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help > RE: "first eigenvariate" vs. mean vs. beta
Feb 19, 2015 03:02 AM | Alfonso Nieto-Castanon - Boston University
RE: "first eigenvariate" vs. mean vs. beta
Hi Patrick,
I am not sure entirely if I am interpreting correctly your measures, but yes, the beta values (from a one-sample t-test for groupA, for example, which will be contained in the file named beta_0001.img in the results folder, or equivalently in con_0001.img there) represent for each voxel the average of the subject-specific rZ scores across the corresponding subjects. You can find those subject-specific rZ values from the files conn_*/results/firstlevel/ANALYSIS01/BETA_Subject#_Condition#_Source#.nii. The t-values from these same analyses (e.g. in spmT_001.nii in the results folder) represent the ratio between the beta values above (the con_0001.img values) and the voxel-specific residuals (in ResMS.nii, with some additional global scaling factor contained in the SPM.mat file), so average t-values across voxels within an ROI are not expected to match the average beta-values across the same voxels in any meaningful way unless the ROI is relatively small and the data relatively smooth (due to the different scaling of different voxels implied by the residual-mean-square division computation).
Last, if you extract the first eigenvariate from your cluster of interest (e.g. in SPM 'V.O.I' button or equivalent), that will give you a "weighted-average" of the rZ values for each subject within your cluster of interest. The "weighted average" is in quotes because it is really the scaled first left singular vector from a SVD decomposition of the subjects-by-voxels matrix of rZ values within your ROI, and it can only be truly interpreted as a weighted average (with weights positive and adding to 1) in the limit of small and homogeneous ROIs (when the right singular vector of that same matrix is roughly constant across voxels; in all other cases the weights add-up to less than 1). This means that in general the subject-specific average rZ values across voxels within an ROI may well be different from the "weighted average" eigenvariate value for that same subject and ROI (and equivalently, the average across-subjects of these values may similarly differ).
Hope this helps clarify (or at least hope this does not confuse things too much :)
Alfonso
Originally posted by Patrick McConnell:
I am not sure entirely if I am interpreting correctly your measures, but yes, the beta values (from a one-sample t-test for groupA, for example, which will be contained in the file named beta_0001.img in the results folder, or equivalently in con_0001.img there) represent for each voxel the average of the subject-specific rZ scores across the corresponding subjects. You can find those subject-specific rZ values from the files conn_*/results/firstlevel/ANALYSIS01/BETA_Subject#_Condition#_Source#.nii. The t-values from these same analyses (e.g. in spmT_001.nii in the results folder) represent the ratio between the beta values above (the con_0001.img values) and the voxel-specific residuals (in ResMS.nii, with some additional global scaling factor contained in the SPM.mat file), so average t-values across voxels within an ROI are not expected to match the average beta-values across the same voxels in any meaningful way unless the ROI is relatively small and the data relatively smooth (due to the different scaling of different voxels implied by the residual-mean-square division computation).
Last, if you extract the first eigenvariate from your cluster of interest (e.g. in SPM 'V.O.I' button or equivalent), that will give you a "weighted-average" of the rZ values for each subject within your cluster of interest. The "weighted average" is in quotes because it is really the scaled first left singular vector from a SVD decomposition of the subjects-by-voxels matrix of rZ values within your ROI, and it can only be truly interpreted as a weighted average (with weights positive and adding to 1) in the limit of small and homogeneous ROIs (when the right singular vector of that same matrix is roughly constant across voxels; in all other cases the weights add-up to less than 1). This means that in general the subject-specific average rZ values across voxels within an ROI may well be different from the "weighted average" eigenvariate value for that same subject and ROI (and equivalently, the average across-subjects of these values may similarly differ).
