R/estimate_funs.R
estimate_sandwich_matrices.RdFor a given set of estimating equations computes the 'meat' (\(B_m\) in Stefanski and Boos notation) and 'bread' (\(A_m\) in Stefanski and Boos notation) matrices necessary to compute the covariance matrix.
estimate_sandwich_matrices(.basis, .theta)basis an object of class m_estimation_basis
vector of parameter estimates (i.e. estimated roots)
a sandwich_components object
For a set of estimating equations (\(\sum_i \psi(O_i, \theta) = 0\)), this function computes:
$$A_i = \partial \psi(O_i, \theta)/\partial \theta$$
$$A = \sum_i A_i$$
$$B_i = \psi(O_i, \theta)\psi(O_i, \theta)^T$$
$$B = \sum_i B_i$$
where all of the above are evaluated at \(\hat{\theta}\). The partial derivatives in \(A_i\)
numerically approximated by the function defined in deriv_control.
Note that \(A = \sum_i A_i\) and not \(\sum_i A_i/m\), and the same for \(B\).
Stefanski, L. A., & Boos, D. D. (2002). The calculus of m-estimation. The American Statistician, 56(1), 29-38.
myee <- function(data){
function(theta){
c(data$Y1 - theta[1],
(data$Y1 - theta[1])^2 - theta[2])
}
}
# Start with a basic basis
mybasis <- create_basis(
estFUN = myee,
data = geexex)
# Now estimate sandwich matrices
estimate_sandwich_matrices(
mybasis, c(mean(geexex$Y1), var(geexex$Y1)))
#> An object of class "sandwich_components"
#> Slot ".A":
#> [,1] [,2]
#> [1,] 1.000000e+02 0
#> [2,] -1.586615e-10 100
#>
#> Slot ".A_i":
#> $`1`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] -2.752514 1
#>
#> $`2`
#> [,1] [,2]
#> [1,] 1.00000 0
#> [2,] 10.81578 1
#>
#> $`3`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] -3.842305 1
#>
#> $`4`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] 6.653878 1
#>
#> $`5`
#> [,1] [,2]
#> [1,] 1.00000 0
#> [2,] -11.75308 1
#>
#> $`6`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] -3.291574 1
#>
#> $`7`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] -6.300465 1
#>
#> $`8`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] -3.043499 1
#>
#> $`9`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] 9.831685 1
#>
#> $`10`
#> [,1] [,2]
#> [1,] 1.0000000 0
#> [2,] -0.9485972 1
#>
#> $`11`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] 1.291621 1
#>
#> $`12`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] 1.947683 1
#>
#> $`13`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] -5.005397 1
#>
#> $`14`
#> [,1] [,2]
#> [1,] 1.00000 0
#> [2,] -11.52285 1
#>
#> $`15`
#> [,1] [,2]
#> [1,] 1.00000 0
#> [2,] -2.73693 1
#>
#> $`16`
#> [,1] [,2]
#> [1,] 1.0000000 0
#> [2,] 0.9379618 1
#>
#> $`17`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] 8.055833 1
#>
#> $`18`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] -2.133716 1
#>
#> $`19`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] -2.509455 1
#>
#> $`20`
#> [,1] [,2]
#> [1,] 1.0000 0
#> [2,] 12.8324 1
#>
#> $`21`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] -6.278834 1
