The design and structure of geex

Bradley Saul

2020-02-17

The details below are for those interested in how geex is organized. It is not necessary for using geex.

The Estimating Function

The design of geex starts with the key to M-estimation, the estimating function:

\[ \psi(O_i, \theta) . \]

geex composes \(\psi\) with two R functions: the “outer” estFUN and the “inner” psiFUN. In pseudocode, \(\psi(O_i, \theta) =\):

estFUN <- function(O_i){
  psiFUN <- function(theta){
     psi(O_i, theta)
  }
  return(psiFUN)
}

The reason for composing the \(\psi\) function in this way is that in order to do estimation (finding roots) and inference (computing the empirical sandwich variance estimator), \(\psi\) needs to be function of \(\theta\). M-estimation theory gives the following instructions:

With \(\hat{\theta}\) in hand, the quantity \(B_i\) is simple to compute. The computational challenges of M-estimation, then, are finding roots of \(G_m\) and calculating the derivative \(A_i\). By composing \(\psi\) of two functions in geex, one can first do all the manipulations of \(O_i\) (data) that are independent of \(\theta\). In a sense, estFUN “fixes” the data so that numerical routines only need deal with \(\theta\) in psiFUN.

M-estimation basis

Before describing the mechanics of how geex finding roots of \(G_m\) and computes derivatives of \(\psi\), let’s look at the m_estimation_basis S4 object which forms the basis of all computations in geex.

An m_estimation_basis object, at a minimum needs two objects: an estFUN and a data.frame. Let’s use a simple estFUN that estimates the mean and variance of Y1 in the geexex dataset.

library(geex)
library(dplyr)

myee <- function(data){
  Y1 <- data$Y1
  function(theta){
    c(Y1 - theta[1],
      (Y1 - theta[1])^2 - theta[2])
  }
}

Now we can create a basis:

mybasis <- new("m_estimation_basis",
               .estFUN = myee,
               .data   = geexex)

And look at what this object contains:

slotNames(mybasis)
## [1] ".data"        ".units"       ".weights"     ".psiFUN_list" ".GFUN"       
## [6] ".control"     ".estFUN"      ".outer_args"  ".inner_args"

Two slots are worth examining. First, .psiFUN_list is a list of functions:

mybasis@.psiFUN_list[1:2]
## $`1`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <environment: 0x7fd9e9d1df58>
## 
## $`2`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9e9cef2a8>

This object is essentially equivalent to:

m <- nrow(geexex)
lapply(split(geexex, f = 1:m), function(O_i){
  myee(O_i)
})

From this list of functions, we can compute \(A_i\), and by summing across the list, form \(G_m\). The latter is found in:

mybasis@.GFUN
## function (theta) 
## {
##     psii <- lapply(psi_list, function(psi) {
##         do.call(psi, args = append(list(theta = theta), [email protected]_args))
##     })
##     compute_sum_of_list(psii, [email protected])
## }
## <environment: 0x7fd9e7de2f50>

Finding roots

Now that we have \(G_m\) as a function of theta, we can found its roots using a root-finding algorithm such as rootSolve::multiroot:

rootSolve::multiroot(
  f = mybasis@.GFUN, 
  start = c(0, 0))
## $root
## [1]  5.044563 10.041239
## 
## $f.root
## [1] -2.131628e-14  4.654055e-13
## 
## $iter
## [1] 4
## 
## $estim.precis
## [1] 2.433609e-13

Within geex this is done with the estimate_GFUN_roots function. To illustrate, I first need to update the .control slot in mybasis with starting values for multiroot.

mycontrol <- new('geex_control', .root = setup_root_control(start = c(1, 1)))
mybasis@.control <- mycontrol
roots <- mybasis %>%
  estimate_GFUN_roots()
roots
## $root
## [1]  5.044563 10.041239
## 
## $f.root
## [1] -2.131628e-14 -2.238210e-13
## 
## $iter
## [1] 4
## 
## $estim.precis
## [1] 1.225686e-13

Note that is bad form to assign S4 slot with [email protected] <- something, but I do so here because I have not created a generic function for setting the .control slot.

Computing the Empirical Sandwich Variance Estimator

In the last section, we found \(\hat{\theta}\), which we now use to compute the \(A_i\) and \(B_i\) matrices.

geex uses the numDeriv::jacobian function to numerically evaluate derivatives. For example, \(A_1 = - (\partial \psi(O_1, \theta)/\partial \theta)|_{\theta = \hat{\theta}}\) for this example is:

-numDeriv::jacobian(func = mybasis@.psiFUN_list[[1]], x = roots$root)
##           [,1] [,2]
## [1,]  1.000000    0
## [2,] -2.752514    1

geex performs this operation for each \(i = 1, \dots, m\) to yield a list of \(A_i\) matrices. Then summing across this list yields \(A = \sum_i A_i\). The estimate_sandwich_matrices function computes the list of \(A_i\), \(B_i\) and \(A\) and \(B\):

mats <- mybasis %>%
  estimate_sandwich_matrices(.theta = roots$root) 

# Compare to the numDeriv computation above
grab_bread_list(mats)[[1]]
##           [,1] [,2]
## [1,]  1.000000    0
## [2,] -2.752514    1

Finally, computing \(\hat{\Sigma} = A^{-1} B (A^{-1})^{\intercal}\) is accomplished with the compute_sigma function.

mats %>%
  {compute_sigma(A = grab_bread(.), B = grab_meat(.))}
##            [,1]       [,2]
## [1,] 0.10041239 0.03667969
## [2,] 0.03667969 2.49219638