Hope this helps clarify (or at least hope this does not confuse things too much :)
Alfonso
Originally posted by Patrick McConnell:
Hello experts,
I have been trying to understand the relationship between the first eigenvariate, mean and mean-beta value across a cluster. For a between-groups analysis (two groups) I have made a t-contrast where group A > group B. A cluster in medial vACC was found to be significantly different in the magnitude of correlation with the seed region between groups. I extracted the first eigenvariate from this cluster, thus obtaining a value for each subject which I interpret as being the weighted-mean correlation across the cluster for each subject. I then (using SPM12) extracted beta-values for the cluster, thus obtaining an rZ score for each voxel in the cluster for each group.
Group-mean analysis for these two measures (first eigenvariate and mean-beta across the cluster) are virtually identical (e.g., group A: eigen = .3113; beta=.3094). To obtain the actual mean, I used custom code to extract the mean value across a mask of the functional cluster from the t-con image. Next, I went into the 1st level results folder and extracted mean values across the functional ROI for each subject. For group A, the mean value was similar to the mean first eigenvariate from the 2nd level (.3386 vs .3114, respectively) but differed significantly for group B (mean = .2183, mean eigenvariate = .0315). The mean value for groups A and B across the functional ROI was the same as found from the t-con analysis. However, mean values obtained from the two 2nd level beta images did not match the mean value from the t-con image... rather, they matched the mean beta values pulled from the 2nd level model.
Could someone please explain what is happening 'behind the curtain' here regarding the large difference between the mean, mean eigenvariate and mean-beta? My understanding was that the t-con image was a linear combination of the beta images, with the spmT map representing (roughly) the relationship between the t-con image and the ResMS image. If this is the case, then why do the beta images at the second level correspond more closely with the mean eigenvariate values rather than the mean values?
Sorry if convoluted, just trying to wrap my head around these measures.
All the best,
Patrick
I have been trying to understand the relationship between the first eigenvariate, mean and mean-beta value across a cluster. For a between-groups analysis (two groups) I have made a t-contrast where group A > group B. A cluster in medial vACC was found to be significantly different in the magnitude of correlation with the seed region between groups. I extracted the first eigenvariate from this cluster, thus obtaining a value for each subject which I interpret as being the weighted-mean correlation across the cluster for each subject. I then (using SPM12) extracted beta-values for the cluster, thus obtaining an rZ score for each voxel in the cluster for each group.
Group-mean analysis for these two measures (first eigenvariate and mean-beta across the cluster) are virtually identical (e.g., group A: eigen = .3113; beta=.3094). To obtain the actual mean, I used custom code to extract the mean value across a mask of the functional cluster from the t-con image. Next, I went into the 1st level results folder and extracted mean values across the functional ROI for each subject. For group A, the mean value was similar to the mean first eigenvariate from the 2nd level (.3386 vs .3114, respectively) but differed significantly for group B (mean = .2183, mean eigenvariate = .0315). The mean value for groups A and B across the functional ROI was the same as found from the t-con analysis. However, mean values obtained from the two 2nd level beta images did not match the mean value from the t-con image... rather, they matched the mean beta values pulled from the 2nd level model.
Could someone please explain what is happening 'behind the curtain' here regarding the large difference between the mean, mean eigenvariate and mean-beta? My understanding was that the t-con image was a linear combination of the beta images, with the spmT map representing (roughly) the relationship between the t-con image and the ResMS image. If this is the case, then why do the beta images at the second level correspond more closely with the mean eigenvariate values rather than the mean values?
Sorry if convoluted, just trying to wrap my head around these measures.
All the best,
Patrick
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| Title | Author | Date |
|---|---|---|
| Patrick McConnell | Feb 8, 2015 | |
| Alfonso Nieto-Castanon | Feb 19, 2015 | |
| Patrick McConnell | Mar 25, 2015 | |
| Jason Craggs | Mar 12, 2015 | |
| Patrick McConnell | Feb 25, 2015 | |
| Patrick McConnell | Mar 11, 2015 | |
| Patrick McConnell | Feb 14, 2015 | |