#>
#> $`22`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] 3.302893 1
#>
#> $`23`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] -4.760703 1
#>
#> $`24`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] 3.231159 1
#>
#> $`25`
#> [,1] [,2]
#> [1,] 1.00000 0
#> [2,] -12.45122 1
#>
#> $`26`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] -4.239123 1
#>
#> $`27`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] -2.327459 1
#>
#> $`28`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] 7.970532 1
#>
#> $`29`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] -3.845686 1
#>
#> $`30`
#> [,1] [,2]
#> [1,] 1.00000 0
#> [2,] 2.29405 1
#>
#> $`31`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] -3.431482 1
#>
#> $`32`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] -6.892173 1
#>
#> $`33`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] 5.423243 1
#>
#> $`34`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] -3.770696 1
#>
#> $`35`
#> [,1] [,2]
#> [1,] 1.00000 0
#> [2,] 10.69635 1
#>
#> $`36`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] 3.455444 1
#>
#> $`37`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] -1.296536 1
#>
#> $`38`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] 3.555264 1
#>
#> $`39`
#> [,1] [,2]
#> [1,] 1.0000000 0
#> [2,] -0.4103641 1
#>
#> $`40`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] 3.559842 1
#>
#> $`41`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] -3.356527 1
#>
#> $`42`
#> [,1] [,2]
#> [1,] 1.00000 0
#> [2,] -17.18108 1
#>
#> $`43`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] 1.165449 1
#>
#> $`44`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] 5.191265 1
#>
#> $`45`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] -7.943802 1
#>
#> $`46`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] -8.998276 1
#>
#> $`47`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] -3.587908 1
#>
#> $`48`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] -4.218017 1
#>
#> $`49`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] 3.262841 1
#>
#> $`50`
#> [,1] [,2]
#> [1,] 1.0000000 0
#> [2,] 0.9841168 1
#>
#> $`51`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] 8.188365 1
#>
#> $`52`
#> [,1] [,2]
#> [1,] 1.0000 0
#> [2,] 13.1389 1
#>
#> $`53`
#> [,1] [,2]
#> [1,] 1.0000000 0
#> [2,] -0.2327012 1
#>
#> $`54`
#> [,1] [,2]
#> [1,] 1.0000000 0
#> [2,] -0.2827533 1
#>
#> $`55`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] 1.912849 1
#>
#> $`56`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] -2.786123 1
#>
#> $`57`
#> [,1] [,2]
#> [1,] 1.0000000 0
#> [2,] -0.9959563 1
#>
#> $`58`
#> [,1] [,2]
#> [1,] 1.00000 0
#> [2,] -0.88019 1
#>
#> $`59`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] 2.023568 1
#>
#> $`60`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] 1.022743 1
#>
#> $`61`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] -2.027283 1