M-estimation with m_estimate

All of the operations described above are wrapped and packaged in the m_estimate function:

m_estimate(
  estFUN = myee,
  data   = geexex,
  root_control = setup_root_control(start = c(0, 0))
)
## An object of class "geex"
## Slot "call":
## m_estimate(estFUN = myee, data = geexex, root_control = setup_root_control(start = c(0, 
##     0)))
## 
## Slot "basis":
## An object of class "m_estimation_basis"
## Slot ".data":
##              Y1          Y2        X1        Y3        W1        Z1 X2
## 1    3.66830660  2.02817177  4.949316 16.345756  4.823768  8.921782  0
## 2   10.45245483  1.64329659  7.851962 25.687417  7.884845 13.909474  0
## 3    3.12341064  2.85262638  4.729075 16.108307  4.709346  9.014695  0
## 4    8.37150253  2.51336525  2.564395 10.579970  2.786091  6.733378  0
## 5   -0.83197489  3.01820300  4.782347 16.464013  4.811590  9.290492  0
## 6    3.39877632  0.97852092  5.335713 18.325769  5.415370 10.322199  0
## 7    1.89433086  1.43833173  1.386442  5.577536  1.240995  3.497873  0
## 8    3.52281395  0.98744392  3.453377 13.074664  3.632010  7.894598  0
## 9    9.96040583 -1.02081430  2.958662 10.050725  2.752347  5.612733  0
## 10   4.57026477  2.33235027  7.591370 24.414247  7.501404 13.027192  0
## 11   5.69037402  3.24051157  6.812940 22.528706  6.835412 12.309296  0
## 12   6.01840507  2.67134960  2.481492  9.540750  2.505561  5.818512  0
## 13   2.54186468  0.66996589  3.307246 11.720103  3.256837  6.759235  0
## 14  -0.71686038  1.14941969  2.366527  9.839421  2.551487  6.289631  0
## 15   3.67609826  0.21116926  6.308752 21.049635  6.339597 11.586507  0
## 16   5.51354425  3.23152191  2.280638  8.812598  2.273309  5.391641  0
## 17   9.07247997  1.66560033  2.872154 10.227607  2.774940  5.919377  0
## 18   3.97770523  1.03267790  4.361465 15.595252  4.489179  9.053054  0
## 19   3.78983596  2.87937035  3.573053 11.805345  3.344600  6.445765  0
## 20  11.46076273  1.74642131  5.556376 20.979426  6.133951 12.644862  0
## 21   1.90514658  0.48212421  7.752991 24.820884  7.643469 13.191397  0
## 22   6.69600961  1.97611674  6.030068 20.854263  6.221083 11.809162  0
## 23   2.66421207  2.02665947  4.213262 14.901747  4.278752  8.581854  0
## 24   6.66014272  2.16368120  2.923132 11.542799  3.116483  7.158102  0
## 25  -1.18104663  2.41000794  5.156830 16.656110  4.953235  8.920865  0
## 26   2.92500198  1.37263740  5.519839 18.121067  5.410226  9.841308  0
## 27   3.88083378  2.63691800  5.477283 17.711627  5.297228  9.495703  0
## 28   9.02982953  0.79806522  4.055430 14.397234  4.113166  8.314089  0
## 29   3.12172019  3.34654241  4.319714 13.801412  4.030281  7.321841  0
## 30   6.19158815  1.40123269 10.283894 33.098758 10.345663 17.672917  0
## 31   3.32882227  2.44220444  2.557841  9.582409  2.535063  5.745648  0
## 32   1.59847689  2.61352641 11.152742 37.215603 11.592086 20.486489  0
## 33   7.75618478  1.70090363  2.538047  9.476212  2.503565  5.669141  0
## 34   3.15921522  0.39941190  7.939765 25.708101  7.911967 13.798454  0
## 35  10.39273751  1.66053304  3.629295 12.197870  3.456791  6.753928  0
## 36   6.77228554  1.41869225  5.644317 18.711156  5.588868 10.244681  0
## 37   4.39629525  1.60963799  1.385403  6.339116  1.431130  4.261012  0
## 38   6.82219543  2.84551436  3.651563 13.372011  3.755894  7.894667  0
## 39   4.83938127  2.68472721  2.075987  9.293362  2.342337  6.179382  0
## 40   6.82448417  2.23771308  7.947636 26.813109  8.190186 14.891656  0
## 41   3.36629988  1.28937811  3.893624 13.579242  3.868217  7.738807  0
## 42  -3.54597542  4.61331896  4.399113 16.600543  4.749914 10.001873  0
## 43   5.62728767  0.37335265  2.019187  6.280784  1.574993  3.252004  0
## 44   7.64019560  0.39269371 10.182047 33.169007 10.337763 17.895937  0
## 45   1.07266235  2.34031745  4.471305 14.891632  4.340734  8.184674  0
## 46   0.54542518  4.72788771  5.445723 19.659399  5.776280 11.490815  0
## 47   3.25060929  1.67280996  5.030453 16.727920  4.939593  9.182240  0
## 48   2.93555501  0.74310325  7.586987 26.080025  7.916753 14.699546  0
## 49   6.67598396  1.56860189  9.452187 30.400340  9.463132 16.222060  0
## 50   5.53662175  4.54885325  8.141977 24.547274  7.672313 12.334309  0
## 51   9.13874582  1.22859200  5.623052 18.422092  5.511286  9.987515  1
## 52  11.61401290  1.49265765  5.066275 15.460228  4.631626  7.860815  1
## 53   4.92821273  1.72997742  2.174904  8.703576  2.219620  5.441220  1
## 54   4.90318672  2.74811656  1.373871  8.019078  1.848237  5.958272  1
## 55   6.00098760  2.66859381  4.252394 12.485257  3.684413  6.106666  1
## 56   3.65150186  1.54470134  1.844766  8.514763  2.089882  5.747614  1
## 57   4.54658518  0.07215478  6.257311 19.373108  5.907605  9.987141  1
## 58   4.60446834  3.88197707  7.640542 26.746499  8.096760 15.285686  1
## 59   6.05634729  0.75028887  3.400547 13.582939  3.745871  8.482119  1
## 60   5.55593474  1.51065503  3.879217 12.798800  3.669504  6.979974  1
## 61   4.03092200  2.21539129  5.044494 16.871488  4.978996  9.304746  1
## 62   5.23612553  2.42210867  3.724228 13.103840  3.707017  7.517498  1
## 63   4.29091253  0.77885172  3.209739 11.250332  3.115018  6.435724  1
## 64   8.17872107  2.31222782  3.503141 15.091380  4.148630  9.836670  1
## 65   5.02695115  2.88646213  3.588984 12.896787  3.621443  7.513311  1
## 66   2.48083883  2.47481069  2.572586  9.004733  2.394330  5.145854  1
## 67   3.99004087  2.86984135  2.321320  9.601955  2.480819  6.119975  1
## 68   2.23831135  1.11347620  7.354859 24.266268  7.405282 13.233980  1
## 69   5.81016858  1.87134447  1.780620  7.271942  1.763140  4.601012  1
## 70   8.38552575  3.09651049  2.438272  9.222328  2.415150  5.564919  1
## 71   7.52829625  2.51802955  4.870025 17.058979  4.982251  9.753941  1
## 72   5.80565410  2.39803318  6.107551 19.258297  5.841462 10.096971  1
## 73   4.63571743  3.06665941  3.068762 10.043868  2.778158  5.440724  1
## 74   6.15793650  1.55045992  8.069649 27.857468  8.481779 15.752995  1
## 75   4.78126024  2.62610198  2.564135  7.630308  2.048611  3.784106  1
## 76  -3.16739941  1.18116405  6.700594 22.114532  6.703782 12.063641  1
## 77   6.43347697  