Fig 1.
Organization of data for MELD analysis.
In (A) you can see the data from a simulated experiment with two independent variables, a behavioral condition (Beh. Condition) and a continuous variable (Cont.), for each of 10 trials for three subjects and examples of corresponding mock neural dependent data. This information is assembled into matrices X (independent data) and Y (dependent data) for each subject and the matrices for each subject are stacked (B).
Fig 2.
Patterns of signal used in simulation Experiment A.
These are the patterns of signal that were added to 100 x 100 noisy fields to generate simulated neural data. Central is a single central 10 x 10 cluster of 100 features. Split has four separate 5 x 5 clusters, each containing 25 features. Dispersed has 25 separate 2 x 2 clusters, each containing 4 features.
Fig 3.
Patterns of signal used in simulation Experiment B.
These are the patterns of signal that were added to 100 x 100 noisey fields to generate simulated neural data for Simulation Experiment B. Percent centrality is defined as the percentage of features in the largest cluster.
Fig 4.
Aggregated results of simulation Experiment A.
This shows the performance of the three different methods (MELD, t+TFCER, and t-test) using three metrics (MCC,TPR, and PPV) for each of 300 simulations. Violin plots in A and B demonstrate the distributions of results for MCC and TPR respectively. The width of the colored section indicates the kernel density estimate. MELD has a greater density of values with high MCC and TPR than either of the two other methods. The colored lines connecting the points indicate results from the same simulation; lines are colored based on the method for which they had the highest value. Gray lines indicate equal values. The paucity of red lines between MELD and t+TFCE reflects very low number of simulations for which t+TFCE performed better than MELD. The distribution of PPV (C) was divided almost entirely between 0 and 1, resulting in a misleading violin plot, so instead we have just plotted a point for each simulation result. The width over which points are spread is indicative of the number of points present at that value. PPV is undefined when a method fails to identify any features as containing signal, so there are unequal numbers of points for each method.
Fig 5.
Expanded results of simulation Experiment A.
This shows the performance of the three different methods (MELD, t+TFCE, and t-test) on simulated data using three metrics (MCC, TPR, and PPV). Each row shows the results for one signal pattern and the final row shows the results collapsed across all signal patterns. Slope refers to the level of contrast between conditions; higher values indicate a stronger signal. Error bars indicate the 95% confidence interval across the simulations run at those conditions. PPV is undefined if a method does not find any significant elements; consequently, PPV results are unreliable for points at which fewer than 5 simulations identified significant features, so these points are not shown. MELD has the clearest advantage for lower levels of signal and for the dispersed signal pattern.
Fig 6.
Aggregated results of simulation Experiment B.
This shows the performance of the three different methods (MELD, t+TFCER, and t-test) using three metrics (MCC,TPR, and PPV) for each of 500 simulations. Violin plots in A and B demonstrate the distributions of results for MCC and TPR respectively. The width of the colored section indicates the density of points. MELD has a greater density of values with high MCC and TPR than either of the two other methods. The colored lines connecting the points indicate results from the same simulation; lines are colored based on the method for which they had the highest value. Gray lines indicate equal values. The paucity of red lines between MELD and t+TFCE reflects very low number of simulations for which t+TFCE performed better than MELD. The distribution of PPV (C) was divided almost entirely between 0 and 1, resulting in a misleading violin plot, so instead we have just plotted a point for each simulation result. The width over which points are spread is indicative of the number of points present at that value. PPV is undefined when a method fails to identify any features as containing signal, so we were unable to connect points across simulations.
Fig 7.
Detailed results of simulation Experiment B.
The results for MCC, TPR, and PPV from 500 simulations at 5 different slopes and 5 different centralities demonstrate the reduced impact of centrality on MELD when compared to t+TFCE. t-test was unaffected by centrality but was much less sensitive than the other two methods. MELD was stable across all levels of centrality at higher levels of slope while t+TFCE was sensitive to differences in centrality at all levels of slope. At a slope of 0.5, MELD was more sensitive to changes in centrality than at higher slopes, but at 10% centrality it still has an MCC of 0.72 ± 0.08 95%CI, compared to t+TFCE with an MCC of 0.12 ± 0.03 95%CI. The gain in overall performance and sensitivity for MELD is clearest at a slope of 0.5, but importantly, MELD is also able to detect some signal at a slope of 0.3, when the other methods are detecting very little.
Fig 8.
Time course of old/new effect assessed by MELD and t+TFCE.
A shows the grand average ERP at channel Pz for old and new trials. B shows the within subject mean difference with the 95% confidence interval in white around it. The blue and red dots indicate time points identified as significant by MELD and t+TFCE respectively.
Fig 9.
Scalp distribution of old/new effect assessed by MELD and t+TFCE.
These topographic plots represent a top down view of the head with the triangle at the top representing the nose. Each dot indicates the location of an EEG channel. Average differences in voltage for significant sensor-channel combinations are plotted for both MELD (A; in blue) and t+TFCE (B; in red). Color only signifies the method used, not the direction of the effect, which is positive for both MELD and t+TFCE. Both techniques identify similar regions, but the effect identified by MELD has greater extent in time and space.