I plan to use 3dlme for a longitudinal (3 time point) fMRI study and I’ve reviewed the documentation and I’ve heard about the benefits of doing this quite a bit, but I’d love to check my logic in some of the specifics of how

- I could model the data to assess how task activation changes across age and how a co-variate collected at time 1 may moderate this relationship
- how I would interpret some of the output of the F and T tests.

This is a hypothetical model so I just made up some info to give more context to the question about interpreting certain type of ttests, but more broadly I’m trying to get a better handle on what questions I could ask and how I’d interpret them, versus which questions am I not modeling or interpreting correctly (or possibly over fitting my data with only 3 time points).

```
3dLME -prefix 3dLME_age -jobs 28 \
-model 'Task*age_c*constant+Task*age2*constant' \
-qVars "age_c,age2,constant" \
-qVarCenters "0,0,0" \
-resid allresids \
-ranEff '~1+age_c' \
-SS_type 3 \
-num_glt 2 \
-gltLabel 1 'age.task1-2.constanthigh' -gltCode 1 'Task : 1*cond1 -1*cond2 age_c : 0 constant : 3' \
-gltLabel 2 'age2.task1-2.constanthigh' -gltCode 2 'Task : 1*cond1 -1*cond2 age2 : constant : 3' \
-dataTable \
Subj Task age_c age2 constant InputFile \
001 cond1 2 6 3 /path/subs/wave1/001/con_0001.nii \
001 cond2 2 6 3 /path/subs/wave1/001/con_0002.nii \
001 cond3 2 6 3 /path/subs/wave1/001/con_0003.nii \
001 cond1 3 9 3 /path/subs/wave2/001/con_0001.nii \
001 cond2 3 9 3 /path/subs/wave2/001/con_0002.nii \
001 cond3 3 9 3 /path/subs/wave2/001/con_0003.nii \
001 cond1 4 16 3 /path/subs/wave3/001/con_0001.nii \
001 cond2 4 16 3 /path/subs/wave3/001/con_0002.nii \
001 cond3 4 16 3 /path/subs/wave3/001/con_0003.nii \
....
180 .....
```

First, would it be correct that I would interpret the F test for Task*age as controlling for age2 and vis-versa Task*age2 F test as controlling for age or is it running two independent F tests?

e.g.,

```
model 'Task*age_c+Task*age2'
```

Second, if I wanted to look at a quantitative variable that occurs at wave 1 (e.g., a constant within subject value across waves) to ask the question of “does this value at time one influence the relationship between task and age on whole brain activation?”, would this be an appropriate way to think about the t test (assuming variables are centered)?

```
-gltLabel 1 'age.task1-2.constanthigh' -gltCode 1 'Task : 1*cond1 -1*cond2 age_c : -1 constant : 3'\
```

Would this be saying activation for task condition 1-2 at age centered at early age at constant variable at value 3. (I’m not clear in this interpretation, as I

m sure it coming across in how I summarized it)

and would

```
-gltLabel 2 'age2.task1-2.constanthigh' -gltCode 2 'Task : 1*cond1 -1*cond2 age2 : constant : 3'\
```

be asking similar question but at centered age squared?

Thanks in advance! I’m excited to use 3dlme to optimize the way I ask some developmental longitudinal questions, but want to make sure I’m understanding the capabilities of model set up in 3dlme in this context and not over-stretching my understanding/interpretation (which I presume I am at the moment).