#>
#> $`62`
#> [,1] [,2]
#> [1,] 1.0000000 0
#> [2,] 0.3831244 1
#>
#> $`63`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] -1.507302 1
#>
#> $`64`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] 6.268315 1
#>
#> $`65`
#> [,1] [,2]
#> [1,] 1.0000000 0
#> [2,] -0.0352244 1
#>
#> $`66`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] -5.127449 1
#>
#> $`67`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] -2.109045 1
#>
#> $`68`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] -5.612504 1
#>
#> $`69`
#> [,1] [,2]
#> [1,] 1.00000 0
#> [2,] 1.53121 1
#>
#> $`70`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] 6.681925 1
#>
#> $`71`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] 4.967466 1
#>
#> $`72`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] 1.522182 1
#>
#> $`73`
#> [,1] [,2]
#> [1,] 1.0000000 0
#> [2,] -0.8176918 1
#>
#> $`74`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] 2.226746 1
#>
#> $`75`
#> [,1] [,2]
#> [1,] 1.0000000 0
#> [2,] -0.5266062 1
#>
#> $`76`
#> [,1] [,2]
#> [1,] 1.00000 0
#> [2,] -16.42393 1
#>
#> $`77`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] 2.777827 1
#>
#> $`78`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] -3.069934 1
#>
#> $`79`
#> [,1] [,2]
#> [1,] 1.00000 0
#> [2,] 10.05734 1
#>
#> $`80`
#> [,1] [,2]
#> [1,] 1.00000 0
#> [2,] 17.25968 1
#>
#> $`81`
#> [,1] [,2]
#> [1,] 1.00000 0
#> [2,] -10.00691 1
#>
#> $`82`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] 4.629864 1
#>
#> $`83`
#> [,1] [,2]
#> [1,] 1.0000000 0
#> [2,] 0.9030276 1
#>
#> $`84`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] -4.278789 1
#>
#> $`85`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] 4.872697 1
#>
#> $`86`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] 5.576646 1
#>
#> $`87`
#> [,1] [,2]
#> [1,] 1.0000000 0
#> [2,] -0.8347135 1
#>
#> $`88`
#> [,1] [,2]
#> [1,] 1.0000 0
#> [2,] -2.4507 1
#>
#> $`89`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] -8.775649 1
#>
#> $`90`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] -5.087647 1
#>
#> $`91`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] -1.953179 1
#>
#> $`92`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] -2.095662 1
#>
#> $`93`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] 7.542036 1
#>
#> $`94`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] -2.216907 1
#>
#> $`95`
#> [,1] [,2]
#> [1,] 1.00000 0
#> [2,] 15.07308 1
#>
#> $`96`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] -3.529053 1
#>
#> $`97`
#> [,1] [,2]
#> [1,] 1.00000 0
#> [2,] 12.51525 1
#>
#> $`98`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] 1.206403 1
#>
#> $`99`
#> [,1] [,2]
#> [1,] 1.00000 0
#> [2,] -8.77275 1
#>
#> $`100`
#> [,1] [,2]
#> [1,] 1.000000 0
#> [2,] 4.526372 1
#>
#>
#> Slot ".B":
#> [,1] [,2]
#> [1,] 1004.1239 366.7969
#> [2,] 366.7969 24922.9925
#>
#> Slot ".B_i":
#> $`1`
#> [,1] [,2]
#> [1,] 1.894083 11.35217