1.73648379  5.381833 17.057971  5.109951  8.985221  1
## 78   3.50959659  2.15457529 12.644899 40.205236 12.712534 21.237888  1
## 79  10.07323536  2.56844555  2.037142  9.119878  2.289255  6.064165  1
## 80  13.67440127 -0.66015968  5.883640 17.576515  5.365039  8.751055  1
## 81   0.04110863  3.13653254  7.093428 24.177106  7.317634 13.536964  1
## 82   7.35949555  2.42177278  4.873831 16.571498  4.861332  9.260751  1
## 83   5.49607715  3.35008260  8.291038 25.527766  7.954701 13.091208  1
## 84   2.90516885  3.10375689  4.051026 12.221867  3.568223  6.145328  1
## 85   7.48091201  2.64704611  7.689539 25.778200  7.866935 14.243891  1
## 86   7.83288634  2.17563581  4.933636 16.643004  4.894160  9.242550  1
## 87   4.62720660  2.65355779  5.774989 19.541334  5.829081 10.878851  1
## 88   3.81921320  1.93450970  4.483566 16.268060  4.687907  9.542711  1
## 89   0.65673908  2.64552217  2.739769 11.946482  3.171563  7.836829  1
## 90   2.50073977  2.36429404  5.286464 17.755621  5.260521  9.825925  1
## 91   4.06797383  2.84344157  3.701213 12.546517  3.561933  6.994698  1
## 92   3.99673254  1.32352113  5.795986 20.816259  6.153061 12.122280  1
## 93   8.81558134  1.60856710  4.883292 15.756919  4.660053  8.431981  1
## 94   3.93610997  2.40494064  7.172253 22.359187  6.882860 11.600808  1
## 95  12.58110379  0.89314130  3.340735 11.491910  3.208161  6.480807  1
## 96   3.28003669  1.61669959  7.262549 26.233329  7.873969 15.339506  1
## 97  11.30218798  2.29402025  1.940701  6.989609  1.732577  4.078556  1
## 98   5.64776480  3.79306067  5.958475 20.288944  6.061855 11.351232  1
## 99   0.65818837  2.81403217  4.432708 14.119440  4.138037  7.470379  1
## 100  7.30774920  0.67997560  3.283518 10.676520  2.990010  5.751243  1
##               Y4 Y5
## 1    0.092739260  1
## 2    1.016727357  1
## 3    0.493990392  0
## 4    1.243224329  0
## 5    0.695205988  1
## 6    0.952201378  1
## 7   -0.343146465  0
## 8    1.159870423  0
## 9   -0.429393276  0
## 10   0.499274828  1
## 11   0.871180147  1
## 12   0.444423658  0
## 13   0.229090617  1
## 14   1.076493168  0
## 15   0.854254673  1
## 16   0.298747112  0
## 17  -0.001638862  0
## 18   1.047002780  1
## 19  -0.456508875  1
## 20   2.965934470  0
## 21   0.437209150  0
## 22   1.467067372  0
## 23   0.783287466  0
## 24   1.165717760  0
## 25  -0.198696160  1
## 26   0.213533342  1
## 27  -0.072493261  1
## 28   0.736487513  1
## 29  -0.625758090  1
## 30   1.375465405  1
## 31   0.264670535  0
## 32   2.972649859  1
## 33   0.215875121  1
## 34   0.782782994  1
## 35  -0.227084853  1
## 36   0.442637449  1
## 37   0.421447969  0
## 38   0.882479555  0
## 39   1.373000995  1
## 40   1.864965592  1
## 41   0.387733146  1
## 42   1.943114799  1
## 43  -1.474856978  0
## 44   1.741072051  1
## 45   0.024847168  1
## 46   1.966803213  1
## 47   0.239605022  0
## 48   2.177764398  1
## 49   1.088997768  1
## 50  -0.964458223  1
## 51   0.715242972  1
## 52  -0.631970427  1
## 53   0.996355205  0
## 54   2.634852773  1
## 55  -1.246686055  1
## 56   1.764940768  0
## 57  -0.173094497  1
## 58   3.188926631  1
## 59   2.321353405  1
## 60   0.149069864  0
## 61   0.842453670  1
## 62   0.903578781  0
## 63   0.542090297  1
## 64   3.532272980  0
## 65   1.088732578  1
## 66   0.144233610  1
## 67   1.470126269  0
## 68   1.537177460  0
## 69   0.708145014  1
## 70   0.751337374  0
## 71   1.535905791  1
## 72   0.146399418  0
## 73  -0.255543077  0
## 74   3.055486628  0
## 75  -1.205682549  1
## 76   1.282809142  1
## 77   0.050654962  1
## 78   2.135029369  1
## 79   1.812166070  1
## 80  -0.886040754  1
## 81   2.206165066  1
## 82   1.037387368  1
## 83   0.083754535  0
## 84  -0.926108918  0
## 85   2.078535519  1
## 86   0.935458616  0
## 87   1.393866742  0
## 88   1.865718680  0
## 89   2.601152645  0
## 90   1.024876085  1
## 91   0.412999035  1
## 92   2.607900007  0
## 93   0.195371813  1
## 94   0.159654048  1
## 95   0.403777090  0
## 96   3.771937632  1
## 97  -0.038425654  1
## 98   1.609367331  0
## 99  -0.135412360  1
## 100 -0.245682938  0
## 
## Slot ".units":
## character(0)
## 
## Slot ".weights":
## numeric(0)
## 
## Slot ".psiFUN_list":
## $`1`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee28c778>
## 
## $`2`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee28db98>
## 
## $`3`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee28b348>
## 
## $`4`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee2889a8>
## 
## $`5`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee289e00>
## 
## $`6`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee285460>
## 
## $`7`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee282900>
## 
## $`8`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
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## 
## $`9`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee281a48>
## 
## $`10`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee27cfc8>
## 
## $`11`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee27a3f8>
## 
## $`12`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee27bab8>
## 
## $`13`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee279118>
## 
## $`14`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee2763f8>
## 
## $`15`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee2775e8>
## 
## $`16`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee272858>
## 
## $`17`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee273c40>
## 
## $`18`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee26e040>
## 
## $`19`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1ff038>
## 
## $`20`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1fd230>
## 
## $`21`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1eeac0>
## 
## $`22`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1ec698>
## 
## $`23`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1edee0>
## 
## $`24`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1ebd20>
## 
## $`25`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1e9b28>
## 
## $`26`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1e4e40>
## 
## $`27`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1e2858>
## 
## $`28`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1e3d90>
## 
## $`29`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1e10e0>
## 
## $`30`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1de900>
## 
## $`31`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1dc008>
## 
## $`32`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1dd658>
## 
## $`33`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1da8c8>
## 
## $`34`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1dbe00>
## 
## $`35`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1d9268>
## 
## $`36`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
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## 
