Version

Weighted

Summary Plots

Without Distance Exclusion

With Distance Exclusion

Distance exclusion only

+ 2SD ceil

+ Subcortical Parcels Exclusion

+ Subcortical Parcels Exclusion + 2SD ceil

Toward LMG

Corr: With Exclusion

  • For each ROI, we computed the relationship between various combinations of the dependent variables (euclidean distance and path length; path length and communicability).
  • We found that there was a strong correlation between euclidean distance and path length across several ROIs (and a p-value distribution suggested that many of these findings were significant), * Similarly, there was a strong [negative] correlation between path length and communicability across several ROIs.
  • These results suggest that the dependent variables for each constructed MLR model may be correlated with each other.

Plot

LMG for Individual R2 Contributions

  • From the correlational analysis, we conclude that the regressions are correlated with each other.

Problems with Existing Models of R2 Decomposition for Correlated Regressors

  • ANOVA in R: The difficulty in decomposing R2 for regression models with correlated regressors lies in the fact that the order in which regressors are entered into the model yields a different decomposition of the model sum of squares (i.e., the order in which regressors are entered into the model can have a very strong impact on their relative R2 contributions).

  • TYPE III SS/Stepwise-Regression: Type III Sum of Squares are often used to to compare what each regressor is able to explain in addition to all other regressors that are available. Here, we ascribe to each regressor the increase in R2 when including this regressor as the last of the p regressors. If regressors are correlated, these contributions do not add up to the overall R2, and typically add up to far less than the overall R2.Moreover, the direct effect of a regressor with the criterion cannot be calculated this way.

Current Approach * We evaluate R2 based on the proportionate contribution each predictor makes to R2, considering both its direct effect (i.e., its correlation with the criterion) and its effect when combined with the other variables in the regression equation.

  • We use LMG, which is based on sequential R2s (like ANOVA), but which takes care of the dependence on orderings by averaging over [permuted] orderings using simple unweighted averages. Johnson and Lebreton (2004) recommend lmg, since it clearly uses both direct effects (orders with xk first) and effects adjusted for other regressors in the model (orders with xk last). LMG decomposes R2 into non-negative contributions that automatically sum to the total R2. This is an advantage over simple metrics. (Grömping, U. (2007). Relative importance for linear regression in R: the package relaimpo. Journal of statistical software, 17, 1-27.)

(LMG: Lindemann, Merenda and Gold-1980)

Individual Plots

Without Exclusion

Sample Table (header rows: ROIs 1 to 10)
Individual R2 Contributions without Distance Exclusion
R2_ed R2_pl R2_co Total
0.0132972 0.0134925 0.0407130 0.0675026
0.0014548 0.0078898 0.0072842 0.0166288
0.0011824 0.0183753 0.0095648 0.0291225
0.0040214 0.0104478 0.0104103 0.0248795
0.0424400 0.0072535 0.0031434 0.0528369
0.0092011 0.0018007 0.0146924 0.0256943
0.0202613 0.0054078 0.0010898 0.0267590
0.0255592 0.0191125 0.0054265 0.0500982
0.0098052 0.0043447 0.0037019 0.0178518
0.0048110 0.0047099 0.0009763 0.0104972
Plot

With Distance Exclusion

Distance exclusion only
Sample Table (header rows: ROIs 1 to 10)
Individual R2 Contributions with Distance Exclusion
R2_ed R2_pl R2_co Total
0.0053436 0.0079660 0.0364724 0.0497820
0.0081277 0.0004494 0.0010041 0.0095812
0.0030708 0.0060107 0.0054695 0.0145510
0.0015326 0.0025806 0.0168749 0.0209881
0.0166577 0.0053538 0.0028679 0.0248794
0.0030255 0.0028830 0.0115605 0.0174690
0.0154155 0.0037191 0.0024277 0.0215623
0.0090706 0.0160500 0.0013725 0.0264931
0.0029328 0.0026680 0.0014045 0.0070053
0.0005422 0.0030071 0.0019519 0.0055013
Plot