#> [2,] 11.352168 68.03912
#>
#> $`2`
#> [,1] [,2]
#> [1,] 29.24529 103.3049
#> [2,] 103.30492 364.9103
#>
#> $`3`
#> [,1] [,2]
#> [1,] 3.690828 12.39497
#> [2,] 12.394966 41.62621
#>
#> $`4`
#> [,1] [,2]
#> [1,] 11.068524 3.0802759
#> [2,] 3.080276 0.8572145
#>
#> $`5`
#> [,1] [,2]
#> [1,] 34.5337 -143.3349
#> [2,] -143.3349 594.9226
#>
#> $`6`
#> [,1] [,2]
#> [1,] 2.708615 12.23486
#> [2,] 12.234864 55.26511
#>
#> $`7`
#> [,1] [,2]
#> [1,] 9.9239647 0.68895834
#> [2,] 0.6889583 0.04783004
#>
#> $`8`
#> [,1] [,2]
#> [1,] 2.315721 11.91065
#> [2,] 11.910648 61.26106
#>
#> $`9`
#> [,1] [,2]
#> [1,] 24.16551 68.93408
#> [2,] 68.93408 196.64009
#>
#> $`10`
#> [,1] [,2]
#> [1,] 0.2249591 4.703954
#> [2,] 4.7039541 98.360900
#>
#> $`11`
#> [,1] [,2]
#> [1,] 0.4170714 -6.280893
#> [2,] -6.2808925 94.587180
#>
#> $`12`
#> [,1] [,2]
#> [1,] 0.9483677 -8.953791
#> [2,] -8.9537909 84.535112
#>
#> $`13`
#> [,1] [,2]
#> [1,] 6.263501 9.708381
#> [2,] 9.708381 15.047921
#>
#> $`14`
#> [,1] [,2]
#> [1,] 33.1940 -132.8085
#> [2,] -132.8085 531.3642
#>
#> $`15`
#> [,1] [,2]
#> [1,] 1.872697 11.31716
#> [2,] 11.317164 68.39238
#>
#> $`16`
#> [,1] [,2]
#> [1,] 0.2199431 -4.653567
#> [2,] -4.6535674 98.460420
#>
#> $`17`
#> [,1] [,2]
#> [1,] 16.22411 24.49556
#> [2,] 24.49556 36.98400
#>
#> $`18`
#> [,1] [,2]
#> [1,] 1.138186 9.606502
#> [2,] 9.606502 81.080647
#>
#> $`19`
#> [,1] [,2]
#> [1,] 1.574341 10.75091
#> [2,] 10.750912 73.41619
#>
#> $`20`
#> [,1] [,2]
#> [1,] 41.16761 199.0623
#> [2,] 199.06226 962.5475
#>
#> $`21`
#> [,1] [,2]
#> [1,] 9.8559376 0.90015836
#> [2,] 0.9001584 0.08221289
#>
#> $`22`
#> [,1] [,2]
#> [1,] 2.727275 -12.24612
#> [2,] -12.246119 54.98802
#>
#> $`23`
#> [,1] [,2]
#> [1,] 5.666072 10.65586
#> [2,] 10.655865 20.03989
#>
#> $`24`
#> [,1] [,2]
#> [1,] 2.610097 -12.16946
#> [2,] -12.169463 56.73959
#>
#> $`25`
#> [,1] [,2]
#> [1,] 38.75822 -178.1493
#> [2,] -178.14928 818.8499
#>
#> $`26`
#> [,1] [,2]
#> [1,] 4.49254 11.97579
#> [2,] 11.97579 31.92391
#>
#> $`27`
#> [,1] [,2]
#> [1,] 1.354266 10.22732
#> [2,] 10.227320 77.23596
#>
#> $`28`
#> [,1] [,2]
#> [1,] 15.88235 22.87416
#> [2,] 22.87416 32.94394
#>
#> $`29`
#> [,1] [,2]
#> [1,] 3.697326 12.39338
#> [2,] 12.393377 41.54240
#>
#> $`30`
#> [,1] [,2]
#> [1,] 1.315666 -10.12479
#> [2,] -10.124788 77.91592
#>
#> $`31`
#> [,1] [,2]
#> [1,] 2.943767 12.35145
#> [2,] 12.351445 51.82413
#>
#> $`32`
#> [,1] [,2]
#> [1,] 11.875512 -5.971538
#> [2,] -5.971538 3.002756
#>
#> $`33`
#> [,1] [,2]
#> [1,] 7.352891 -7.564813
#> [2,] -7.564813 7.782843
#>
#> $`34`
#> [,1] [,2]
#> [1,] 3.554538 12.42091
#> [2,] 12.420915 43.40343
#>
#> $`35`
#> [,1] [,2]
#> [1,] 28.60297 98.72891
#> [2,] 98.72891 340.78273
#>
#> $`36`
#> [,1] [,2]
#> [1,] 2.985024 -12.36642
#> [2,] -12.366416 51.23183
#>
#> $`37`
#> [,1] [,2]
#> [1,] 0.4202515 6.302731
#> [2,] 6.3027308 94.525334
#>
#> $`38`
#> [,1] [,2]
#> [1,] 3.159976 -12.41265
#> [2,] -12.412653 48.75796
#>
