Dear Adele

You are exactly right, the lack of centering for this sort of variables may very well explain the large discrepancy, as without centering the adjusted means are telling you the expected connectivity difference between the two seeds for a subject with age=0 and sex=0 (which in this case would try to extrapolate from your current subject pool to newborns, which may be a somewhat meaningless extrapolation depending on your actual subjects age range). Once the control variables are centered, the adjusted means become more interpretable, as age_centered=0 and sex_centered=0 can represent something as simple as the average age and sex in your sample if your control variables are centered to their sample means. 

Which brings us to your question about which centering procedure to use. In general I recommend using the average values of the subjects within your planned analyses, as that makes the interpretation simpler/cleaner. That said, it is perfectly fine to center using other values, like the means in a different or more general pool of subjects, but this makes the statistical results slightly more complex to interpret, as the hypothesis being evaluated combines the observed differences in connectivity between the two seeds with the expected changes of those differences with age and/or sex. 

Also, just to provide some larger context, for this type of analysis (a within-subject design comparing connectivity between the two seeds) perhaps the most standard approach would be simply NOT to include age and sex as covariates, as the within-subjects nature of your design (namely that you are comparing connectivity differences between the two seeds from the same subjects) already provides generally-sufficient control for between-subject differences in factors like age and sex. That said, when adding age and sex control variables to these analyses it provides additional control for potential age*seed and sex*seed interactions (e.g. if the connectivity with the two seeds changes differently with age), but that additional control comes at the cost of increased difficulty in the interpretation of the main effects in the presence of those possible interactions, which is why in these cases people would often recommended to center the control variables in order to simplify that interpretation.

Hope this helps

Alfonso

Originally posted by adeleh:

Dear Alfonso,

Thank you very much for your explanation. It is now clear to me that the bars displayed in the "Display effects" window correspond to the adjusted means estimated by the second-level model!

However, I am still confused by the magnitude of the difference between the raw and adjusted values.

In my exported raw data, the average Fisher-transformed connectivity values are:

• V1 = 0.1904


• V3 = 0.1802

whereas the adjusted means displayed by CONN are:

• V1 = -0.1256


• V3 = 0.6076

Thus, the adjustment not only changes the absolute values, but also reverses the apparent direction of the V1–V3 difference.

My second-level model includes only two covariates (age and sex), and age and sex were entered without centering (and sex coded as 0/1).

Could this large discrepancy simply result from the lack of centering, or should I expect the adjusted means to remain relatively close to the raw means in this situation?

Also, if centering is recommended, should the age covariate be centered using the mean age of the subjects included in the second-level model (patients only), rather than all subjects in the project (patients + controls) ?

Thank you very much again for your help !

Adèle

 

Originally posted by Alfonso Nieto-Castanon:

Dear Adele,

Effect-size refers to the effects estimated in your particular second-level model and used for statistical inference. In your case, for example, with a paired analysis comparing V1 vs V3 while controlling for age and gender, effect sizes represent the "adjusted means" in your model (i.e. the average difference between V1 and V3 estimated at the zero-level of your covariates; e.g. if your age/gender covariates are centered the zero-level of those covariates will correspond to the average age/gender in your sample)

More generally, if your second level model design matrix is X, your between-subjects contrast vector is C, and your between-conditions vector is M, then the second-level analysis will fit to your data matrix Y a model of the form:

Y ~ X*B 

where B is the estimated matrix of regressor coefficients. The "effect-sizes" displayed in CONN's plot always correspond to the elements of

effects = C*B*M'

In your particular case, X=[Subjects Age Gender], Y=[V1 V3], C=[1 0 0] and M=[-1 1], so the effect sizes are displaying the difference between B(1,1) and B(1,2), containing respectively the estimated adjusted means from your data Y.

Hope this helps

Alfonso 

Originally posted by adeleh:

Dear Alfonso,

I am currently finalizing the results for my PhD thesis, so I would be extremely grateful if you could help clarify this point.

I am running a seed-to-voxel paired analysis comparing V1 vs V3, with age and sex included as second-level covariates.

For three significant clusters, I opened the REX Results window, then the plot window and exported both:

• Export raw data


• Export effect sizes

From the exported rawdata.mat file, I obtained a 46 × 3 matrix (23 subjects × 2 conditions, 3 significant clusters). The first 23 rows correspond to V1 and the last 23 rows correspond to V3.

For the first cluster, the average raw connectivity values are:

• V1: 0.1904


• V3: 0.1802

Thus, the raw functional connectivity appears to decrease slightly from V1 to V3.

However, the exported effectsize.mat file contains:

effectsize.data =



          Cluster1   Cluster2   Cluster3

V1        -0.1256    -0.1184     0.1258

V3         0.6076     0.6259     0.7745

For the same cluster, the "Display effects" plot therefore shows a large increase from V1 to V3, which seems inconsistent with the raw connectivity values.

My question is:

What exactly do the two bars in the "Display effects" plot represent?

I initially thought that the bars represented the average functional connectivity for each condition, but the exported raw data suggest that this is not the case.

Thank you very much for your time !

Best regards,

Adele