+ 2SD ceil
Sample Table (header rows: ROIs 1 to 10)
Individual R2 Contributions with Distance Exclusion and 2SD ceil
R2_ed R2_pl2SDceil R2_co2SDceil Total
0.0045098 0.0085365 0.0297464 0.0427927
0.0076761 0.0006020 0.0003276 0.0086057
0.0027062 0.0077401 0.0011110 0.0115573
0.0007387 0.0039420 0.0022163 0.0068970
0.0168337 0.0066026 0.0014437 0.0248799
0.0033952 0.0016574 0.0051411 0.0101937
0.0153807 0.0038641 0.0017099 0.0209547
0.0085277 0.0134875 0.0050121 0.0270273
0.0027787 0.0019248 0.0027577 0.0074612
0.0005586 0.0029915 0.0014265 0.0049766
Plot

+ Subcortical Parcels Exclusion
Sample Table (header rows: ROIs 1 to 10)
Individual R2 Contributions with Distance and Subcortical Exclusion
R2_ed R2_pl R2_co Total
0.0110446 0.0044222 0.0460938 0.0615606
0.0174879 0.0072278 0.0040658 0.0287815
0.0134469 0.0208386 0.0047687 0.0390542
0.0039015 0.0024345 0.0191300 0.0254661
0.0351053 0.0026881 0.0009222 0.0387156
0.0118636 0.0109848 0.0107419 0.0335903
0.0155839 0.0117328 0.0027330 0.0300497
0.0307579 0.0188446 0.0015419 0.0511443
0.0101823 0.0034296 0.0016439 0.0152559
0.0020646 0.0044202 0.0056786 0.0121634
Plot

+ Subcortical Parcels Exclusion + 2SD ceil
Sample Table (header rows: ROIs 1 to 10)
Individual R2 Contributions with Distance and Subcortical Exclusion
R2_ed R2_pl R2_co Total
0.0103770 0.0042317 0.0413243 0.0559331
0.0184961 0.0057260 0.0081182 0.0323403
0.0130315 0.0208174 0.0028885 0.0367374
0.0037198 0.0026347 0.0197082 0.0260626
0.0340920 0.0045924 0.0056731 0.0443575
0.0115163 0.0098508 0.0078111 0.0291783
0.0153820 0.0117452 0.0024083 0.0295356
0.0299945 0.0158191 0.0047423 0.0505558
0.0101585 0.0028641 0.0026672 0.0156899
0.0018685 0.0033859 0.0103025 0.0155568
Plot

Specific Analyses

Functional Connectivity with Minimum Path Length

Median Path Length and Median ROI volume

R2-Brain Parcellation Map

  • These brain maps were generated from a Matlab code (and on workbench)

Subcortical and 2SD

Binarized

Summary Plots

0.01 threshold

0.02 threshold

0.04 threshold

0.05 threshold

0.06 threshold

0.08 threshold

0.1 threshold

0.15 threshold

0.2 threshold

0.25 threshold

0.3 threshold

Individual Plots

0.01 threshold

0.02 threshold

0.04 threshold

0.05 threshold

0.06 threshold

0.08 threshold

0.10 threshold

0.15 threshold

0.20 threshold

0.25 threshold

0.30 threshold

Specific Analyses

0.01 threshold

Low R2 (<0.08)

Summary Statistics
Variable Min Mean Median Max
functional connectivity -0.6 0.015 -0.034 1.782
path length 1 2.127 2 4
High R2 (> 0.08)

Summary Statistics
Variable Min Mean Median Max
functional connectivity -0.6 0.014 -0.034 1.733
path length 1 2.023 2 4

0.02 threshold

Low R2 (<0.07)

Summary Statistics
Variable Min Mean Median Max
functional connectivity -0.6 0.014 -0.035 1.782
path length 1 2.245 2 4
High R2 (> 0.07)

Summary Statistics
Variable Min Mean Median Max
functional connectivity -0.6 0.015 -0.033 1.733
path length 1 2.138 2 4

0.04 threshold

Low R2 (<0.07)

