`compute_tfce()` would fail to calculate the correct TFCE values when the original statistics are too small

[psychelzh]

For example, I generated some random numbers. At first it could give the correct values:

set.seed(42)
stat_map <- as.matrix(rnorm(100))
permuco::compute_tfce(stat_map, ndh = 100)
#> $main
#>      statistic pvalue
#> [1,] 0.5066432   0.17
#> 
#> $distribution
#>   [1] 0.5066432 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.5066432
#>   [8] 0.0000000 1.9848038 0.0000000 0.5066432 1.9848038 0.0000000 0.0000000
#>  [15] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.5066432 0.0000000
#>  [22] 0.0000000 0.0000000 0.5066432 0.5066432 0.0000000 0.0000000 0.0000000
#>  [29] 0.0000000 0.0000000 0.0000000 0.0000000 0.5066432 0.0000000 0.0000000
#>  [36] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#>  [43] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.5066432 0.0000000
#>  [50] 0.0000000 0.0000000 0.0000000 0.5066432 0.0000000 0.0000000 0.0000000
#>  [57] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#>  [64] 0.5066432 0.0000000 0.5066432 0.0000000 0.5066432 0.0000000 0.0000000
#>  [71] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#>  [78] 0.0000000 0.0000000 0.0000000 0.5066432 0.0000000 0.0000000 0.0000000
#>  [85] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.5066432
#>  [92] 0.0000000 0.0000000 0.5066432 0.0000000 0.0000000 0.0000000 0.0000000
#>  [99] 0.0000000 0.0000000
#> 
#> $E
#> [1] 0.5
#> 
#> $H
#> [1] 1
#> 
#> $dhi
#>   [1] 0.03612261 0.06599097 0.09585932 0.12572768 0.15559604 0.18546440
#>   [7] 0.21533276 0.24520112 0.27506947 0.30493783 0.33480619 0.36467455
#>  [13] 0.39454291 0.42441127 0.45427962 0.48414798 0.51401634 0.54388470
#>  [19] 0.57375306 0.60362142 0.63348977 0.66335813 0.69322649 0.72309485
#>  [25] 0.75296321 0.78283157 0.81269992 0.84256828 0.87243664 0.90230500
#>  [31] 0.93217336 0.96204172 0.99191007 1.02177843 1.05164679 1.08151515
#>  [37] 1.11138351 1.14125187 1.17112022 1.20098858 1.23085694 1.26072530
#>  [43] 1.29059366 1.32046202 1.35033037 1.38019873 1.41006709 1.43993545
#>  [49] 1.46980381 1.49967217 1.52954052 1.55940888 1.58927724 1.61914560
#>  [55] 1.64901396 1.67888232 1.70875067 1.73861903 1.76848739 1.79835575
#>  [61] 1.82822411 1.85809247 1.88796082 1.91782918 1.94769754 1.97756590
#>  [67] 2.00743426 2.03730262 2.06717097 2.09703933 2.12690769 2.15677605
#>  [73] 2.18664441 2.21651277 2.24638112 2.27624948 2.30611784 2.33598620
#>  [79] 2.36585456 2.39572292 2.42559127 2.45545963 2.48532799 2.51519635
#>  [85] 2.54506471 2.57493307 2.60480142 2.63466978 2.66453814 2.69440650
#>  [91] 2.72427486 2.75414322 2.78401157 2.81387993 2.84374829 2.87361665
#>  [97] 2.90348501 2.93335337 2.96322172 2.99309008

Then I rescale the numbers to smaller values, and the calculations failed.

