Hello, I would like to ask about the estimated beta values from 3dMEMA.
I also tried to check the AFNI message board, and I could find that we can’t get the residual from 3dMEMA currently.
However, I’m not sure whether that is the one, which I wanted to check.
Therefore, the questions which I want to ask are:

[1]
I read the paper related to the MEMA.
I could find that MEMA considered the subject variability, and estimate the beta values again (add subject variabilities…).
Regarding the estimated beta values, as I understood, we could get the beta values individually (e.g. if there are 20 subjects I used for the MEMA, the 20 subject’s estimated MEMA beta values will be observe)
Thus, I thought I could get each MEMA estimated beta values from the result, but I’m not clear which one is it…
I could get mema_result, mema_result_ICC, and mema_result_resZ.
I thought one of mema_result_ICC or mema_result_resZ could show the MEMA estimated beta value.
However, I couldn’t find which one shows the MEMA estimated beta value.
Thus, may I ask you, how can I get the MEMA estimated beta values?

I’m trying to get this value because I wanted to extract the averaged MEMA beta value from specific brain region.

[2]
This is a simple question…
I tried to conduct main-effect using MEMA.
From the other Q&A and materials, I could find how to get the interaction.
(i.e, use the contrast, made from GLT, which is (AA-AB)-(BA-BB))
However in the case of main-effect case, is it correct to use the contrast from GLT, which (AA+BA)-(AB+BB) = AA + BA - AB - BBA?

I appreciate for your comments. I understood about the main effect but I still have a problem related to the MEMA…
I tried to find out, however I couldn’t figure out which shows the MEMA beta value…
Thus, as you mentioned… I brought the command line result.

path/test.001.3dMEMA/test.results> 3dinfo -verb ./data+tlrc.HEAD
++ 3dinfo: AFNI version=AFNI_17.0.04 (Jul 26 2009) [64-bit]
Dataset File: data+tlrc
Identifier Code: XYZ_213UtD29w08ibU4u43UmFS Creation Date:
Template Space: MNI
Dataset Type: Func-Bucket (-fbuc)
Byte Order: LSB_FIRST [this CPU native = LSB_FIRST]
Storage Mode: BRIK
Storage Space: 2,173,064 (2.2 million [mega]) bytes
Geometry String: "MATRIX(-3,0,0,90,0,-3,0,126,0,0,3,-72):61,73,61"
Data Axes Tilt: Plumb
Data Axes Orientation:
first (x) = Left-to-Right
second (y) = Posterior-to-Anterior
third (z) = Inferior-to-Superior [-orient LPI]
R-to-L extent: -90.000 [R] -to- 90.000 [L] -step- 3.000 mm [ 61 voxels]
A-to-P extent: -90.000 [A] -to- 126.000 [P] -step- 3.000 mm [ 73 voxels]
I-to-S extent: -72.000 [I] -to- 108.000 [S] -step- 3.000 mm [ 61 voxels]
Number of values stored at each pixel = 4
-- At sub-brick #0 'abs_sat:b' datum type is short: -32767 to 8707 [internal]
[* 0.000586786] -19.2272 to 5.10914 [scaled]
-- At sub-brick #1 'abs_sat:t' datum type is short: -32767 to 24120 [internal]
[* 0.000170646] -5.59157 to 4.11599 [scaled]
statcode = fitt; statpar = 17
-- At sub-brick #2 'tau^2' datum type is short: 0 to 32767 [internal]
[* 0.00305185] 0 to 100 [scaled]
-- At sub-brick #3 'QE:Chisq' datum type is short: 0 to 32767 [internal]
[* 0.00305185] 0 to 100 [scaled]
statcode = fict; statpar = 17
----- HISTORY -----
[Tue Oct 17 21:11:18 2017] [Tue Oct 17 20:59:39 2017] 3dMEMA -prefix test.results/smk -mask /path/mask/mask_overlap+tlrc -HKtest -model_outliers -unequal_variance -residual_Z -set abs_sat 10 '/path/data/REML/abs_sat/stats.s10_abs_sat+tlrc[0]' '/path/data/REML/abs_sat/stats.s10_abs_sat+tlrc[1]' 11 '/path/data/REML/abs_sat/stats.s11_abs_sat+tlrc[0]' '/path/data/REML/abs_sat/stats.s11_abs_sat+tlrc[1]' 12 '/path/data/REML/abs_sat/stats.s12_abs_sat+tlrc[0]' '/path/data/REML/abs_sat/stats.s12_abs_sat+tlrc[1]' 13 '/path/data/REML/abs_sat/stats.s13_abs_sat+tlrc[0]' '/path/data/REML/abs_sat/stats.s13_abs_sat+tlrc[1]' 14 '/path/data/REML/abs_sat/stats.s14_abs_sat+tlrc[0]' '/path/data/REML/abs_sat/stats.s14_abs_sat+tlrc[1]' 16 '/path/data/REML/abs_sat/stats.s16_abs_sat+tlrc[0]' '/path/data/REML/abs_sat/stats.s16_abs_sat+tlrc[1]' 18 '/path/data/REML/abs_sat/stats.s18_abs_sat+tlrc[0]' '/path/data/REML/abs_sat/stats.s18_abs_sat+tlrc[1]' 19 '/path/data/REML/abs_sat/stats.s19_abs_sat+tlrc[0]' '/path/data/REML/abs_sat/stats.s19_abs_sat+tlrc[1]' 20 '/path/data/REML/abs_sat/stats.s20_abs_sat+tlrc[0]' '/path/data/REML/abs_sat/stats.s20_abs_sat+tlrc[1]' 21 '/path/data/REML/abs_sat/stats.s21_abs_sat+tlrc[0]' '/path/data/REML/abs_sat/stats.s21_abs_sat+tlrc[1]' 22 '/path/data/REML/abs_sat/stats.s22_abs_sat+tlrc[0]' '/path/data/REML/abs_sat/stats.s22_abs_sat+tlrc[1]' 24 '/path/data/REML/abs_sat/stats.s24_abs_sat+tlrc[0]' '/path/data/REML/abs_sat/stats.s24_abs_sat+tlrc[1]' 25 '/path/data/REML/abs_sat/stats.s25_abs_sat+tlrc[0]' '/path/data/REML/abs_sat/stats.s25_abs_sat+tlrc[1]' 26 '/path/data/REML/abs_sat/stats.s26_abs_sat+tlrc[0]' '/path/data/REML/abs_sat/stats.s26_abs_sat+tlrc[1]' 27 '/path/data/REML/abs_sat/stats.s27_abs_sat+tlrc[0]' '/path/data/REML/abs_sat/stats.s27_abs_sat+tlrc[1]' 29 '/path/data/REML/abs_sat/stats.s29_abs_sat+tlrc[0]' '/path/data/REML/abs_sat/stats.s29_abs_sat+tlrc[1]' 30 '/path/data/REML/abs_sat/stats.s30_abs_sat+tlrc[0]' '/path/data/REML/abs_sat/stats.s30_abs_sat+tlrc[1]' 31 '/path/data/REML/abs_sat/stats.s31_abs_sat+tlrc[0]' '/path/data/REML/abs_sat/stats.s31_abs_sat+tlrc[1]'