## $`37`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1d7d20>
## 
## $`38`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1d0fc8>
## 
## $`39`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1ce7b0>
## 
## $`40`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
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## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1cc0e8>
## 
## $`41`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1cde00>
## 
## $`42`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
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## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1c9770>
## 
## $`43`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
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## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1c6f58>
## 
## $`44`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
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## <bytecode: 0x7fd9e9a54348>
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## 
## $`45`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
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## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1c5540>
## 
## $`46`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
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## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1c0890>
## 
## $`47`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
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## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1c1b28>
## 
## $`48`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
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## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1bf0e0>
## 
## $`49`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1bc4a0>
## 
## $`50`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1bd8c0>
## 
## $`51`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1baee8>
## 
## $`52`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1b8858>
## 
## $`53`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1b9e38>
## 
## $`54`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1b78c0>
## 
## $`55`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1b33f0>
## 
## $`56`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1ae7b0>
## 
## $`57`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
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## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1afcb0>
## 
## $`58`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1ad2d8>
## 
## $`59`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1aacb8>
## 
## $`60`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1a6e78>
## 
## $`61`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
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## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1a4a50>
## 
## $`62`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
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## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1a5d90>
## 
## $`63`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1a3188>
## 
## $`64`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1a05f0>
## 
## $`65`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1a1a48>
## 
## $`66`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
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## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee19d230>
## 
## $`67`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
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## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee19a548>
## 
## $`68`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
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## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee19b770>
## 
## $`69`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
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## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee198ac0>
## 
## $`70`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee196190>
## 
## $`71`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee197498>
## 
## $`72`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee194970>
## 
## $`73`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1921c8>
## 
## $`74`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee193700>
## 
## $`75`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee190ac0>
## 
## $`76`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee18a238>
## 
## $`77`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee18b4d0>
## 
## $`78`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee188ac0>
## 
## $`79`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1865f0>
## 
## $`80`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1877a8>
## 
## $`81`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee182cf0>
## 
## $`82`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1808c8>
## 
## $`83`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee181d58>
## 
## $`84`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
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## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee17d188>
