Thanks very much for your reply.

-------------------------------------------------------
> Xiaowei,
>
> > I used the z-value of the Pearson correlation as
> the weight info to check the ICC of correlation
> maps.
>
> Are you using both correlation coefficients and
> their Z-values as input for 3dICC with the latter
> under the option -tStat?
>
Yes.
-------------------------------------------------------

> > Do you think this weighting is meaningful? Or
> should I put the inverse of z-value as the weight
> parameter (I am a
> > little confused on MME method mentioned in your
> paper and the example usage on 3dICC)?
>
> Hmm... in this case I tend to think that the
> weighting is difficult to justify. If I understand
> your situation accurately, the Fisher Z-values are
> simply a transformed version of your original
> correlation coefficients. Then, you seem to be
> double-dipping the data: using the same data to
> reenforce the original information.

I am not sure about the double-dipping, since I am not sure if the input weight should be the sample variance estimation or its inverse.

In your paper of the MME, the input weight is assumed to replace the unknown sample error's variance \sigma_e, which is same across all subjects and all sessions in LME (no subscript i or j, but same subscript e across all subjects (i) and all sessions (j) ).
When I put the Z-values (a non-linear transformation of Pearson correlation, not as simple as a linear mapping) as the weight into MME, with a bigger correlation value, the sample error's variance \sigma_ij is "made" bigger since its z-score is usually higher. This bigger error variance \sigma_ij should hurt the bigger correlation value in the ICC calculation, since the error variance should be as small as 0 in the ideal case. Is my understanding right?
If I am right, then this may not reinforce the original information.

Or I may understand wrongly, the weight input should be the precision or the inverse of the \sigma_ij, and I should input the inverse of Z-values. In this case, there will be enhancement instead of ICC undermining, then this seems not appropriate.
Sorry for many questions, I am just very curious about MME and have many confusions while not put my time into reading the code to align with your paper.



Edited 2 time(s). Last edit at 12/18/2020 10:38AM by Xiaowei Song.