#> $`39`
#> [,1] [,2]
#> [1,] 0.04209968 2.072455
#> [2,] 2.07245503 102.021430
#>
#> $`40`
#> [,1] [,2]
#> [1,] 3.168118 -12.41414
#> [2,] -12.414142 48.64431
#>
#> $`41`
#> [,1] [,2]
#> [1,] 2.816568 12.29512
#> [2,] 12.295121 53.67170
#>
#> $`42`
#> [,1] [,2]
#> [1,] 73.79736 -546.8281
#> [2,] -546.82809 4051.9197
#>
#> $`43`
#> [,1] [,2]
#> [1,] 0.3395676 -5.712504
#> [2,] -5.7125035 96.100728
#>
#> $`44`
#> [,1] [,2]
#> [1,] 6.737307 -8.839059
#> [2,] -8.839059 11.596468
#>
#> $`45`
#> [,1] [,2]
#> [1,] 15.77600 -22.37504
#> [2,] -22.37504 31.73443
#>
#> $`46`
#> [,1] [,2]
#> [1,] 20.24224 -45.4394
#> [2,] -45.43940 102.0015
#>
#> $`47`
#> [,1] [,2]
#> [1,] 3.218271 12.42205
#> [2,] 12.422045 47.94724
#>
#> $`48`
#> [,1] [,2]
#> [1,] 4.447916 12.01027
#> [2,] 12.010274 32.43017
#>
#> $`49`
#> [,1] [,2]
#> [1,] 2.661533 -12.20487
#> [2,] -12.204873 55.96734
#>
#> $`50`
#> [,1] [,2]
#> [1,] 0.2421215 -4.871646
#> [2,] -4.8716459 98.020772
#>
#> $`51`
#> [,1] [,2]
#> [1,] 16.76233 27.10211
#> [2,] 27.10211 43.81996
#>
#> $`52`
#> [,1] [,2]
#> [1,] 43.15767 216.8904
#> [2,] 216.89039 1089.9904
#>
#> $`53`
#> [,1] [,2]
#> [1,] 0.01353747 1.17853
#> [2,] 1.17853029 102.59924
#>
#> $`54`
#> [,1] [,2]
#> [1,] 0.01998735 1.43111
#> [2,] 1.43111012 102.46861
#>
#> $`55`
#> [,1] [,2]
#> [1,] 0.9147474 -8.825805
#> [2,] -8.8258048 85.154474
#>
#> $`56`
#> [,1] [,2]
#> [1,] 1.94062 11.42595
#> [2,] 11.42595 67.27355
#>
#> $`57`
#> [,1] [,2]
#> [1,] 0.2479823 4.927336
#> [2,] 4.9273362 97.904757
#>
#> $`58`
#> [,1] [,2]
#> [1,] 0.1936836 4.378497
#> [2,] 4.3784973 98.982241
#>
#> $`59`
#> [,1] [,2]
#> [1,] 1.023707 -9.226416
#> [2,] -9.226416 83.155409
#>
#> $`60`
#> [,1] [,2]
#> [1,] 0.2615007 -5.052945
#> [2,] -5.0529451 97.637418
#>
#> $`61`
#> [,1] [,2]
#> [1,] 1.027469 9.23954
#> [2,] 9.239540 83.08681
#>
#> $`62`
#> [,1] [,2]
#> [1,] 0.03669607 -1.935922
#> [2,] -1.93592154 102.130619
#>
#> $`63`
#> [,1] [,2]
#> [1,] 0.5679896 7.215962
#> [2,] 7.2159624 91.674420
#>
#> $`64`
#> [,1] [,2]
#> [1,] 9.822945 -1.0020556
#> [2,] -1.002056 0.1022214
#>
#> $`65`
#> [,1] [,2]
#> [1,] 0.0003101896 0.1786292
#> [2,] 0.1786291886 102.8673716
#>
#> $`66`
#> [,1] [,2]
#> [1,] 6.572683 9.152451
#> [2,] 9.152451 12.744772
#>
#> $`67`
#> [,1] [,2]
#> [1,] 1.112018 9.523021
#> [2,] 9.523021 81.552601
#>
#> $`68`
#> [,1] [,2]
#> [1,] 7.87505 6.363500
#> [2,] 6.36350 5.142079
#>
#> $`69`
#> [,1] [,2]
#> [1,] 0.5861514 -7.316517
#> [2,] -7.3165173 91.326963
#>
#> $`70`
#> [,1] [,2]
#> [1,] 11.162030 3.405658
#> [2,] 3.405658 1.039104
#>
#> $`71`
#> [,1] [,2]
#> [1,] 6.168929 -9.86970
#> [2,] -9.869700 15.79058
#>
#> $`72`
#> [,1] [,2]
#> [1,] 0.5792591 -7.27862
#> [2,] -7.2786202 91.45874
#>
#> $`73`
#> [,1] [,2]
#> [1,] 0.167155 4.078447
#> [2,] 4.078447 99.510810
#>
#> $`74`
#> [,1] [,2]
#> [1,] 1.239600 -9.912434
#> [2,] -9.912434 79.264580
#>
#> $`75`
#> [,1] [,2]
#> [1,] 0.06932852 2.652341
#> [2,] 2.65234089 101.472118