## 
## $`85`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee17a7b0>
## 
## $`86`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee178468>
## 
## $`87`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee176388>
## 
## $`88`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1777a8>
## 
## $`89`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee175118>
## 
## $`90`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee1725f0>
## 
## $`91`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee173e70>
## 
## $`92`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee171380>
## 
## $`93`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee16c858>
## 
## $`94`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee16a0e8>
## 
## $`95`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee16b460>
## 
## $`96`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee168858>
## 
## $`97`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee169c78>
## 
## $`98`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee166f90>
## 
## $`99`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee164468>
## 
## $`100`
## function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## <bytecode: 0x7fd9e9a54348>
## <environment: 0x7fd9ee165738>
## 
## 
## Slot ".GFUN":
## function (theta) 
## {
##     psii <- lapply(psi_list, function(psi) {
##         do.call(psi, args = append(list(theta = theta), [email protected]_args))
##     })
##     compute_sum_of_list(psii, [email protected])
## }
## <environment: 0x7fd9ee12f7a8>
## 
## Slot ".control":
## An object of class "geex_control"
## Slot ".approx":
## An object of class "approx_control"
## Slot ".FUN":
## function () 
## NULL
## <bytecode: 0x7fd9e35a06a0>
## 
## Slot ".options":
## list()
## 
## 
## Slot ".root":
## An object of class "root_control"
## Slot ".object_name":
## [1] "root"
## 
## Slot ".FUN":
## function (f, start, maxiter = 100, rtol = 1e-06, atol = 1e-08, 
##     ctol = 1e-08, useFortran = TRUE, positive = FALSE, jacfunc = NULL, 
##     jactype = "fullint", verbose = FALSE, bandup = 1, banddown = 1, 
##     parms = NULL, ...) 
## {
##     initfunc <- NULL
##     if (is.list(f)) {
##         if (!is.null(jacfunc) & "jacfunc" %in% names(f)) 
##             stop("If 'f' is a list that contains jacfunc, argument 'jacfunc' should be NULL")
##         jacfunc <- f$jacfunc
##         initfunc <- f$initfunc
##         f <- f$func
##     }
##     N <- length(start)
##     if (!is.numeric(start)) 
##         stop("start conditions should be numeric")
##     if (!is.numeric(maxiter)) 
##         stop("`maxiter' must be numeric")
##     if (as.integer(maxiter) < 1) 
##         stop("maxiter must be >=1")
##     if (!is.numeric(rtol)) 
##         stop("`rtol' must be numeric")
##     if (!is.numeric(atol)) 
##         stop("`atol' must be numeric")
##     if (!is.numeric(ctol)) 
##         stop("`ctol' must be numeric")
##     if (length(atol) > 1 && length(atol) != N) 
##         stop("`atol' must either be a scalar, or as long as `start'")
##     if (length(rtol) > 1 && length(rtol) != N) 
##         stop("`rtol' must either be a scalar, or as long as `y'")
##     if (length(ctol) > 1) 
##         stop("`ctol' must be a scalar")
##     if (useFortran) {
##         if (!is.compiled(f) & is.null(parms)) {
##             Fun1 <- function(time = 0, x, parms = NULL) list(f(x, 
##                 ...))
##             Fun <- Fun1
##         }
##         else if (!is.compiled(f)) {
##             Fun2 <- function(time = 0, x, parms) list(f(x, parms, 
##                 ...))
##             Fun <- Fun2
##         }
##         else {
##             Fun <- f
##             f <- function(x, ...) Fun(n = length(start), t = 0, 
##                 x, f = rep(0, length(start)), 1, 1)$f
##         }
##         JacFunc <- jacfunc
##         if (!is.null(jacfunc)) 
##             if (!is.compiled(JacFunc) & is.null(parms)) 
##                 JacFunc <- function(time = 0, x, parms = parms) jacfunc(x, 
##                   ...)
##             else if (!is.compiled(JacFunc)) 
##                 JacFunc <- function(time = 0, x, parms = parms) jacfunc(x, 
##                   parms, ...)
##             else JacFunc <- jacfunc
##         method <- "stode"
##         if (jactype == "sparse") {
##             method <- "stodes"
##             if (!is.null(jacfunc)) 
##                 stop("jacfunc can not be used when jactype='sparse'")
##             x <- stodes(y = start, time = 0, func = Fun, atol = atol, 
##                 positive = positive, rtol = rtol, ctol = ctol, 
##                 maxiter = maxiter, verbose = verbose, parms = parms, 
##                 initfunc = initfunc)
##         }
##         else x <- steady(y = start, time = 0, func = Fun, atol = atol, 
##             positive = positive, rtol = rtol, ctol = ctol, maxiter = maxiter, 
##             method = method, jacfunc = JacFunc, jactype = jactype, 
##             verbose = verbose, parms = parms, initfunc = initfunc, 
##             bandup = bandup, banddown = banddown)
##         precis <- attr(x, "precis")
##         attributes(x) <- NULL
##         x <- unlist(x)
##         if (is.null(parms)) 
##             reffx <- f(x, ...)
##         else reffx <- f(x, parms, ...)
##         i <- length(precis)
##     }
##     else {
##         if (is.compiled(f)) 
##             stop("cannot combine compiled code with R-implemented solver")
##         precis <- NULL
##         x <- start
##         jacob <- matrix(nrow = N, ncol = N, data = 0)
##         if (is.null(parms)) 
##             reffx <- f(x, ...)
##         else reffx <- f(x, parms, ...)
##         if (length(reffx) != N) 
##             stop("'f', function must return as many function values as elements in start")
##         for (i in 1:maxiter) {
##             refx <- x
##             pp <- mean(abs(reffx))
##             precis <- c(precis, pp)
##             ewt <- rtol * abs(x) + atol
##             if (max(abs(reffx/ewt)) < 1) 
##                 break
##             delt <- perturb(x)
##             for (j in 1:N) {
##                 x[j] <- x[j] + delt[j]
##                 if (is.null(parms)) 
##                   fx <- f(x, ...)
##                 else fx <- f(x, parms, ...)
