Let \(y_{ijf}\) be the one-dimensional array of the simulated feature \(f\), for the single-center \(i\), and participant \(j\), for a total of \(k\) single-center datasets,\(n_i\) participants for each center, and \(V\) features. We simulated MRI-derived cortical thickness (CT) and fractal dimension (FD) data for \(k = 3, 10, 36\) single-centers. Each single-center dataset provided the same number of participants (i.e., \(n_i = n\)), with \(n\) assuming the values \(25, 50, 100, 250\). Totally, we did 24 experiments, i.e., we simulated 24 different multicenter datasets (12 for the CT features and 12 for the FD measures). Each \(y_{ijf}\) was generated using the model proposed by Johnson and colleagues [1] and recently used for neuroimaging features’ simulation by Chen and collaborators [2]: \(y_{ijf} = \alpha_f + \beta_{f1}x_{ij} + \beta_{f2}x_{ij}^2 + \gamma_{if} + \delta_{if}\epsilon_{ijf}\) where \(\alpha_f\) is the average value of the feature \(f\) in the single-center ICBM dataset [3], \(\beta_{f1}\)and \(\beta_{f2}\) are the linear and quadratic effects of the age on the feature \(f\), respectively, and \(x_{ij}\) is a simulated age variable drawn from a uniform distribution \(X \sim uniform([20, 90])\). The mean site effect \(\gamma_{if}\) was drawn from a normal distribution with zero mean and standard deviation equal to 0.1, while the variance site effect \(\delta_{if}\) was drawn from a center-specific inverse gamma distribution with chosen parameters. For our simulations, we chose to distinguish the site-specific location factors by assuming independent and identically distributed (i.i.d.) normal distributions and scaling factors using the parameters described as follows. We set the value of the inverse gamma shape, for each center, as {46, 51, 56}, respectively, when k = 3, as {40, 42, .., 58} when k = 10, and as {10, 12, .., 40, 41, .., 50, .., 70} when k = 36. In all cases, the inverse gamma scale was set to 50. Each CSV file contains the following columns: SITE: simulated imaging site label (i.e., a, b, c, ..., j) age: each subject's simulated age, expressed in years cortex_CT (FD): CT (or FD) of the cerebral cortical gray matter (GM). lh_cortex_CT (FD), rh_cortex_CT (FD): CT (or FD) of the left (lh) and right (rh) cerebral cortical GM. lh_frontal_cortex_CT (FD), rh_frontal_cortex_CT (FD): CT (or FD) of the left (lh) and right (rh) cerebral cortical GM of the frontal lobe. lh_temporal_cortex_CT (FD), rh_temporal_cortex_CT (FD): CT (or FD) of the left (lh) and right (rh) cerebral cortical GM of the temporal lobe. lh_parietal_cortex_CT (FD), rh_parietal_cortex_CT (FD): CT (or FD) of the left (lh) and right (rh) cerebral cortical GM of the parietal lobe. lh_occipital_cortex_CT (FD), rh_occipital_cortex_CT (FD): CT (or FD) of the left (lh) and right (rh) cerebral cortical GM of the occipital lobe. References [1] Johnson, W. E., Li, C. & Rabinovic, A. Adjusting batch effects in microarray expression data using empirical Bayes methods. Biostat. Oxf. Engl. 8, 118–127 (2007). [2] Chen, A. A. et al. Mitigating site effects in covariance for machine learning in neuroimaging data. Hum. Brain Mapp. 43, 1179–1195 (2022). [3] 1000 Functional Connectomes Project (FCP) – ICBM dataset.