#>
#> $`76`
#> [,1] [,2]
#> [1,] 67.43633 -470.4935
#> [2,] -470.49346 3282.5643
#>
#> $`77`
#> [,1] [,2]
#> [1,] 1.929081 -11.40796
#> [2,] -11.407959 67.46297
#>
#> $`78`
#> [,1] [,2]
#> [1,] 2.356123 11.95208
#> [2,] 11.952084 60.63025
#>
#> $`79`
#> [,1] [,2]
#> [1,] 25.28754 76.15862
#> [2,] 76.15862 229.36729
#>
#> $`80`
#> [,1] [,2]
#> [1,] 74.4741 555.1699
#> [2,] 555.1699 4138.5338
#>
#> $`81`
#> [,1] [,2]
#> [1,] 25.03456 -74.51092
#> [2,] -74.51092 221.76849
#>
#> $`82`
#> [,1] [,2]
#> [1,] 5.358911 -11.07407
#> [2,] -11.074067 22.88431
#>
#> $`83`
#> [,1] [,2]
#> [1,] 0.2038647 -4.487506
#> [2,] -4.4875058 98.779761
#>
#> $`84`
#> [,1] [,2]
#> [1,] 4.577009 11.90714
#> [2,] 11.907135 30.97653
#>
#> $`85`
#> [,1] [,2]
#> [1,] 5.935795 -10.24940
#> [2,] -10.249404 17.69776
#>
#> $`86`
#> [,1] [,2]
#> [1,] 7.774745 -6.602527
#> [2,] -6.602527 5.607047
#>
#> $`87`
#> [,1] [,2]
#> [1,] 0.1741867 4.160412
#> [2,] 4.1604120 99.370571
#>
#> $`88`
#> [,1] [,2]
#> [1,] 1.501483 10.58847
#> [2,] 10.588474 74.67004
#>
#> $`89`
#> [,1] [,2]
#> [1,] 19.25300 -39.97455
#> [2,] -39.97455 82.99823
#>
#> $`90`
#> [,1] [,2]
#> [1,] 6.471038 9.339972
#> [2,] 9.339972 13.480846
#>
#> $`91`
#> [,1] [,2]
#> [1,] 0.9537271 8.973821
#> [2,] 8.9738210 84.436589
#>
#> $`92`
#> [,1] [,2]
#> [1,] 1.097949 9.477332
#> [2,] 9.477332 81.806890
#>
#> $`93`
#> [,1] [,2]
#> [1,] 14.22058 15.37788
#> [2,] 15.37788 16.62936
#>
#> $`94`
#> [,1] [,2]
#> [1,] 1.228669 9.88075
#> [2,] 9.880750 79.45934
#>
#> $`95`
#> [,1] [,2]
#> [1,] 56.79944 351.6307
#> [2,] 351.63068 2176.8548
#>
#> $`96`
#> [,1] [,2]
#> [1,] 3.113554 12.40305
#> [2,] 12.403054 49.40840
#>
#> $`97`
#> [,1] [,2]
#> [1,] 39.15787 181.5662
#> [2,] 181.56623 841.8819
#>
#> $`98`
#> [,1] [,2]
#> [1,] 0.363852 -5.898595
#> [2,] -5.898595 95.625194
#>
#> $`99`
#> [,1] [,2]
#> [1,] 19.24029 -39.90557
#> [2,] -39.90557 82.76669
#>
#> $`100`
#> [,1] [,2]
#> [1,] 5.12201 -11.36268
#> [2,] -11.36268 25.20698
#>
#>
#> Slot ".ee_i":
#> $`1`
#> [1] -1.376257 -8.248583
#>
#> $`2`
#> [1] 5.407891 19.102625
#>
#> $`3`
#> [1] -1.921153 -6.451838
#>
#> $`4`
#> [1] 3.3269392 0.9258588
#>
#> $`5`
#> [1] -5.876538 24.391036
#>
#> $`6`
#> [1] -1.645787 -7.434051
#>
#> $`7`
#> [1] -3.1502325 -0.2187008
#>
#> $`8`
#> [1] -1.521749 -7.826944
#>
#> $`9`
#> [1] 4.915842 14.022842
#>
#> $`10`
#> [1] -0.4742986 -9.9177064
#>
#> $`11`
#> [1] 0.6458107 -9.7255941
#>
#> $`12`
#> [1] 0.9738417 -9.1942978
#>
#> $`13`
#> [1] -2.502699 -3.879165
#>
#> $`14`
#> [1] -5.761424 23.051338
#>
#> $`15`
#> [1] -1.368465 -8.269969
#>
#> $`16`
#> [1] 0.4689809 -9.9227224
#>
#> $`17`
#> [1] 4.027917 6.081447
#>
#> $`18`
#> [1] -1.066858 -9.004479
#>
#> $`19`
#> [1] -1.254727 -8.568325
#>
#> $`20`
#> [1] 6.416199 31.024949
#>
#> $`21`
#> [1] -3.1394168 -0.2867279
#>
#> $`22`
#> [1] 1.651446 -7.415391
#>
#> $`23`
#> [1] -2.380351 -4.476593
#>
#> $`24`
#> [1] 1.615579 -7.532569
#>
#> $`25`
