# Model interpretation lmer?

I have 139 subjects (ID), with measurements taken at two time points (Time1, Time2), at 148 brain regions, a dependent measure called volume, and a covariate called thickness.

Each subject has 148 brain regions with volume and thickness measured twice

I am trying to find out if there is a difference in volume between timepoint 1 and timepoint 2 while controlling for thickness. I want to know which brain regions show this difference. I need help setting up the model. Specifically the timepoint part is throwing me off...

I am using R. and trying to figure out a model with linear mixed models with (1|ID) as random factor, fixed factors regions, thickness.

What I have is:

delta-volume <- volume_time 2 - volume_time1

 Mod1   lmer(delta-volume ~ delta.thickness + volume_time_1 + regions + (1|ID))


Mod2 lmer(delta-volume ~ delta.thickness + regions + (1|ID)

 Mod3 lmer(delta-volume ~ delta.thickness + (1|ID/regions)


from model 1

1) is there a difference in volume from from timepoint 1 to timepoint 2?

2) Which regions show a significant difference?

The way I interpreted is for question 1) is that the fixed effect intercept is the value of the depedent variable when the IV variables are defaults so, in my case, the intercept was positive, I interpreted it as there was a decrease in volume. Is this correct?

2) stuck on how to see which regions....I get estimates for them but what do those mean?

Also would very much appreciate an explanation about how the models differ... Thank you!

Are the 148 regions together spanning the entire brain? In other words, are these regions the only ones you could have included in your study or did you leave some brain regions out of your study?

You do have a lot of regions but let's say you included all regions of interest in your study (leaving none out). Then you will find it easier to formulate your model like this:

Mod1   lmer(volume ~ time + region + thickness + (1|ID)


or

Mod2   lmer(volume ~ time*region + thickness + (1|ID)


Model 1 assumes that the (true) change in volume from time 1 to time 2 (controlling for thickness) for a given subject is the same across all brain regions. It also assumes that change is consistent (i.e., the same) across subjects.

Model 2 assumes that the (true) change in volume from time 1 to time 2 (controlling for thickness) is different across regions within the same subject, but the region-specific change in volume from time 1 to time 2 is assumed to be consistent across subjects.

For both models, you can replace (1|ID) with (1 + time|ID) if you believe the changes in volume are inconsistent (i.e., different) across subjects.

Both Model 1 and Model 2 assume that each individual is measured twice for each region, so your data would look like this:

ID    time region volume etc.
1     1     1     ?
1     2     1     ?
.
.
.
139   1     138   ?
139   2     138   ?


The coefficient of time in model 1 will represent the true change in volume between time 1 and time 2 for a typical subject given a region and thickness (assuming time was coded as a factor whose reference/baseline level is time 1). Since this coefficient is the same for all regions, you would test whether or not it is equal to 0 and also report a confidence interval for it.

For Model2, you would have to set up contrasts to test whether the true change in volume between time 1 and time 2 is different from 0 for each of your regions of interest. With so many regions, you will need to control for multiplicity of your tests.

You should determine first which of Model 1 or Model 2 is more appropriate for your data.

If the 138 regions are not exhausting all of the brain regions one could possibly consider, things are a bit more complicated. I'll let others on this forum address that scenario.

• Did you delete the comment which said those were ALL the regions included? Jan 12, 2019 at 16:51
• Your Mod3 would make sense if the regions included in your study were not exhuasting the entire brain and were selected to be representative of a larger set of regions. Jan 12, 2019 at 16:52
• 1. those are all the brain regions included 2. if I understand correctly you are suggesting to get rid of delta.volume and use volume ? 3. Model 2 makes more sense physiologically 4. "would have to set up contrasts to test whether the true change in volume between time 1 and time 2 is different from 0 for each of your regions of interest." - How could I do that? 5. I have time coded as a factor timepoint 1 = 1 timepoint 2 = 2. Is that what you meant? Jan 12, 2019 at 16:54
• Great idea. Would I still include volume at time 1 as a fixed effect ? In the older lm model a positive volume at timepoint 1 estimate means an increase in volume at time 2? Is that correct ? Jan 13, 2019 at 13:32
• Awesome! This has been a huge learning experience for me! For the model with all the regions a positive estimate at time2 means increased volume at time 2? Jan 13, 2019 at 18:24