Summary Statistics
Variable Min Mean Median Max
functional connectivity -0.6 0.014 -0.036 1.782
path length 1 2.36 2 5
High R2 (> 0.07)

Summary Statistics
Variable Min Mean Median Max
functional connectivity -0.5 0.015 -0.032 1.733
path length 1 2.248 2 5

0.05 threshold

Low R2 (<0.07)

Summary Statistics
Variable Min Mean Median Max
functional connectivity -0.6 0.013 -0.036 1.782
path length 1 2.409 2 5
High R2 (> 0.07)

Summary Statistics
Variable Min Mean Median Max
functional connectivity -0.5 0.016 -0.032 1.733
path length 1 2.283 2 5

0.06 threshold

Low R2 (<0.07)

Summary Statistics
Variable Min Mean Median Max
functional connectivity -0.6 0.014 -0.036 1.782
path length 1 2.437 2 5
High R2 (> 0.07)

Summary Statistics
Variable Min Mean Median Max
functional connectivity -0.5 0.015 -0.032 1.733
path length 1 2.308 2 5

0.08 threshold

Low R2 (<0.07)

Summary Statistics
Variable Min Mean Median Max
functional connectivity -0.6 0.013 -0.036 1.782
path length 1 2.486 2 5
High R2 (> 0.07)

Summary Statistics
Variable Min Mean Median Max
functional connectivity -0.5 0.016 -0.032 1.733
path length 1 2.367 2 5

0.10 threshold

Low R2 (<0.07)

Summary Statistics
Variable Min Mean Median Max
functional connectivity -0.6 0.014 -0.035 1.782
path length 1 2.53 3 5
High R2 (> 0.07)

Summary Statistics
Variable Min Mean Median Max
functional connectivity -0.6 0.014 -0.033 1.733
path length 1 2.406 2 5

0.20 threshold

Low R2 (<0.07)

Summary Statistics
Variable Min Mean Median Max
functional connectivity -0.6 0.014 -0.035 1.782
path length 1 2.677 3 5
High R2 (> 0.07)

Summary Statistics
Variable Min Mean Median Max
functional connectivity -0.5 0.015 -0.033 1.733
path length 1 2.581 3 5

0.25 threshold

Low R2 (<0.07)

Summary Statistics
Variable Min Mean Median Max
functional connectivity -0.6 0.014 -0.035 1.782
path length 1 2.748 3 6
High R2 (> 0.07)

Summary Statistics
Variable Min Mean Median Max
functional connectivity -0.5 0.014 -0.033 1.733
path length 1 2.644 3 5

0.30 threshold

Low R2 (<0.07)

Summary Statistics
Variable Min Mean Median Max
functional connectivity -0.6 0.013 -0.035 1.782
path length 1 2.792 3 6
High R2 (> 0.07)

Summary Statistics
Variable Min Mean Median Max
functional connectivity -0.6 0.016 -0.032 1.733
path length 1 2.694 3 5

Consolidated

func ~ pl

func ~ R2 category (low, high)

Some reflections from Tukey Plots

See each thresholded Tukey plot.

  • It’s not that shorter path lengths have higher functional connectivity. What we tend to see across thresholds is that after path length 1, functional connectivity differences are less significant.

  • By extension, there is not much of an effect of multi-hop paths. True, there are significant difference, but these are inconsistent across thresholds and not in a direction we would predict.

  • We might infer that R2 contributions to functional connectivity are driven by path length 1 (primarily). There is not an overall linear relationship between path length and functional connectivity. A few directly connected regions are driving high functional connecitivty.

  • This is an important finding from a biological standpoint and can be better illustrated from specific rois.

ROI-Specific

Motivations/Working Hypotheses

  • We hypothesize that R2 contributions are primarily driven by a path length of 1. There is not an overall linear relationship between path length and functional connectivity. A few directly connected regions are driving functional connectivity.

  • By extension, there is not much of an effect of multi-hop paths (path lengths >1).