#> [1] -6.22561 28.61555
#>
#> $`26`
#> [1] -2.119561 -5.650125
#>
#> $`27`
#> [1] -1.163730 -8.788399
#>
#> $`28`
#> [1] 3.985266 5.739681
#>
#> $`29`
#> [1] -1.922843 -6.445340
#>
#> $`30`
#> [1] 1.147025 -8.827000
#>
#> $`31`
#> [1] -1.715741 -7.198898
#>
#> $`32`
#> [1] -3.446086 1.732846
#>
#> $`33`
#> [1] 2.711621 -2.789775
#>
#> $`34`
#> [1] -1.885348 -6.588128
#>
#> $`35`
#> [1] 5.348174 18.460301
#>
#> $`36`
#> [1] 1.727722 -7.157642
#>
#> $`37`
#> [1] -0.6482681 -9.7224140
#>
#> $`38`
#> [1] 1.777632 -6.982690
#>
#> $`39`
#> [1] -0.2051821 -10.1005658
#>
#> $`40`
#> [1] 1.779921 -6.974547
#>
#> $`41`
#> [1] -1.678263 -7.326097
#>
#> $`42`
#> [1] -8.590539 63.654691
#>
#> $`43`
#> [1] 0.5827243 -9.8030979
#>
#> $`44`
#> [1] 2.595632 -3.405359
#>
#> $`45`
#> [1] -3.971901 5.633332
#>
#> $`46`
#> [1] -4.499138 10.099579
#>
#> $`47`
#> [1] -1.793954 -6.924394
#>
#> $`48`
#> [1] -2.109008 -5.694749
#>
#> $`49`
#> [1] 1.631421 -7.481132
#>
#> $`50`
#> [1] 0.4920584 -9.9005441
#>
#> $`51`
#> [1] 4.094182 6.619665
#>
#> $`52`
#> [1] 6.56945 33.01500
#>
#> $`53`
#> [1] -0.1163506 -10.1291281
#>
#> $`54`
#> [1] -0.1413766 -10.1226782
#>
#> $`55`
#> [1] 0.9564243 -9.2279182
#>
#> $`56`
#> [1] -1.393061 -8.202045
#>
#> $`57`
#> [1] -0.4979782 -9.8946833
#>
#> $`58`
#> [1] -0.440095 -9.948982
#>
#> $`59`
#> [1] 1.011784 -9.118959
#>
#> $`60`
#> [1] 0.5113714 -9.8811648
#>
#> $`61`
#> [1] -1.013641 -9.115197
#>
#> $`62`
#> [1] 0.1915622 -10.1059695
#>
#> $`63`
#> [1] -0.7536508 -9.5746760
#>
#> $`64`
#> [1] 3.1341577 -0.3197209
#>
#> $`65`
#> [1] -0.0176122 -10.1423553
#>
#> $`66`
#> [1] -2.563725 -3.569982
#>
#> $`67`
#> [1] -1.054522 -9.030648
#>
#> $`68`
#> [1] -2.806252 -2.267615
#>
#> $`69`
#> [1] 0.7656052 -9.5565141
#>
#> $`70`
#> [1] 3.340962 1.019364
#>
#> $`71`
#> [1] 2.483733 -3.973736
#>
#> $`72`
#> [1] 0.7610908 -9.5634064
#>
#> $`73`
#> [1] -0.4088459 -9.9755105
#>
#> $`74`
#> [1] 1.113373 -8.903066
#>
#> $`75`
#> [1] -0.2633031 -10.0733370
#>
#> $`76`
#> [1] -8.211963 57.293667
#>
#> $`77`
#> [1] 1.388914 -8.213584
#>
#> $`78`
#> [1] -1.534967 -7.786543
#>
#> $`79`
#> [1] 5.028672 15.144877
#>
#> $`80`
#> [1] 8.629838 64.331437
#>
#> $`81`
#> [1] -5.003455 14.891894
#>
#> $`82`
#> [1] 2.314932 -4.783754
#>
#> $`83`
#> [1] 0.4515138 -9.9388008
#>
#> $`84`
#> [1] -2.139394 -5.565657
#>
#> $`85`
#> [1] 2.436349 -4.206871
#>
#> $`86`
#> [1] 2.788323 -2.367920
#>
#> $`87`
#> [1] -0.4173568 -9.9684789
#>
#> $`88`
#> [1] -1.225350 -8.641183
#>
#> $`89`
#> [1] -4.387824 9.110336
#>
#> $`90`
#> [1] -2.543824 -3.671627
#>
#> $`91`
#> [1] -0.9765895 -9.1889384
#>
#> $`92`
#> [1] -1.047831 -9.044716
#>
#> $`93`
#> [1] 3.771018 4.077911
#>
#> $`94`
#> [1] -1.108453 -8.913997
#>
#> $`95`
#> [1] 7.53654 46.65678
#>
#> $`96`
#> [1] -1.764527 -7.029111
#>
#> $`97`
#> [1] 6.257625 29.015201
#>
#> $`98`
#> [1] 0.6032015 -9.7788135
#>
#> $`99`
#> [1] -4.386375 9.097620
#>
#> $`100`
#> [1] 2.263186 -5.020655
#>
#>