Conflicting LME results

I re-looked through the forum and the LME documentation and I think I have a good understanding of what the LME outputs are saying but I still have some questions.

Two forum posts that I found extremely helpful were this one and this one. These two forum posts helped explain the parts of the LME model results extremely well and it was easy to understand.

So if we look at my Shannon diversity LME time_group results here: shannon-LME-grp.qzv (450.4 KB).

We can see that the intercept group is the Early time group and that its significantly different from 0. We can see if we swapped the time group from Early to the other two we can see that they aren't significantly different from 0. We can see that there isn't a change over time in the reference group and we can see that there isn't a change over time in the different groups.

  1. Is this interpretation correct? I do believe that this interpretation of the model results is correct, but I want to make sure.

Now with this LME usage, I think I used the wrong group variable, since the Early, Mid, and Late time_groups don't span the entire time span of the experiment.

  1. So to see if the diversity scores significantly change over time I would just re-run the LME again but with just the time variable?

Which I did that here: shannon-LME-time.qzv (406.5 KB).

Where we can see that the intercept and the time_day parts are significant.

  1. What are the intercept and time_day outputs saying in a LME that is just looking at how the shannon_diversity changes over time?

My final question is that I was also using the first difference function from the q2-longitudinal plug-in and when I was generating the LME results for this matrix, I got this error:

Plugin error from longitudinal:

  Cannot predict random effects from singular covariance structure.
  1. Why would I get this error from trying to run an LME on the first difference output when I can use an LME on the first distance output?

Shannon first difference artifacts here:

shannon-baseline-differences.qza (123.3 KB)
shannon-first-differences.qza (123.3 KB)

Prompts that gave me this issue are below.

qiime longitudinal linear-mixed-effects \
  --m-metadata-file sample-metadata.tsv \
  --m-metadata-file First/shannon-first-differences.qza \
  --p-metric Difference \
  --p-individual-id-column Characteristics.Subject. \
  --p-state-column time_day \
  --p-group-columns time_group \
  --o-visualization First/shannon-diff-LME.qzv

qiime longitudinal linear-mixed-effects \
  --m-metadata-file sample-metadata.tsv \
  --m-metadata-file First/shannon-baseline-differences.qza \
  --p-metric Difference \
  --p-individual-id-column Characteristics.Subject. \
  --p-group-columns time_group \
  --p-state-column time_day \
  --o-visualization First/shannon-baseline-LME.qzv