ROIs of Interest Based on Binarized Path Length
  • 171
  • 173
  • 277
  • 279
  • 375
  • 376
  • 521
  • 522
  • 556
  • 558

ROIs of Interest Based on Binarized Path Length

HISTOGRAM F-PL COMPARISONS
ROI 171:0.02T:High R2 (<0.07)

ROI 173:0.02T:High R2 (<0.07)

ROI 277:0.02T:High R2 (<0.07)

ROI 279:0.02T:High R2 (<0.07)

ROI 375:0.02T:High R2 (<0.07)

ROI 376:0.02T:High R2 (<0.07)

ROI 521:0.02T:High R2 (<0.07)

ROI 522:0.02T:High R2 (<0.07)

ROI 556:0.02T:High R2 (<0.07)

ROI 558:0.02T:High R2 (<0.07)

ANOVA/POST-HOC COMPARISONS
ROI 171:0.02T:High R2 (<0.07)

## Levene's Test for Homogeneity of Variance (center = mean)
##        Df F value    Pr(>F)    
## group   2  27.871 4.528e-12 ***
##       407                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##  One-way analysis of means (not assuming equal variances)
## 
## data:  func and pl
## F = 34.941, num df = 2.00, denom df = 120.82, p-value = 1.061e-12

  • Cohen suggested that d = 0.2 be considered a ‘small’ effect size, 0.5 represents a ‘medium’ effect size and 0.8 a ‘large’ effect size. This means that if the difference between two groups’ means is less than 0.2 standard deviations, the difference is negligible, even if it is statistically significant.

  • The “sign of the Cohen’s d effect (M1-M2/SDpooled) tells us the direction of the effect. In this instance, a negative effect size for the path comparison 2-1 (and 3-1) suggests that the mean functional connectivity associated with path length 2 (and 3) is less than the mean functional connectivity associated with path length 1.The effect size difference is small-to-medium for the path comparison 2-1 and 3-1.

  • There are no significant effect size differences for path comparison 3-2.

ROI 173:0.02T:High R2 (<0.07)

## Levene's Test for Homogeneity of Variance (center = mean)
##        Df F value    Pr(>F)    
## group   2  20.808 2.483e-09 ***
##       408                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##  One-way analysis of means (not assuming equal variances)
## 
## data:  func and pl
## F = 24.902, num df = 2.000, denom df = 72.143, p-value = 5.977e-09

  • Cohen suggested that d = 0.2 be considered a ‘small’ effect size, 0.5 represents a ‘medium’ effect size and 0.8 a ‘large’ effect size. This means that if the difference between two groups’ means is less than 0.2 standard deviations, the difference is negligible, even if it is statistically significant.

  • The “sign of the Cohen’s d effect (M1-M2/SDpooled) tells us the direction of the effect. In this instance, a negative effect size for the path comparison 2-1 (and 3-1) suggests that the mean functional connectivity associated with path length 2 (and 3) is less than the mean functional connectivity associated with path length 1.The effect size difference is small-to-medium for the path comparison 3-1.

  • There are no significant effect size differences for path comparison 3-2.

ROI 277:0.02T:High R2 (<0.07)

## Levene's Test for Homogeneity of Variance (center = mean)
##        Df F value    Pr(>F)    
## group   2  13.013 3.332e-06 ***
##       405                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##  One-way analysis of means (not assuming equal variances)
## 
## data:  func and pl
## F = 9.0451, num df = 2.00, denom df = 113.47, p-value = 0.0002265

  • Cohen suggested that d = 0.2 be considered a ‘small’ effect size, 0.5 represents a ‘medium’ effect size and 0.8 a ‘large’ effect size. This means that if the difference between two groups’ means is less than 0.2 standard deviations, the difference is negligible, even if it is statistically significant.

  • The “sign of the Cohen’s d effect (M1-M2/SDpooled) tells us the direction of the effect. In this instance, a negative effect size for the path comparison 2-1 (and 3-1) suggests that the mean functional connectivity associated with path length 2 (and 3) is less than the mean functional connectivity associated with path length 1.The effect size difference is small-to-medium for the path comparison 3-1.

  • There are no significant effect size differences for path comparison 3-2.

