Regression fitting in single source capture-recapture models
Source:R/estimatePopsizeFit.R
estimatePopsizeFit.RdestimatePopsizeFit does for estimatePopsize what
glm.fit does for glm. It is internally called in
estimatePopsize. Since estimatePopsize does much more than
just regression fitting estimatePopsizeFit is much faster.
Usage
estimatePopsizeFit(
y,
X,
family,
control,
method,
priorWeights,
coefStart,
etaStart,
offset,
...
)Arguments
- y
vector of dependent variables.
- X
model matrix, the vglm one.
- family
same as model in
estimatePopsize.- control
control parameters created in
controlModel.- method
method of estimation same as in
estimatePopsize.- priorWeights
vector of prior weights its the same argument as weights in
estimatePopsize.- etaStart, coefStart
initial value of regression parameters or linear predictors.
- offset
offset passed from by default passed from
estimatePopsize().- ...
arguments to pass to other methods.
Value
List with regression parameters, working weights (if IRLS fitting method) was chosen and number of iterations taken.
Details
If method argument was set to "optim" the stats::optim
function will be used to fit regression with analytically computed gradient and
(minus) log likelihood functions as gr and fn arguments.
Unfortunately optim does not allow for hessian to be specified.
More information about how to modify optim fitting is included in
controlMethod().
If method argument was set to "IRLS" the iteratively reweighted
least squares. The algorithm is well know in generalised linear models.
Thomas W. Yee later extended this algorithm to vector generalised linear models
and in more general terms it can roughly be described as
(this is Yee's description after changing some conventions):
Initialize with:
converged <- FALSEiter <- 1\(\boldsymbol{\beta}\)
<- start\(\boldsymbol{W}\)
<- prior\(\ell\)
<-\(\ell(\boldsymbol{\beta})\)
If
convergedoriter > Maxitermove to step 7.Store values from previous algorithm step:
\(\boldsymbol{W}_{-}\)
<-\(\boldsymbol{W}\)\(\ell_{-}\)
<-\(\ell\)\(\boldsymbol{\beta}_{-}\)
<-\(\boldsymbol{\beta}\)
and assign values at current step:
\(\boldsymbol{\eta}\)
<-\(\boldsymbol{X}_{vlm}\boldsymbol{\beta}\)\(Z_{i}\)
<-\( \eta_{i}+\frac{\partial\ell_{i}}{\partial\eta_{i}} \mathbb{E}\left(\frac{\partial^{2}\ell_{i}}{ \partial\eta_{i}^{T}\partial\eta_{i}}\right)^{-1}\)\(\boldsymbol{W}_{ij}\)
<-\(\mathbb{E}\left(\frac{\partial^{2}\ell}{ \partial\boldsymbol{\eta}_{j}^{T}\partial\boldsymbol{\eta}_{i}}\right)\)
where \(\ell_{i}\) is the ith component of log likelihood function, \(\eta_{i}\) is the vector of linear predictors associated with ith row and \(\mathbb{E}\left(\frac{\partial^{2}\ell_{i}}{ \partial\eta_{i}^{T}\partial\eta_{i}}\right)\) corresponds to weights associated with ith row and \(\boldsymbol{W}\) is a block matrix, made of diagonal matrixes \(\mathbb{E}\left(\frac{\partial^{2}\ell}{ \partial\boldsymbol{\eta}_{j}^{T}\partial\boldsymbol{\eta}_{i}}\right)\)
Regress \(\boldsymbol{Z}\) on \(\boldsymbol{X}_{vlm}\) to obtain \(\boldsymbol{\beta}\) as: \[\boldsymbol{\beta}= \left(\boldsymbol{X}_{vlm}^{T}\boldsymbol{W}\boldsymbol{X}_{vlm}\right)^{-1} \boldsymbol{X}_{vlm}^{T}\boldsymbol{W}\boldsymbol{Z}\]
Assign:
converged <-\( \ell(\boldsymbol{\beta})-\ell_{-} \( ||\boldsymbol{\beta}-\boldsymbol{\beta}_{-}||_{\infty}iter <- iter + 1
where \(\varepsilon\) is the relative tolerance level, by default
1e-8.Return to step 2.
Return \(\boldsymbol{\beta}, \boldsymbol{W}\),
iter.
In this package we use different conventions for \(\boldsymbol{X}_{vlm}\) matrix hence slight differences are present in algorithm description but results are identical.
References
Yee, T. W. (2015). Vector Generalized Linear and Additive Models: With an Implementation in R. New York, USA: Springer. ISBN 978-1-4939-2817-0.
