),
    weights = varComb(varIdent(form = ~1|time),
                      varIdent(form = ~1|cal)))

### Narrative Interpretation:
First, the model assumed that CAL measures used in our study were a random
sample of a larger set of possible CAL measures available in the
literature. As a result, CAL measures were considered to be random-effects
for each participant across all the participants in the study.

Second, these CAL measure random-effects were found to be non-overlapping
(uncorrelated) with one another within each participant across all the
participants.

Third, the CAL measure random-effects seemed to have varying amounts of
variation in them (i.e., were heterogeneous) across the participants.

Fourth, although the random-effects seemed to be uncorrelated, the
residuals of the model seemed to be slightly correlated symmetrically for
each participant across all the participants.

Finally, in addition to their correlation, the residuals of the model
seemed to change as a function of different CAL measures as well as the
timing of CAL measurement.

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