3dLME three-way interaction continuous variables interpretation

AFNI Message Board
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AFNI version info (afni -ver): AFNI_22.2.10 'Marcus Aurelius'

Hi all!

I am interested in how changing hormones in the menopause transition relate to seed-connectivity and performance on cognitive tasks. My hypothesis is that as estrogen decreases (Estradiol), task performance (Pattcomp) and attention network-connectivity will also decrease (all three continuous variables).

To test this, I ran 3dLME with the model of Estradiol + Pattcomp + EstPatt. The last is my interaction term and is the product of Estradiol and Pattcomp, based on this prior post of how to represent the interaction of two continuous variables: 3dlme with multiple covariates of interest. The input files are the seed-connectivity images.

3dLME -prefix peri_estradiol_pattcomp_RIPS.nii.gz -jobs 4   \
      -mask /data1/software/bioimagesuite35/images/MNI_T1_1mm_mask.nii.gz \
      -model  'Estradiol+Pattcomp+EstPatt'   \
      -qVars 'Estradiol,Pattcomp,EstPatt'    \
      -qVarCenters '129.957,48.357,6648.59'  \
      -SS_type 3     \
      -ranEff '~1'   \
      -num_glt 3 \
      -gltLabel 1 'Estradiol-Zscore'    -gltCode 1 'Estradiol : '               \
      -gltLabel 2 'Pattcomp-Zscore'      -gltCode 2 'Pattcomp : '               \
      -gltLabel 3 'EstPatt-Zscore'   -gltCode 3 'EstPatt : '    \
      -resid peri_estradiol_pattcomp_RIPS_resid.nii.gz  \
      -dataTable                                  \
Subj    Estradiol       Pattcomp        EstPatt InputFile \

I then cluster corrected with 3dFWHMx and 3dClustSim and used bioimage suite to visualize at the 0.01/0.01 threshold. The interaction results were really striking at this threshold in one brain region, but looking at the estrogen z-score map alone or the pattcomp z-score map alone shows absolutely nothing in that brain region. I also pulled the connectivity values of that ROI from the original seed-connectivity maps and plotted them against estrogen and pattcomp separately, and there's no main effects against either or their product.

So I'm at a loss for how to interpret my results and wanting advice on how to investigate this relationship further, if there is a way to plot the interaction between pattcomp and estrogen for example or something else.

Any ideas are very helpful!

Jordan

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Jordan,

Just to clarify, does each participant have a single input file or multiple input files?

Gang Chen

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Each participant has a single input file.

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First, since all the explanatory variables are between-individual variables, 3dLME is not suitable for this analysis. I recommend using 3dMVM instead.

Second, to model the interaction term, center both Estradiol and Pattcomp individually by subtracting their respective center values (e.g., means). Then compute their interaction as the product of these two centered variables. Include the two centered variables and their interaction in your data table. In your script, add the following line:

-qVarCenters '0,0,0'  \

Does this approach make sense to you?

Gang Chen

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I think so! So instead of inputting the means of all three to qVarCenters, I should modify my datatable to have the values of Estradiol and Pattcomp as the value that I currently have for each variable in the datatable minus the mean I have listed in my current qVarCenters and then multiple for the interaction term in the datatable? When I run 3dLME it seems to be doing that automatically in the printout when it is loading my variables, but you are suggesting I do that manually in the datatable before running the script? And is that just for 3dMVM specifically or would that also be the case for 3dLME? Thank you for your help!

Edit: I mixed up the order for centering the values

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you are suggesting I do that manually in the datatable before running the script? And is that just for 3dMVM specifically or would that also be the case for 3dLME?

Without an interaction term, programs like 3dMVM and 3dLMEr can automatically center each quantitative variable by removing its mean. However, the complication here arises from the inclusion of an interaction term; it’s not specific to the program. When an interaction is involved, the interpretation of the main effects depends on the product of centered variables, not on the mean of the interaction term itself. Therefore, the variables must be manually centered before computing the interaction, and the resulting values should be entered directly into the data table.

Gang Chen

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That makes sense! I'll do that instead - thank you for your help, Gang!

Jordan