Examples
# \donttest{
summary(farmsubmission)
#> TOTAL_SUB log_size log_distance C_TYPE
#> Min. : 1.00 Min. : 0.000 Min. : 4.102 Beef :5336
#> 1st Qu.: 1.00 1st Qu.: 4.673 1st Qu.:10.351 Dairy:6700
#> Median : 1.00 Median : 5.347 Median :10.778
#> Mean : 2.34 Mean : 5.259 Mean :10.662
#> 3rd Qu.: 3.00 3rd Qu.: 5.940 3rd Qu.:11.099
#> Max. :47.00 Max. :10.480 Max. :12.097
# construct vglm model matrix
X <- matrix(data = 0, nrow = 2 * NROW(farmsubmission), ncol = 7)
X[1:NROW(farmsubmission), 1:4] <- model.matrix(
~ 1 + log_size + log_distance + C_TYPE,
farmsubmission
)
X[-(1:NROW(farmsubmission)), 5:7] <- X[1:NROW(farmsubmission), c(1, 3, 4)]
# this attribute tells the function which elements of the design matrix
# correspond to which linear predictor
attr(X, "hwm") <- c(4, 3)
# get starting points
start <- glm.fit(
y = farmsubmission$TOTAL_SUB,
x = X[1:NROW(farmsubmission), 1:4],
family = poisson()
)$coefficients
res <- estimatePopsizeFit(
y = farmsubmission$TOTAL_SUB,
X = X,
method = "IRLS",
priorWeights = 1,
family = ztoigeom(),
control = controlMethod(verbose = 5),
coefStart = c(start, 0, 0, 0),
etaStart = matrix(X %*% c(start, 0, 0, 0), ncol = 2),
offset = cbind(rep(0, NROW(farmsubmission)), rep(0, NROW(farmsubmission)))
)
#> Iteration number 1 log-likelihood: -17455.372
#> Parameter vector: -2.255494347 0.521900283 -0.048255922 0.321168020 -1.297382847 0.049409082 -0.726587214
#> log-likelihood reduction: Inf
#> Value of gradient at current step:
#> 639.53919 4035.62183 6732.72078 672.31223 -316.39394 -3358.16739 -229.50394
#> Algorithm will terminate if one of following conditions will be met:
#> The increase to minus log-likelihood will be bellow chosen value of epsilon 1e-08
#> Maximum change to the vector of regression parameters will be bellow the chosen value of epsilon.
#> At current step the highest change was: 2.2554943
#> ----
#> Iteration number 2 log-likelihood: -17289.531
#> Parameter vector: -2.859491920 0.627917105 -0.063516471 0.573159952 -2.327571214 0.074464787 -0.734988992
#> log-likelihood reduction: 165.84115
#> Value of gradient at current step:
#> 77.37365182 329.72667483 823.92206208 0.28711463 -53.27713944 -568.21808076 -29.69092406
#> Algorithm will terminate if one of following conditions will be met:
#> The increase to minus log-likelihood will be bellow chosen value of epsilon 1e-08
#> Maximum change to the vector of regression parameters will be bellow the chosen value of epsilon.
#> At current step the highest change was: 1.0301884
#> ----
#> Iteration number 3 log-likelihood: -17279.272
#> Parameter vector: -2.710874025 0.613067896 -0.069548715 0.537208696 -2.550651004 0.071488122 -0.939145580
#> log-likelihood reduction: 10.258788
#> Value of gradient at current step:
#> 35.9649654 218.1210745 385.4441808 32.8759028 -6.8429684 -71.8589804 -5.7178443
#> Algorithm will terminate if one of following conditions will be met:
#> The increase to minus log-likelihood will be bellow chosen value of epsilon 1e-08
#> Maximum change to the vector of regression parameters will be bellow the chosen value of epsilon.
#> At current step the highest change was: 0.22307979
#> ----
#> Iteration number 4 log-likelihood: -17278.776
#> Parameter vector: -2.78426085 0.61628333 -0.06440012 0.53843272 -3.10491635 0.12060422 -1.04138882
#> log-likelihood reduction: 0.49548535
#> Value of gradient at current step:
#> 1.67966432 11.13935043 16.42827781 1.15147049 -0.53787945 -5.57182317 -0.74695785
#> Algorithm will terminate if one of following conditions will be met:
#> The increase to minus log-likelihood will be bellow chosen value of epsilon 1e-08
#> Maximum change to the vector of regression parameters will be bellow the chosen value of epsilon.
#> At current step the highest change was: 0.55426534
#> ----
#> Iteration number 5 log-likelihood: -17278.762
#> Parameter vector: -2.77818073 0.61674992 -0.06504016 0.53517478 -3.10447410 0.12145802 -1.08163762
#> log-likelihood reduction: 0.014133264
#> Value of gradient at current step:
#> 0.232501334 2.204257359 2.694809270 0.131590616 -0.071608376 -0.605938875 -0.064356213
#> Algorithm will terminate if one of following conditions will be met:
#> The increase to minus log-likelihood will be bellow chosen value of epsilon 1e-08
#> Maximum change to the vector of regression parameters will be bellow the chosen value of epsilon.