ROI 279:0.02T:High R2 (<0.07)

## Levene's Test for Homogeneity of Variance (center = mean)
##        Df F value    Pr(>F)    
## group   2  18.767 1.608e-08 ***
##       404                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##  One-way analysis of means (not assuming equal variances)
## 
## data:  func and pl
## F = 11.669, num df = 2.00, denom df = 142.03, p-value = 2.032e-05

  • Cohen suggested that d = 0.2 be considered a ‘small’ effect size, 0.5 represents a ‘medium’ effect size and 0.8 a ‘large’ effect size. This means that if the difference between two groups’ means is less than 0.2 standard deviations, the difference is negligible, even if it is statistically significant.

  • The “sign of the Cohen’s d effect (M1-M2/SDpooled) tells us the direction of the effect. In this instance, a negative effect size for the path comparison 2-1 (and 3-1) suggests that the mean functional connectivity associated with path length 2 (and 3) is less than the mean functional connectivity associated with path length 1.The effect size difference is small-to-medium for the path comparison 3-1.

  • There are no significant effect size differences for path comparison 3-2.

ROI 375:0.02T:High R2 (<0.07)

## Levene's Test for Homogeneity of Variance (center = mean)
##        Df F value    Pr(>F)    
## group   2  21.961 8.722e-10 ***
##       409                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##  One-way analysis of means (not assuming equal variances)
## 
## data:  func and pl
## F = 13.783, num df = 2.000, denom df = 95.645, p-value = 5.498e-06

  • Cohen suggested that d = 0.2 be considered a ‘small’ effect size, 0.5 represents a ‘medium’ effect size and 0.8 a ‘large’ effect size. This means that if the difference between two groups’ means is less than 0.2 standard deviations, the difference is negligible, even if it is statistically significant.

  • In general, in contrast to other ROIs, there was also a negligible but significant [and positive] effect size difference when comparing path lengths 3 and 2.

  • Furthermore, in general, in contrast to other ROIs, there were no significant effect size difference when comparing path lengths 3 and 1.

ROI 376:0.02T:High R2 (<0.07)

## Levene's Test for Homogeneity of Variance (center = mean)
##        Df F value    Pr(>F)    
## group   2  20.451 3.412e-09 ***
##       411                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##  One-way analysis of means (not assuming equal variances)
## 
## data:  func and pl
## F = 10.892, num df = 2.000, denom df = 93.902, p-value = 5.572e-05

  • Cohen suggested that d = 0.2 be considered a ‘small’ effect size, 0.5 represents a ‘medium’ effect size and 0.8 a ‘large’ effect size. This means that if the difference between two groups’ means is less than 0.2 standard deviations, the difference is negligible, even if it is statistically significant.

  • The “sign of the Cohen’s d effect (M1-M2/SDpooled) tells us the direction of the effect. In this instance, a negative effect size for the path comparison 2-1 (and 3-1) suggests that the mean functional connectivity associated with path length 2 (and 3) is less than the mean functional connectivity associated with path length 1.The effect size difference is small for the path comparison 2-1 and small-to-negligible for 3-1.

  • There were no significant effect size differences for the path comparison 3-2.

ROI 521:0.02T:High R2 (<0.07)

## Levene's Test for Homogeneity of Variance (center = mean)
##        Df F value    Pr(>F)    
## group   2   29.45 1.165e-12 ***
##       401                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##  One-way analysis of means (not assuming equal variances)
## 
## data:  func and pl
## F = 14.559, num df = 2.000, denom df = 86.871, p-value = 3.524e-06

  • Cohen suggested that d = 0.2 be considered a ‘small’ effect size, 0.5 represents a ‘medium’ effect size and 0.8 a ‘large’ effect size. This means that if the difference between two groups’ means is less than 0.2 standard deviations, the difference is negligible, even if it is statistically significant.

  • The “sign of the Cohen’s d effect (M1-M2/SDpooled) tells us the direction of the effect. In this instance, a negative effect size for the path comparison 2-1 (and 3-1) suggests that the mean functional connectivity associated with path length 2 (and 3) is less than the mean functional connectivity associated with path length 1.The effect size difference is tending toward medium for both path comparisons 2-1 and 3-1, and appears slightly stronger compared to other ROIs.