This is the output which I could get from the MEMA (i.e. “name+tlrc.HEAD”), and also there are some other output such as “name_ICC+tlrc.BRIK”, “name_ICC+tlrc.head” “name_resZ+tlrc.BRIK”, “name_resZ+tlrc.BRIK”.

Thank you for your answer.
However, I have another several question…

Background knowledge which I understood
From the paper, I understood that the MEMA is one of the group level inference (am I right?)…
Also the method of the MEMA is to estimate beta value with considering the subject variability.
By the estimated beta value using MEMA (beta = sum(alpha[sub]i[/sub] * x[sub]i[/sub]) + delta; approximately, not exact same as the paper),
we could get one beta map from each subject (e.g. i = 1, …, 20),
and we use that beta map to estimate one-sample t-test, chi-square, and so on…

-Question

I thought I could get the individual MEMA beta map, when I check the MEMA model (e.g. by setting ‘i’ for only one subject).
Therefore, is there some other method to get individual MEMA beta map? (e.g. (individual GLT beta map) + (resZ+tlrc’[0]'))
because, I could find 20 subjects of resZ (i.e. 0 to 19 brick; input number of subject was 20 in my study),
so I thought I could measure or find each subject’s MEMA beta map.
As I understood, the first brick (i.e. sub-brick #0 ‘abs_sat:b’) seems that it is for the overall beta map (maybe, it will be the general? result…)

I’m trying to find this MEMA beta map, due to check the correlation between voxels in the specific cluster from the MEMA “t” result and behavioral data.

The usage/visualizing(?) of the Chi-square
As I understood, Chi-square shows the subject variability.
Therefore, It seems that it also could use for checking the correlation between behavioral data and the voxels from specific area.
To check the value, from the paper, I could find that the setting threshold is 80,
and put the color bar (the bar in the left-side of the color bar in AFNI gui) into 50.
However, I also could find set % threshold instead of the ChiS value…
Thus, may I ask you for a comment how to set the threshold and check the p or q value?

Always, thank you for your advises and kind explanation.

3dMEMA is a group analysis program that has similar functionality as 3dttest++ with the difference that 3dMEMA also takes into consideration the measuring precision from the individual subject analysis.

I could get the individual MEMA beta map

By “individual beta map” do you mean that voxel-wise statistical significance for each subject? If so, you already have that information from your individual subject analysis. Again 3dMEMA is used to make inference at the group – not subject – level.