#> At current step the highest change was: 0.040248796
#> ----
#> Iteration number 6 log-likelihood: -17278.761
#> Parameter vector: -2.78602286 0.61698772 -0.06441877 0.53495927 -3.19325142 0.12969021 -1.08314735
#> log-likelihood reduction: 0.00072206104
#> Value of gradient at current step:
#> -0.0149254818 -0.0442854059 -0.2585639447 -0.0671445437 -0.0089103073 -0.1428452785 -0.0408361062
#> Algorithm will terminate if one of following conditions will be met:
#> The increase to minus log-likelihood will be bellow chosen value of epsilon 1e-08
#> Maximum change to the vector of regression parameters will be bellow the chosen value of epsilon.
#> At current step the highest change was: 0.088777321
#> ----
#> Iteration number 7 log-likelihood: -17278.761
#> Parameter vector: -2.783307402 0.617006834 -0.064659772 0.534565433 -3.160032510 0.126742033 -1.087078105
#> log-likelihood reduction: 0.000086867327
#> Value of gradient at current step:
#> 0.0219006963 0.2137543746 0.2878052108 0.0210725209 -0.0038258075 -0.0055588958 0.0088000042
#> Algorithm will terminate if one of following conditions will be met:
#> The increase to minus log-likelihood will be bellow chosen value of epsilon 1e-08
#> Maximum change to the vector of regression parameters will be bellow the chosen value of epsilon.
#> At current step the highest change was: 0.033218913
#> ----
#> Iteration number 8 log-likelihood: -17278.761
#> Parameter vector: -2.785132183 0.617029483 -0.064506904 0.534668321 -3.181900933 0.128724679 -1.085840518
#> log-likelihood reduction: 0.00002149725
#> Value of gradient at current step:
#> -0.00917986045 -0.07823752458 -0.12764140882 -0.01528913765 0.00031447068 -0.01459257981 -0.00776040765
#> Algorithm will terminate if one of following conditions will be met:
#> The increase to minus log-likelihood will be bellow chosen value of epsilon 1e-08
#> Maximum change to the vector of regression parameters will be bellow the chosen value of epsilon.
#> At current step the highest change was: 0.021868422
#> ----
#> Iteration number 9 log-likelihood: -17278.761
#> Parameter vector: -2.784182050 0.617023943 -0.064588093 0.534586386 -3.170374939 0.127687086 -1.086727858
#> log-likelihood reduction: 0.0000064244196
#> Value of gradient at current step:
#> 0.00580810482 0.05244014319 0.07853720954 0.00778331025 -0.00057098473 0.00429221923 0.00373823937
#> Algorithm will terminate if one of following conditions will be met:
#> The increase to minus log-likelihood will be bellow chosen value of epsilon 1e-08
#> Maximum change to the vector of regression parameters will be bellow the chosen value of epsilon.
#> At current step the highest change was: 0.011525994
#> ----
#> Iteration number 10 log-likelihood: -17278.761
#> Parameter vector: -2.784725925 0.617028507 -0.064541975 0.534626993 -3.176948180 0.128280435 -1.086273279
#> log-likelihood reduction: 0.0000019945583
#> Value of gradient at current step:
#> -0.00307033641 -0.02728421588 -0.04201045335 -0.00448214638 0.00022935424 -0.00326931976 -0.00221219809
#> Algorithm will terminate if one of following conditions will be met:
#> The increase to minus log-likelihood will be bellow chosen value of epsilon 1e-08
#> Maximum change to the vector of regression parameters will be bellow the chosen value of epsilon.
#> At current step the highest change was: 0.006573241
#> ----
#> Iteration number 11 log-likelihood: -17278.761
#> Parameter vector: -2.78442528 0.61702627 -0.06456754 0.53460327 -3.17330966 0.12795232 -1.08653540
#> log-likelihood reduction: 0.00000061988248
#> Value of gradient at current step:
#> 0.00175710833 0.01568170299 0.02390375498 0.00247668339 -0.00014882078 0.00161926855 0.00120723719
#> Algorithm will terminate if one of following conditions will be met:
#> The increase to minus log-likelihood will be bellow chosen value of epsilon 1e-08
#> Maximum change to the vector of regression parameters will be bellow the chosen value of epsilon.