permuco::compute_tfce(stat_map * 1e-3, ndh = 100)
#> $main
#>      statistic pvalue
#> [1,]         0      1
#> 
#> $distribution
#>   [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#>  [38] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#>  [75] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#> 
#> $E
#> [1] 0.5
#> 
#> $H
#> [1] 1
#> 
#> $dhi
#>   [1] 3.612261e-05 6.599097e-05 9.585932e-05 1.257277e-04 1.555960e-04
#>   [6] 1.854644e-04 2.153328e-04 2.452011e-04 2.750695e-04 3.049378e-04
#>  [11] 3.348062e-04 3.646745e-04 3.945429e-04 4.244113e-04 4.542796e-04
#>  [16] 4.841480e-04 5.140163e-04 5.438847e-04 5.737531e-04 6.036214e-04
#>  [21] 6.334898e-04 6.633581e-04 6.932265e-04 7.230948e-04 7.529632e-04
#>  [26] 7.828316e-04 8.126999e-04 8.425683e-04 8.724366e-04 9.023050e-04
#>  [31] 9.321734e-04 9.620417e-04 9.919101e-04 1.021778e-03 1.051647e-03
#>  [36] 1.081515e-03 1.111384e-03 1.141252e-03 1.171120e-03 1.200989e-03
#>  [41] 1.230857e-03 1.260725e-03 1.290594e-03 1.320462e-03 1.350330e-03
#>  [46] 1.380199e-03 1.410067e-03 1.439935e-03 1.469804e-03 1.499672e-03
#>  [51] 1.529541e-03 1.559409e-03 1.589277e-03 1.619146e-03 1.649014e-03
#>  [56] 1.678882e-03 1.708751e-03 1.738619e-03 1.768487e-03 1.798356e-03
#>  [61] 1.828224e-03 1.858092e-03 1.887961e-03 1.917829e-03 1.947698e-03
#>  [66] 1.977566e-03 2.007434e-03 2.037303e-03 2.067171e-03 2.097039e-03
#>  [71] 2.126908e-03 2.156776e-03 2.186644e-03 2.216513e-03 2.246381e-03
#>  [76] 2.276249e-03 2.306118e-03 2.335986e-03 2.365855e-03 2.395723e-03
#>  [81] 2.425591e-03 2.455460e-03 2.485328e-03 2.515196e-03 2.545065e-03
#>  [86] 2.574933e-03 2.604801e-03 2.634670e-03 2.664538e-03 2.694406e-03
#>  [91] 2.724275e-03 2.754143e-03 2.784012e-03 2.813880e-03 2.843748e-03
#>  [96] 2.873617e-03 2.903485e-03 2.933353e-03 2.963222e-03 2.993090e-03

^{Created on 2024-08-25 with reprex v2.1.0}

[jaromilfrossard]

Hello,

Thanks you for reporting the bug. I think there is indeed something wrong with the approximation of the integral of the TFCE, when the values of the statistics are below 1. The issue might come from the cpp code.

#zero
permuco:::tfce_distribution(distribution = matrix(.9),E=0.5,H=1,dh=.1,dhi=c(0.6,.7,.8,.9)) 

#not zero
permuco:::tfce_distribution(distribution = matrix(1.1),E=0.5,H=1,dh=.1,dhi=c(0.6,.7,.8,.9,1,1.1))
permuco:::tfce_distribution(distribution = matrix(1.1),E=0.5,H=1,dh=.1,dhi=c(.8,.9,1,1.1))

#also zero !?
permuco:::tfce_distribution(distribution = matrix(1.1),E=0.5,H=1,dh=.1,dhi=c(1,1.1))

I double check the cpp code, and I think:

• the cluster_extend() is fine (even when signal of length 1)
• the problem shoud come from :

https://github.com/jaromilfrossard/permuco/blob/19ec0f916f5a090a532cf423adb584d6a15369b3/src/tfce.cpp#L61C1-L68C4

[jaromilfrossard]

In line

• https://github.com/jaromilfrossard/permuco/blob/19ec0f916f5a090a532cf423adb584d6a15369b3/src/tfce.cpp#L62C1-L62C45 the maximal value is saved as an integer (instead of double) which is likely the source of the error. I will see if it is the source of the error.

[jaromilfrossard]

Fixed in 1.1.3 This bug should not have affected the results of TFCE with the usually statistics as they usually have greater than 1.