The usage/visualizing(?) of the Chi-square

The Chi-square is used to examine the significance of the cross-subjects variability. In other words, it indicates how different are those subjects.

It seems that it also could use for checking the correlation between behavioral data and the voxels from specific area.

What do you mean by “behavioral data”? Do you have a quantitative covariate in the model?

Thank you for your comments.
I think I should write it more detail and generally… my apologies.
Regarding your comments, I wrote the related question in green color.
Again, thank you for the kindness comments.

By “individual beta map” do you mean that voxel-wise statistical significance for each subject? If so, you already have that information from your individual subject analysis. Again 3dMEMA is used to make inference at the group – not subject – level.

I thought that MEMA estimate their own beta values by considering the subject variability.
In other word, from the equation (1) of the paper “FMRI group analysis combining effect estimates and their variances”,
I thought MEMA estimate ‘a’, and also get ‘sampling error’ from subject variability.
Therefore, following by the equation (1), I thought I could get the beta values from each subjects
(e.g., subject 1 beta map: β[sub]1[/sub], subject 2 beta map: β[sub]2[/sub], and so on…), which is slightly(?) different as the beta value from GLM analysis.

What do you mean by “behavioral data”? Do you have a quantitative covariate in the model?

My apologies regarding this one. The behavioral data mean, the questionnaire which I get during the experiment…
Thus I just wanted to measure the correlation between the specific brain region and a behavioral data.
I mean, like beta mean from specific brain region (e.g., 10 voxels from ACC) and a behavioral data (e.g., stress related questionnaire)
(explanation in graph-wise → x axis will be the score of one behavioral data and y axis will be the averaged beta value).

from the equation (1) of the paper “FMRI group analysis combining effect estimates and their variances”,
I thought MEMA estimate ‘a’, and also get ‘sampling error’ from subject variability.

The parameter ‘a’ in equation (1) is the group effect for those group-level explanatory variables x_j.

Therefore, following by the equation (1), I thought I could get the beta values from each subjects
(e.g., subject 1 beta map: β1, subject 2 beta map: β2, and so on…), which is slightly(?) different as the beta value from GLM analysis.

Using the symbols in equation (1), those beta values (plus their t-statistics) are input for 3dMEMA (the values at the left-hand of the equation). The output is those parameters ‘a’ plus their t-statistics. Hope this clarifies the situation.

The behavioral data mean, the questionnaire which I get during the experiment…
Thus I just wanted to measure the correlation between the specific brain region and a behavioral data.
I mean, like beta mean from specific brain region (e.g., 10 voxels from ACC) and a behavioral data (e.g., stress related questionnaire)
(explanation in graph-wise → x axis will be the score of one behavioral data and y axis will be the averaged beta value).

Then in the output you should have the effect of the behavior data (‘a’ in the equation (1)).

Thank you so much for your detailed and kind answers.
However… I still have some questions…

First, to summarize…

Beta and t-statistics values from GLT is input for measuring MEMA, and it’s output is ‘a’ (i.e., group effect) and their t-statistics.

From this point… I thought using a, x, subject-specific error, sampling error, etc.,
the MEMA will be measured (by the equation (3) from the paper “FMRI group analysis combining effect estimates and their variances” ).
Therefore, the MEMA is equal to beta-hat (equation (3)), and ‘i’ refers to the subject number (e.g., if there are 20 subjects, i = 1, …, 20).

From that point, I thought there will be beta-hat-values for each subject (i.e., MEMA beta-value for each subject).
(That’s why I thought I could get the individual MEMA beta-value map…)
However, from the 3dMEMA result, I could find only one beta-value (which is in “sub-brick #0 ‘abs_sat:b’” from my data).

Therefore… may I ask you which is the point that I misunderstood?
(My apologies in advance, if I missed some points that you mentioned previously…)

Again, thank you so much for your considerate comments.

From that point, I thought there will be beta-hat-values for each subject (i.e., MEMA beta-value for each subject).
(That’s why I thought I could get the individual MEMA beta-value map…)

The notation beta_hat in the paper is meant to represent the regression coefficients from each subject; in the other words, they serve as input for 3dMEMA. At the group level, the model coefficients are coded as ‘a’ in the paper.

However, from the 3dMEMA result, I could find only one beta-value (which is in “sub-brick #0 ‘abs_sat:b’” from my data).

You already have the beta values from each subject (the input), so I’m not sure why you’re asking for that again at the group level. The purpose of the group analysis (e.g., 3dMEMA) is to make statistical inferences about the population (not individual) effect.

Thank you for the comments.
Now I understand whole issues that I had…
I think I confused with the beta-hat, which is the regression coefficients from each subject.
Again, I really appreciate for your consistent explanation (thank you so much).

Regards,
dawoon

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