##                 jacob[, j] <- (fx - reffx)/delt[j]
##                 x[j] <- refx[j]
##             }
##             relchange <- as.numeric(solve(jacob, -1 * reffx))
##             if (max(abs(relchange)) < ctol) 
##                 break
##             x <- x + relchange
##             if (is.null(parms)) 
##                 reffx <- f(x, ...)
##             else reffx <- f(x, parms, ...)
##         }
##     }
##     names(x) <- names(start)
##     return(list(root = x, f.root = reffx, iter = i, estim.precis = precis[length(precis)]))
## }
## <bytecode: 0x7fd9e35d20d0>
## <environment: namespace:rootSolve>
## 
## Slot ".options":
## $start
## [1] 0 0
## 
## 
## 
## Slot ".deriv":
## An object of class "deriv_control"
## Slot ".FUN":
## function (func, x, method = "Richardson", side = NULL, method.args = list(), 
##     ...) 
## UseMethod("jacobian")
## <bytecode: 0x7fd9e35b3f30>
## <environment: namespace:numDeriv>
## 
## Slot ".options":
## $method
## [1] "Richardson"
## 
## 
## 
## 
## Slot ".estFUN":
## function(data){
##   Y1 <- data$Y1
##   function(theta){
##     c(Y1 - theta[1],
##       (Y1 - theta[1])^2 - theta[2])
##   }
## }
## <bytecode: 0x7fd9e9a4fa50>
## 
## Slot ".outer_args":
## list()
## 
## Slot ".inner_args":
## list()
## 
## 
## Slot "rootFUN_results":
## $root
## [1]  5.044563 10.041239
## 
## $f.root
## [1] -2.131628e-14  4.654055e-13
## 
## $iter
## [1] 4
## 
## $estim.precis
## [1] 2.433609e-13
## 
## 
## Slot "sandwich_components":
## An object of class "sandwich_components"
## Slot ".A":
##              [,1] [,2]
## [1,]  1.00000e+02    0
## [2,] -1.65139e-11  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 24921.9638
## 
## Slot ".B_i":
## $`1`
##           [,1]     [,2]
## [1,]  1.894083 11.21258
## [2,] 11.212579 66.37615
## 
## $`2`
##           [,1]     [,2]
## [1,]  29.24529 103.8534
## [2,] 103.85343 368.7956
## 
## $`3`
##           [,1]     [,2]
## [1,]  3.690828 12.20011
## [2,] 12.200110 40.32772
## 
## $`4`
##           [,1]     [,2]
## [1,] 11.068524 3.417716
## [2,]  3.417716 1.055315
## 
## $`5`
##           [,1]      [,2]
## [1,]   34.5337 -143.9309
## [2,] -143.9309  599.8807
## 
## $`6`
##           [,1]     [,2]
## [1,]  2.708615 12.06794
## [2,] 12.067937 53.76737
## 
## $`7`
##           [,1]       [,2]
## [1,] 9.9239647 0.36944079
## [2,] 0.3694408 0.01375322
## 
## $`8`
##           [,1]     [,2]
## [1,]  2.315721 11.75630
## [2,] 11.756302 59.68362
## 
## $`9`
##          [,1]      [,2]
## [1,] 24.16551  69.43268
## [2,] 69.43268 199.49496
## 
## $`10`
##           [,1]      [,2]
## [1,] 0.2249591  4.655848
## [2,] 4.6558475 96.359348
## 
## $`11`
##            [,1]     [,2]
## [1,]  0.4170714 -6.21539
## [2,] -6.2153901 92.62460
## 
## $`12`
##            [,1]      [,2]
## [1,]  0.9483677 -8.855017
## [2,] -8.8550173 82.680306
## 
## $`13`
##          [,1]      [,2]
## [1,] 6.263501  9.454541
## [2,] 9.454541 14.271306
## 
## $`14`
##           [,1]      [,2]
## [1,]   33.1940 -133.3929
## [2,] -133.3929  536.0505
## 
## $`15`
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## [1,]  1.872697 11.17836
## [2,] 11.178365 66.72508
## 
## $`16`
##            [,1]     [,2]
## [1,]  0.2199431 -4.60600
## [2,] -4.6060002 96.45785
## 
## $`17`
##          [,1]     [,2]
## [1,] 16.22411 24.90410
## [2,] 24.90410 38.22792
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## $`18`
##          [,1]      [,2]
## [1,] 1.138186  9.498294
## [2,] 9.498294 79.264346
## 
## $`19`
##           [,1]     [,2]
## [1,]  1.574341 10.62365
## [2,] 10.623649 71.68836
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## $`20`
##           [,1]     [,2]
## [1,]  41.16761 199.7130
## [2,] 199.71303 968.8513
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## $`21`
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## [1,] 9.8559376 0.58173782
## [2,] 0.5817378 0.03433655
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## $`22`
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## [1,]   2.727275 -12.07862
## [2,] -12.078619  53.49407
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## $`23`
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## [1,]  5.666072 10.41443
## [2,] 10.414434 19.14208
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## $`24`
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## [1,]   2.610097 -12.00560
## [2,] -12.005600  55.22187
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## $`25`
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## [1,]   38.75822 -178.7807
## [2,] -178.78072  824.6650
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## $`26`
##          [,1]     [,2]
## [1,]  4.49254 11.76081
## [2,] 11.76081 30.78805
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## $`27`
##           [,1]     [,2]
## [1,]  1.354266 10.10929
## [2,] 10.109287 75.46349
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## $`28`
##          [,1]     [,2]
## [1,] 15.88235 23.27837
## [2,] 23.27837 34.11854
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## $`29`
##           [,1]     [,2]
## [1,]  3.697326 12.19835
## [2,] 12.198350 40.24523
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## $`30`
##            [,1]      [,2]
## [1,]   1.315666 -10.00845
## [2,] -10.008449  76.13562
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## $`31`
##           [,1]     [,2]
## [1,]  2.943767 12.17742
## [2,] 12.177423 50.37410
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## $`32`
##           [,1]      [,2]
## [1,] 11.875512 -6.321063
## [2,] -6.321063  3.364557
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## $`33`
##           [,1]      [,2]
## [1,]  7.352891 -7.289782
## [2,] -7.289782  7.227215
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## $`34`
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## [1,]  3.554538 12.22969
## [2,] 12.229690 42.07729
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## $`35`
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## [1,] 28.60297  99.27135
## [2,] 99.27135 344.53775
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## $`36`
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## [1,]   2.985024 -12.19118