  • There were no significant effect size differences for the path comparison 3-2.

ROI 522:0.02T:High R2 (<0.07)

## Levene's Test for Homogeneity of Variance (center = mean)
##        Df F value   Pr(>F)   
## group   2  6.9283 0.001101 **
##       401                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##  One-way analysis of means (not assuming equal variances)
## 
## data:  func and pl
## F = 27.695, num df = 2.00, denom df = 108.57, p-value = 1.912e-10

  • Cohen suggested that d = 0.2 be considered a ‘small’ effect size, 0.5 represents a ‘medium’ effect size and 0.8 a ‘large’ effect size. This means that if the difference between two groups’ means is less than 0.2 standard deviations, the difference is negligible, even if it is statistically significant.

  • The “sign of the Cohen’s d effect (M1-M2/SDpooled) tells us the direction of the effect. In this instance, a negative effect size for the path comparison 2-1 (and 3-1) suggests that the mean functional connectivity associated with path length 2 (and 3) is less than the mean functional connectivity associated with path length 1.The effect size difference is tending toward medium for both path comparisons 2-1 and 3-1, and appears slightly stronger compared to other ROIs.

-There were no significant effect size differences for the path comparison 3-2.

ROI 556:0.02T:High R2 (<0.07)

## Levene's Test for Homogeneity of Variance (center = mean)
##        Df F value    Pr(>F)    
## group   2  23.663 1.881e-10 ***
##       410                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##  One-way analysis of means (not assuming equal variances)
## 
## data:  func and pl
## F = 14.047, num df = 2.00, denom df = 87.14, p-value = 5.153e-06

  • Cohen suggested that d = 0.2 be considered a ‘small’ effect size, 0.5 represents a ‘medium’ effect size and 0.8 a ‘large’ effect size. This means that if the difference between two groups’ means is less than 0.2 standard deviations, the difference is negligible, even if it is statistically significant.

  • The “sign of the Cohen’s d effect (M1-M2/SDpooled) tells us the direction of the effect. In this instance, a negative [small-to-negligible] effect size for the path comparison 2-1 (and 3-1) suggests that the mean functional connectivity associated with path length 2 (and 3) is less than the mean functional connectivity associated with path length 1.

ROI 558:0.02T:High R2 (<0.07)

## Levene's Test for Homogeneity of Variance (center = mean)
##        Df F value  Pr(>F)  
## group   2  3.0115 0.05031 .
##       410                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##  One-way analysis of means (not assuming equal variances)
## 
## data:  func and pl
## F = 1.2762, num df = 2.000, denom df = 16.914, p-value = 0.3046

  • Cohen suggested that d = 0.2 be considered a ‘small’ effect size, 0.5 represents a ‘medium’ effect size and 0.8 a ‘large’ effect size. This means that if the difference between two groups’ means is less than 0.2 standard deviations, the difference is negligible, even if it is statistically significant.

  • The “sign of the Cohen’s d effect (M1-M2/SDpooled) tells us the direction of the effect. In this instance, and in contrast to all other ROIs, there were no significant effect size differences in mean functional connectivity between any of the path lengths (2-1, 3-1, or 3-2).

Conclusions
  • In general, we find that high R2 appears to be driven by strong functional connectivity for direct connections (i.e., when path length = 1). This interpretation is more neurobiologically plausible than the conclusions drawn by Vasquez and colleagues. In a stricter sense, stronger connections are the only ways to get high R2.
  • Put differently, the data are pointing towards it being [if highFC then path length 1], but not necessarily [if path length 1 then highFC]. That is, stronger functional connections imply a direct structural connection. However, we cannot ascertain whether a direct structural connection is indicative of a strong functional connection. The latter is something we cannot test because of present limitations in tractography (we do not have the resolution/sensitivity to trace fibers that directly and specifically go from one ROI to another indicating a direct structural connection).
  • Summarily, we conclude that our present data suggest strong FC = short PL, but short PL does not imply strong FC.