#> At current step the highest change was: 0.0036385179
#> ----
#> Iteration number 12 log-likelihood: -17278.761
#> Parameter vector: -2.784593634 0.617027580 -0.064553239 0.534616288 -3.175346365 0.128136053 -1.086390890
#> log-likelihood reduction: 0.00000019314757
#> Value of gradient at current step:
#> -0.000968762323 -0.008641334475 -0.013216142970 -0.001385713879 0.000077984443 -0.000953809240 -0.000679710377
#> Algorithm will terminate if one of following conditions will be met:
#> The increase to minus log-likelihood will be bellow chosen value of epsilon 1e-08
#> Maximum change to the vector of regression parameters will be bellow the chosen value of epsilon.
#> At current step the highest change was: 0.0020367031
#> ----
#> Iteration number 13 log-likelihood: -17278.761
#> Parameter vector: -2.784499807 0.617026860 -0.064561213 0.534608978 -3.174211159 0.128033659 -1.086471902
#> log-likelihood reduction: 0.000000060121238
#> Value of gradient at current step:
#> 0.000543879322 0.004849594735 0.007409081651 0.000772957763 -0.000044801248 0.000519451058 0.000377932800
#> Algorithm will terminate if one of following conditions will be met:
#> The increase to minus log-likelihood will be bellow chosen value of epsilon 1e-08
#> Maximum change to the vector of regression parameters will be bellow the chosen value of epsilon.
#> At current step the highest change was: 0.0011352061
#> ----
#> Iteration number 14 log-likelihood: -17278.761
#> Parameter vector: -2.784552191 0.617027265 -0.064556762 0.534613048 -3.174844941 0.128090828 -1.086426773
#> log-likelihood reduction: 0.000000018728315
#> Value of gradient at current step:
#> -0.000302564127 -0.002699091075 -0.004124826709 -0.000431270327 0.000024661481 -0.000293282189 -0.000211223041
#> Algorithm will terminate if one of following conditions will be met:
#> The increase to minus log-likelihood will be bellow chosen value of epsilon 1e-08
#> Maximum change to the vector of regression parameters will be bellow the chosen value of epsilon.
#> At current step the highest change was: 0.00063378216
#> ----
#> Iteration number 15 log-likelihood: -17278.761
#> Parameter vector: -2.784522964 0.617027040 -0.064559245 0.534610775 -3.174491334 0.128058932 -1.086451974
#> log-likelihood reduction: 0.00000000583168
#> Value of gradient at current step:
#> 0.000169118292 0.001508137356 0.002304647172 0.000240720368 -0.000013855242 0.000162719781 0.000117791117
#> Algorithm will terminate if one of following conditions will be met:
#> The increase to minus log-likelihood will be bellow chosen value of epsilon 1e-08
#> Maximum change to the vector of regression parameters will be bellow the chosen value of epsilon.
#> At current step the highest change was: 0.00035360721
#> ----
#> Value of analytically computed hessian at fitted regression coefficients:
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] -5533.0360 -31139.1628 -58786.3824 -3921.3952 407.46348 23473.8262
#> [2,] -31139.1628 -179723.7217 -330742.8394 -22956.5461 4362.01544 1060.0139
#> [3,] -58786.3824 -330742.8394 -627035.9660 -41504.3671 185.81715 4362.0154
#> [4,] -3921.3952 -22956.5461 -41504.3671 -3921.3952 2193.72685 46845.5137
#> [5,] 407.4635 185.8172 46845.5137 1060.0139 -88.14760 -948.1115
#> [6,] 2193.7268 4362.0154 1971.9380 1971.9380 -948.11154 -10234.8910
#> [7,] 4362.0154 23473.8262 185.8172 185.8172 -28.97964 -312.6869
#> [,7]
#> [1,] 1971.93804
#> [2,] 185.81715
#> [3,] 1971.93804
#> [4,] 185.81715
#> [5,] -28.97964
#> [6,] -312.68692
#> [7,] -28.97964
#> The matrix above has the following eigen values:
#> -811159.7+0i -17207.51+0i -2161.919+9274.748i -2161.919-9274.748i 6057.218+0i 1581.239+0i -1513.504+0i
# extract results
# regression coefficient vector
res$beta
#> [1] -2.78452296 0.61702704 -0.06455925 0.53461077 -3.17449133 0.12805893
#> [7] -1.08645197
# check likelihood
ll <- ztoigeom()$makeMinusLogLike(y = farmsubmission$TOTAL_SUB, X = X)
-ll(res$beta)
#> [1] -17278.76
# number of iterations
res$iter
#> [1] 15
# working weights
head(res$weights)
#> lambda mixed mixed omega
#> [1,] 0.22688312 -0.03207963 -0.03207963 0.006351956
#> [2,] 0.66642253 -0.03199578 -0.03199578 0.006238854
#> [3,] 0.08469406 -0.01202233 -0.01202233 0.001899477
#> [4,] 0.14084340 -0.01990317 -0.01990317 0.003397031
#> [5,] 0.34099080 -0.04762290 -0.04762290 0.012045206
#> [6,] 0.42290801 -0.05782236 -0.05782236 0.018478738
# Compare with optim call
res2 <- estimatePopsizeFit(
y = farmsubmission$TOTAL_SUB,
X = X,
method = "optim",
priorWeights = 1,
family = ztoigeom(),
coefStart = c(start, 0, 0, 0),
control = controlMethod(verbose = 1, silent = TRUE),
offset = cbind(rep(0, NROW(farmsubmission)), rep(0, NROW(farmsubmission)))
)
#> Nelder-Mead direct search function minimizer
#> function value for initial parameters = 18634.249443
#> Scaled convergence tolerance is 0.000186342
#> Stepsize computed as 0.082584
#> BUILD 8 20695.993313 18634.249443
#> LO-REDUCTION 10 20521.906450 18634.249443
#> REFLECTION 12 19390.030449 18203.536957
#> LO-REDUCTION 14 18936.678302 18203.536957
#> LO-REDUCTION 16 18749.996003 18203.536957
#> LO-REDUCTION 18 18737.148786 18203.536957
#> LO-REDUCTION 20 18718.703486 18203.536957
#> EXTENSION 22 18670.005025 17895.311480
#> LO-REDUCTION 24 18634.249443 17895.311480
#> LO-REDUCTION 26 18560.534560 17895.311480
#> EXTENSION 28 18449.746468 17588.420920
#> LO-REDUCTION 30 18295.895431 17588.420920
#> LO-REDUCTION 32 18222.396059 17588.420920
#> LO-REDUCTION 34 18203.536957 17588.420920
#> LO-REDUCTION 36 18087.422161 17588.420920
#> LO-REDUCTION 38 18005.031702 17588.420920
#> REFLECTION 40 18001.913029 17584.422405
#> REFLECTION 42 17895.311480 17527.021914
#> LO-REDUCTION 44 17780.944181 17527.021914
#> LO-REDUCTION 46 17712.559384 17527.021914
#> HI-REDUCTION 48 17643.578220 17527.021914
#> EXTENSION 50 17621.199586 17473.997274
#> LO-REDUCTION 52 17602.520321 17473.997274
#> HI-REDUCTION 54 17594.799573 17473.997274
#> LO-REDUCTION 56 17588.420920 17473.997274
#> LO-REDUCTION 58 17584.422405 17473.997274
#> EXTENSION 60 17556.846275 17447.303959
#> EXTENSION 62 17555.104630 17408.736552
#> LO-REDUCTION 64 17528.536402 17408.736552
#> LO-REDUCTION 66 17527.021914 17408.736552
#> EXTENSION 68 17511.009990 17375.624732
#> LO-REDUCTION 70 17506.001244 17375.624732
#> LO-REDUCTION 72 17473.997274 17375.624732
#> LO-REDUCTION 74 17459.682283 17375.624732
#> REFLECTION 76 17447.303959 17374.438952
#> EXTENSION 78 17431.820752 17359.678457
#> REFLECTION 80 17410.856537 17352.512930
#> LO-REDUCTION 82 17408.736552 17352.512930
#> LO-REDUCTION 84 17392.430571 17352.512930
#> LO-REDUCTION 86 17383.843739 17352.512930
#> LO-REDUCTION 88 17375.624732 17352.512930
#> HI-REDUCTION 90 17374.438952 17352.512930
#> REFLECTION 92 17364.440518 17351.391717
#> LO-REDUCTION 94 17361.269788 17351.391717
#> HI-REDUCTION 96 17359.678457 17351.391717
#> LO-REDUCTION 98 17359.333428 17351.391717
#> EXTENSION 100 17359.195000 17340.073149
#> LO-REDUCTION 102 17355.280449 17340.073149
#> LO-REDUCTION 104 17354.737924 17340.073149
#> LO-REDUCTION 106 17352.512930 17340.073149
#> LO-REDUCTION 108 17352.283989 17340.073149