## [2,] -12.191179  49.79017
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## $`37`
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## [1,] 0.4202515  6.236979
## [2,] 6.2369792 92.563397
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## $`38`
##            [,1]      [,2]
## [1,]   3.159976 -12.23235
## [2,] -12.232354  47.35178
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## $`39`
##            [,1]      [,2]
## [1,] 0.04209968  2.051644
## [2,] 2.05164409 99.982784
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## $`40`
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## [1,]   3.168118 -12.23361
## [2,] -12.233611  47.23979
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## $`41`
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## [1,]  2.816568 12.12490
## [2,] 12.124901 52.19587
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## $`42`
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## [1,]   73.79736 -547.6994
## [2,] -547.69940 4064.8425
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## $`43`
##            [,1]     [,2]
## [1,]  0.3395676 -5.65340
## [2,] -5.6533998 94.12242
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## $`44`
##           [,1]      [,2]
## [1,]  6.737307 -8.575793
## [2,] -8.575793 10.915967
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## $`45`
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## [1,]  15.77600 -22.77789
## [2,] -22.77789  32.88746
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## $`46`
##           [,1]      [,2]
## [1,]  20.24224 -45.89573
## [2,] -45.89573 104.06051
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## $`47`
##           [,1]     [,2]
## [1,]  3.218271 12.24009
## [2,] 12.240091 46.55289
## 
## $`48`
##           [,1]     [,2]
## [1,]  4.447916 11.79636
## [2,] 11.796364 31.28526
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## $`49`
##            [,1]      [,2]
## [1,]   2.661533 -12.03940
## [2,] -12.039404  54.46006
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## $`50`
##            [,1]      [,2]
## [1,]  0.2421215 -4.821738
## [2,] -4.8217380 96.022702
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## $`51`
##          [,1]     [,2]
## [1,] 16.76233 27.51737
## [2,] 27.51737 45.17307
## 
## $`52`
##           [,1]      [,2]
## [1,]  43.15767  217.5567
## [2,] 217.55671 1096.6978
## 
## $`53`
##            [,1]       [,2]
## [1,] 0.01353747   1.166729
## [2,] 1.16672924 100.554795
## 
## $`54`
##            [,1]       [,2]
## [1,] 0.01998735   1.416771
## [2,] 1.41677076 100.425482
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## $`55`
##            [,1]      [,2]
## [1,]  0.9147474 -8.728798
## [2,] -8.7287978 83.292847
## 
## $`56`
##          [,1]     [,2]
## [1,]  1.94062 11.28466
## [2,] 11.28466 65.62002
## 
## $`57`
##           [,1]      [,2]
## [1,] 0.2479823  4.876828
## [2,] 4.8768280 95.907875
## 
## $`58`
##           [,1]     [,2]
## [1,] 0.1936836  4.33386
## [2,] 4.3338599 96.97434
## 
## $`59`
##           [,1]      [,2]
## [1,]  1.023707 -9.123794
## [2,] -9.123794 81.315885
## 
## $`60`
##            [,1]      [,2]
## [1,]  0.2615007 -5.001078
## [2,] -5.0010784 95.643278
## 
## $`61`
##          [,1]     [,2]
## [1,] 1.027469  9.13673
## [2,] 9.136730 81.24805
## 
## $`62`
##             [,1]       [,2]
## [1,]  0.03669607  -1.916492
## [2,] -1.91649203 100.090877
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## $`63`
##           [,1]      [,2]
## [1,] 0.5679896  7.139522
## [2,] 7.1395221 89.742452
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## $`64`
##            [,1]        [,2]
## [1,]  9.8229447 -0.68416849
## [2,] -0.6841685  0.04765236
## 
## $`65`
##              [,1]        [,2]
## [1,] 0.0003101896   0.1768428
## [2,] 0.1768428421 100.8202487
## 
## $`66`
##          [,1]      [,2]
## [1,] 6.572683  8.892421
## [2,] 8.892421 12.030877
## 
## $`67`
##          [,1]      [,2]
## [1,] 1.112018  9.416064
## [2,] 9.416064 79.730991
## 
## $`68`
##          [,1]     [,2]
## [1,] 7.875050 6.078871
## [2,] 6.078871 4.692373
## 
## $`69`
##            [,1]      [,2]
## [1,]  0.5861514 -7.238864
## [2,] -7.2388645 89.398679
## 
## $`70`
##          [,1]     [,2]
## [1,] 11.16203 3.744520
## [2,]  3.74452 1.256172
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## $`71`
##           [,1]      [,2]
## [1,]  6.168929 -9.617783
## [2,] -9.617783 14.994783
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## $`72`
##            [,1]      [,2]
## [1,]  0.5792591 -7.201425
## [2,] -7.2014253 89.529060
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## $`73`
##          [,1]      [,2]
## [1,] 0.167155  4.036979
## [2,] 4.036979 97.497532
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## $`74`
##           [,1]      [,2]
## [1,]  1.239600 -9.799509
## [2,] -9.799509 77.468851
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## $`75`
##            [,1]      [,2]
## [1,] 0.06932852  2.625635
## [2,] 2.62563494 99.438996
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## $`76`
##            [,1]      [,2]
## [1,]   67.43633 -471.3264
## [2,] -471.32637 3294.1968
## 
## $`77`
##            [,1]      [,2]
## [1,]   1.929081 -11.26709
## [2,] -11.267086  65.80710
## 
## $`78`
##           [,1]     [,2]
## [1,]  2.356123 11.79640
## [2,] 11.796397 59.06101
## 
## $`79`
##          [,1]      [,2]
## [1,] 25.28754  76.66866
## [2,] 76.66866 232.44977
## 
## $`80`
##          [,1]      [,2]
## [1,]  74.4741  556.0452
## [2,] 556.0452 4151.5939
## 
## $`81`
##           [,1]     [,2]
## [1,]  25.03456 -75.0184
## [2,] -75.01840 224.7997
## 
## $`82`
##            [,1]      [,2]
## [1,]   5.358911 -10.83927
## [2,] -10.839271  21.92419
## 
## $`83`
##            [,1]     [,2]
## [1,]  0.2038647 -4.44171
## [2,] -4.4417103 96.77393
## 
## $`84`
##           [,1]     [,2]
## [1,]  4.577009 11.69014
## [2,] 11.690144 29.85781
## 
## $`85`
##            [,1]      [,2]
## [1,]   5.935795 -10.00229
## [2,] -10.002293  16.85467
## 
## $`86`
##           [,1]      [,2]
## [1,]  7.774745 -6.319717
## [2,] -6.319717  