#> EXTENSION 110 17351.931319 17334.816229
#> LO-REDUCTION 112 17351.391717 17334.816229
#> LO-REDUCTION 114 17349.077477 17334.816229
#> LO-REDUCTION 116 17346.861518 17334.816229
#> EXTENSION 118 17344.774811 17327.221865
#> LO-REDUCTION 120 17344.768718 17327.221865
#> EXTENSION 122 17340.363390 17314.895018
#> LO-REDUCTION 124 17340.073149 17314.895018
#> LO-REDUCTION 126 17337.014069 17314.895018
#> LO-REDUCTION 128 17336.611433 17314.895018
#> LO-REDUCTION 130 17334.816229 17314.895018
#> EXTENSION 132 17330.280767 17308.580216
#> LO-REDUCTION 134 17327.221865 17308.580216
#> LO-REDUCTION 136 17324.616040 17308.580216
#> REFLECTION 138 17320.961818 17307.339443
#> LO-REDUCTION 140 17320.314061 17307.339443
#> REFLECTION 142 17316.412981 17307.294606
#> LO-REDUCTION 144 17314.895018 17307.294606
#> HI-REDUCTION 146 17311.221319 17307.294606
#> REFLECTION 148 17310.240780 17305.855235
#> LO-REDUCTION 150 17309.024781 17305.855235
#> HI-REDUCTION 152 17308.580216 17305.855235
#> REFLECTION 154 17307.909389 17304.751271
#> LO-REDUCTION 156 17307.607430 17304.751271
#> HI-REDUCTION 158 17307.339443 17304.751271
#> EXTENSION 160 17307.294606 17303.969236
#> LO-REDUCTION 162 17306.726648 17303.969236
#> LO-REDUCTION 164 17306.486915 17303.969236
#> LO-REDUCTION 166 17306.013269 17303.969236
#> LO-REDUCTION 168 17305.855235 17303.969236
#> REFLECTION 170 17305.566500 17303.365745
#> HI-REDUCTION 172 17304.769833 17303.365745
#> LO-REDUCTION 174 17304.751271 17303.365745
#> EXTENSION 176 17304.679762 17302.760257
#> LO-REDUCTION 178 17304.415232 17302.760257
#> LO-REDUCTION 180 17304.272835 17302.760257
#> EXTENSION 182 17304.232531 17301.382173
#> LO-REDUCTION 184 17303.969236 17301.382173
#> LO-REDUCTION 186 17303.740306 17301.382173
#> LO-REDUCTION 188 17303.561302 17301.382173
#> LO-REDUCTION 190 17303.365745 17301.382173
#> REFLECTION 192 17303.285629 17301.216054
#> EXTENSION 194 17302.760257 17300.566315
#> EXTENSION 196 17302.374881 17299.438766
#> EXTENSION 198 17302.365881 17298.338665
#> EXTENSION 200 17301.538607 17296.617465
#> LO-REDUCTION 202 17301.386247 17296.617465
#> LO-REDUCTION 204 17301.382173 17296.617465
#> LO-REDUCTION 206 17301.216054 17296.617465
#> EXTENSION 208 17300.566315 17294.656203
#> EXTENSION 210 17299.438766 17292.415140
#> LO-REDUCTION 212 17298.338665 17292.415140
#> LO-REDUCTION 214 17297.787001 17292.415140
#> REFLECTION 216 17297.283737 17292.315917
#> REFLECTION 218 17296.776034 17290.819569
#> EXTENSION 220 17296.617465 17289.284957
#> LO-REDUCTION 222 17294.656203 17289.284957
#> LO-REDUCTION 224 17294.447369 17289.284957
#> LO-REDUCTION 226 17292.619840 17289.284957
#> REFLECTION 228 17292.415140 17289.050671
#> LO-REDUCTION 230 17292.315917 17289.050671
#> HI-REDUCTION 232 17290.819569 17289.050671
#> LO-REDUCTION 234 17290.333239 17289.050671
#> HI-REDUCTION 236 17290.198503 17289.050671
#> LO-REDUCTION 238 17290.030554 17289.050671
#> HI-REDUCTION 240 17289.707101 17289.050671
#> REFLECTION 242 17289.446684 17289.049956
#> REFLECTION 244 17289.402572 17288.762931
#> LO-REDUCTION 246 17289.314216 17288.762931
#> LO-REDUCTION 248 17289.284957 17288.762931
#> LO-REDUCTION 250 17289.237020 17288.755874
#> REFLECTION 252 17289.231432 17288.591829
#> LO-REDUCTION 254 17289.050671 17288.591829
#> HI-REDUCTION 256 17289.049956 17288.591829
#> LO-REDUCTION 258 17288.965069 17288.591829
#> LO-REDUCTION 260 17288.779011 17288.591829
#> LO-REDUCTION 262 17288.766114 17288.591829
#> REFLECTION 264 17288.762931 17288.553874
#> LO-REDUCTION 266 17288.760612 17288.553874