5.136994
## 
## $`87`
##           [,1]      [,2]
## [1,] 0.1741867  4.118081
## [2,] 4.1180809 97.358719
## 
## $`88`
##           [,1]     [,2]
## [1,]  1.501483 10.46419
## [2,] 10.464191 72.92743
## 
## $`89`
##          [,1]      [,2]
## [1,]  19.2530 -40.41960
## [2,] -40.4196  84.85658
## 
## $`90`
##          [,1]     [,2]
## [1,] 6.471038  9.08196
## [2,] 9.081960 12.74633
## 
## $`91`
##           [,1]      [,2]
## [1,] 0.9537271  8.874769
## [2,] 8.8747688 82.582870
## 
## $`92`
##          [,1]      [,2]
## [1,] 1.097949  9.371054
## [2,] 9.371054 79.982427
## 
## $`93`
##          [,1]     [,2]
## [1,] 14.22058 15.76036
## [2,] 15.76036 17.46687
## 
## $`94`
##          [,1]      [,2]
## [1,] 1.228669  9.768323
## [2,] 9.768323 77.661390
## 
## $`95`
##           [,1]      [,2]
## [1,]  56.79944  352.3951
## [2,] 352.39509 2186.3295
## 
## $`96`
##           [,1]     [,2]
## [1,]  3.113554 12.22408
## [2,] 12.224084 47.99281
## 
## $`97`
##           [,1]     [,2]
## [1,]  39.15787 182.2009
## [2,] 182.20092 847.7780
## 
## $`98`
##           [,1]      [,2]
## [1,]  0.363852 -5.837414
## [2,] -5.837414 93.651817
## 
## $`99`
##           [,1]      [,2]
## [1,]  19.24029 -40.35047
## [2,] -40.35047  84.62246
## 
## $`100`
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## [1,]   5.12201 -11.13313
## [2,] -11.13313  24.19881
## 
## 
## Slot ".ee_i":
## $`1`
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## 
## $`2`
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## $`3`
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## 
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## 
## $`9`
## [1]  4.915842 14.124269
## 
## $`10`
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## 
## $`11`
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## $`12`
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## $`13`
## [1] -2.502699 -3.777738
## 
## $`14`
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## 
## $`15`
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## 
## $`16`
## [1]  0.4689809 -9.8212958
## 
## $`17`
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## $`18`
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## $`19`
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## 
## $`20`
## [1]  6.416199 31.126376
## 
## $`21`
## [1] -3.1394168 -0.1853012
## 
## $`22`
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## 
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## $`24`
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## $`25`
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## $`26`
## [1] -2.119561 -5.548698
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## $`27`
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## 
## $`28`
## [1] 3.985266 5.841108
## 
## $`29`
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## 
## $`30`
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## $`32`
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## $`35`
## [1]  5.348174 18.561728
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## $`36`
## [1]  1.727722 -7.056215
## 
## $`37`
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## $`38`
## [1]  1.777632 -6.881263
## 
## $`39`
## [1] -0.2051821 -9.9991392
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## $`40`
## [1]  1.779921 -6.873121
## 
## $`41`
## [1] -1.678263 -7.224671
## 
## $`42`
## [1] -8.590539 63.756117
## 
## $`43`
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## $`44`
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## 
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## $`49`
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## [1] 4.094182 6.721091
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## [1]  6.56945 33.11643
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## [1]  -0.1413766 -10.0212515
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## [1]  0.9564243 -9.1264915
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## $`56`
## [1] -1.393061 -8.100619
## 
## $`57`
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## $`58`
## [1] -0.440095 -9.847555
## 
## $`59`
## [1]  1.011784 -9.017532
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## $`60`
## [1]  0.5113714 -9.7797382
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## $`61`
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## $`67`
## [1] -1.054522 -8.929221
## 
## $`68`
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## 
## $`69`
## [1]  0.7656052 -9.4550875
## 
## $`70`
## [1] 3.340962 1.120791
## 
## $`71`
## [1]  2.483733 -3.872310
## 
## $`72`
## [1]  0.7610908 -9.4619797
## 
## $`73`
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## 
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## [1]  1.113373 -8.801639
## 
## $`75`
## [1] -0.2633031 -9.9719103
## 
## $`76`
## [1] -8.211963 57.395094
## 
## $`77`
## [1]  1.388914 -8.112158
## 
## $`78`
## [1] -1.534967 -7.685116
## 
## $`79`
## [1]  5.028672 15.246303
## 
## $`80`
## [1]  8.629838 64.432864
## 
## $`81`
## [1] -5.003455 14.993320
## 
## $`82`
## [1]  2.314932 -4.682328
## 
## $`83`
## [1]  0.4515138 -9.8373741
## 
## $`84`
## [1] -2.139394 -5.464230
## 
## $`85`
## [1]  2.436349 -4.105444
## 
## $`86`
## [1]  2.788323 -2.266494
## 
## $`87`
## [1] -0.4173568 -9.8670522
## 
## $`88`
## [1] -1.225350 -8.539756
## 
## $`89`
## [1] -4.387824  9.211763
## 
## $`90`
## [1] -2.543824 -3.570200
## 
## $`91`
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## 
## $`92`
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## 
## $`93`
## [1] 3.771018 4.179338
## 
## $`94`
## [1] -1.108453 -8.812570
## 
## $`95`
## [1]  7.53654 46.75820
## 
## $`96`
## [1] -1.764527 -6.927685
## 
## $`97`
## [1]  6.257625 29.116627
## 
## $`98`
## [1]  0.6032015 -9.6773869
## 
## $`99`
## [1] -4.386375  9.199047
## 
## $`100`
## [1]  2.263186 -4.919229
## 
## 
## 
## Slot "GFUN":
## function () 
## NULL
## <bytecode: 0x7fd9e355f6a8>
## 
## Slot "corrections":
## list()
## 
## Slot "estimates":
## [1]  5.044563 10.041239
## 
## Slot "vcov":
##            [,1]       [,2]
## [1,] 0.10041239 0.03667969
## [2,] 0.03667969 2.49219638