#> LO-REDUCTION 268 17288.755874 17288.553874
#> REFLECTION 270 17288.712718 17288.530741
#> LO-REDUCTION 272 17288.644400 17288.530741
#> EXTENSION 274 17288.613052 17288.437051
#> HI-REDUCTION 276 17288.606964 17288.437051
#> EXTENSION 278 17288.591829 17288.369092
#> LO-REDUCTION 280 17288.588782 17288.369092
#> LO-REDUCTION 282 17288.553874 17288.369092
#> EXTENSION 284 17288.542682 17288.275532
#> LO-REDUCTION 286 17288.531198 17288.275532
#> LO-REDUCTION 288 17288.530741 17288.275532
#> LO-REDUCTION 290 17288.469459 17288.275532
#> EXTENSION 292 17288.461014 17288.127850
#> LO-REDUCTION 294 17288.437051 17288.127850
#> LO-REDUCTION 296 17288.369092 17288.127850
#> LO-REDUCTION 298 17288.347618 17288.127850
#> LO-REDUCTION 300 17288.313219 17288.127850
#> EXTENSION 302 17288.295935 17288.071792
#> EXTENSION 304 17288.275532 17287.915686
#> LO-REDUCTION 306 17288.214888 17287.915686
#> LO-REDUCTION 308 17288.211032 17287.915686
#> EXTENSION 310 17288.173100 17287.842214
#> LO-REDUCTION 312 17288.141906 17287.842214
#> LO-REDUCTION 314 17288.127850 17287.842214
#> EXTENSION 316 17288.071792 17287.733682
#> EXTENSION 318 17288.054470 17287.663282
#> EXTENSION 320 17287.989272 17287.507624
#> LO-REDUCTION 322 17287.919537 17287.507624
#> LO-REDUCTION 324 17287.915686 17287.507624
#> LO-REDUCTION 326 17287.856498 17287.507624
#> REFLECTION 328 17287.842214 17287.490634
#> LO-REDUCTION 330 17287.733682 17287.490634
#> REFLECTION 332 17287.663282 17287.438068
#> LO-REDUCTION 334 17287.555894 17287.438068
#> LO-REDUCTION 336 17287.551441 17287.438068
#> REFLECTION 338 17287.547247 17287.422322
#> REFLECTION 340 17287.542002 17287.418701
#> REFLECTION 342 17287.507624 17287.368868
#> LO-REDUCTION 344 17287.490634 17287.368868
#> LO-REDUCTION 346 17287.444486 17287.368868
#> LO-REDUCTION 348 17287.438762 17287.368868
#> HI-REDUCTION 350 17287.438068 17287.368868
#> EXTENSION 352 17287.422322 17287.329022
#> EXTENSION 354 17287.418701 17287.274393
#> LO-REDUCTION 356 17287.391509 17287.274393
#> LO-REDUCTION 358 17287.381359 17287.274393
#> LO-REDUCTION 360 17287.375030 17287.274393
#> LO-REDUCTION 362 17287.371807 17287.274393
#> LO-REDUCTION 364 17287.368868 17287.274393
#> REFLECTION 366 17287.329022 17287.274032
#> LO-REDUCTION 368 17287.327098 17287.274032
#> EXTENSION 370 17287.322765 17287.246248
#> LO-REDUCTION 372 17287.316574 17287.246248
#> EXTENSION 374 17287.308329 17287.210843
#> LO-REDUCTION 376 17287.304794 17287.210843
#> LO-REDUCTION 378 17287.279608 17287.210843
#> REFLECTION 380 17287.274393 17287.210366
#> REFLECTION 382 17287.274032 17287.209122
#> LO-REDUCTION 384 17287.264744 17287.209122
#> REFLECTION 386 17287.246248 17287.183411
#> LO-REDUCTION 388 17287.223877 17287.183411
#> LO-REDUCTION 390 17287.214413 17287.183411
#> LO-REDUCTION 392 17287.213088 17287.183411
#> EXTENSION 394 17287.210843 17287.178084
#> LO-REDUCTION 396 17287.210366 17287.178084
#> LO-REDUCTION 398 17287.209122 17287.178084
#> REFLECTION 400 17287.197803 17287.172953
#> EXTENSION 402 17287.196607 17287.164829
#> LO-REDUCTION 404 17287.192398 17287.164829
#> EXTENSION 406 17287.183411 17287.148789
#> LO-REDUCTION 408 17287.183094 17287.148789
#> LO-REDUCTION 410 17287.181404 17287.148789
#> LO-REDUCTION 412 17287.178084 17287.148789
#> LO-REDUCTION 414 17287.173517 17287.148789
#> LO-REDUCTION 416 17287.172953 17287.148789
#> LO-REDUCTION 418 17287.165027 17287.148789
#> EXTENSION 420 17287.164829 17287.142664
#> LO-REDUCTION 422 17287.164534 17287.142664
#> EXTENSION 424 17287.161998 17287.140674
#> LO-REDUCTION 426 17287.160519 17287.140674
#> EXTENSION 428 17287.154476 17287.127103
#> LO-REDUCTION 430 17287.153672 17287.127103
#> LO-REDUCTION 432 17287.148789 17287.127103
#> LO-REDUCTION 434 17287.147540 17287.127103
#> LO-REDUCTION 436 17287.146752 17287.127103
#> LO-REDUCTION 438 17287.142664 17287.127103
#> LO-REDUCTION 440 17287.140674 17287.127103
#> REFLECTION 442 17287.138106 17287.127061
#> EXTENSION 444 17287.131886 17287.110761
#> LO-REDUCTION 446 17287.130480 17287.110761
#> LO-REDUCTION 448 17287.129088 17287.110761
#> LO-REDUCTION 450 17287.128934 17287.110761
#> LO-REDUCTION 452 17287.128336 17287.110761
#> LO-REDUCTION 454 17287.127103 17287.110761
#> LO-REDUCTION 456 17287.127061 17287.110761
#> EXTENSION 458 17287.122784 17287.105926
#> LO-REDUCTION 460 17287.121627 17287.105926
#> EXTENSION 462 17287.120146 17287.101582
#> LO-REDUCTION 464 17287.118771 17287.101582
#> LO-REDUCTION 466 17287.117855 17287.101582
#> EXTENSION 468 17287.117130 17287.090721
#> LO-REDUCTION 470 17287.110761 17287.090721
#> LO-REDUCTION 472 17287.108359 17287.090721
#> LO-REDUCTION 474 17287.107134 17287.090721
#> EXTENSION 476 17287.105926 17287.081849
#> LO-REDUCTION 478 17287.104244 17287.081849
#> EXTENSION 480 17287.101582 17287.080130
#> LO-REDUCTION 482 17287.096149 17287.080130
#> EXTENSION 484 17287.095793 17287.074699
#> LO-REDUCTION 486 17287.093227 17287.074699
#> LO-REDUCTION 488 17287.090721 17287.074699
#> LO-REDUCTION 490 17287.086551 17287.074699
#> REFLECTION 492 17287.086412 17287.074418
#> LO-REDUCTION 494 17287.081849 17287.074418
#> LO-REDUCTION 496 17287.080130 17287.074418
#> REFLECTION 498 17287.077153 17287.073950
#> REFLECTION 500 17287.076483 17287.072432
#> LO-REDUCTION 502 17287.075898 17287.072432
#> LO-REDUCTION 504 17287.075565 17287.072432
#> LO-REDUCTION 506 17287.075074 17287.072432
#> LO-REDUCTION 508 17287.074699 17287.072432
#> LO-REDUCTION 510 17287.074418 17287.072432
#> HI-REDUCTION 512 17287.073950 17287.072432
#> LO-REDUCTION 514 17287.073404 17287.072432
#> EXTENSION 516 17287.072984 17287.071689
#> LO-REDUCTION 518 17287.072957 17287.071689
#> EXTENSION 520 17287.072911 17287.071281
#> LO-REDUCTION 522 17287.072872 17287.071281
#> EXTENSION 524 17287.072566 17287.070932
#> LO-REDUCTION 526 17287.072496 17287.070932
#> REFLECTION 528 17287.072432 17287.070705
#> LO-REDUCTION 530 17287.072040 17287.070705
#> EXTENSION 532 17287.071689 17287.069928
#> LO-REDUCTION 534 17287.071602 17287.069928
#> LO-REDUCTION 536 17287.071281 17287.069928
#> LO-REDUCTION 538 17287.071085 17287.069928
#> REFLECTION 540 17287.070932 17287.069704
#> LO-REDUCTION 542 17287.070818 17287.069704
#> REFLECTION 544 17287.070705 17287.069688
#> REFLECTION 546 17287.070279 17287.069497
#> REFLECTION 548 17287.070113 17287.069324
#> HI-REDUCTION 550 17287.070091 17287.069324
#> LO-REDUCTION 552 17287.070013 17287.069324
#> REFLECTION 554 17287.069928 17287.069224
#> LO-REDUCTION 556 17287.069704 17287.069224
#> EXTENSION 558 17287.069688 17287.069019
#> EXTENSION 560 17287.069605 17287.068864
#> LO-REDUCTION 562 17287.069502 17287.068864
#> LO-REDUCTION 564 17287.069497 17287.068864
#> EXTENSION 566 17287.069324 17287.068482
#> LO-REDUCTION 568 17287.069285 17287.068482
#> EXTENSION 570 17287.069224 17287.068173
#> EXTENSION 572 17287.069019 17287.067727
#> LO-REDUCTION 574 17287.068980 17287.067727
#> EXTENSION 576 17287.068959 17287.066896
#> EXTENSION 578 17287.068864 17287.065841
#> LO-REDUCTION 580 17287.068771 17287.065841
#> EXTENSION 582 17287.068482 17287.064747
#> LO-REDUCTION 584 17287.068173 17287.064747
#> EXTENSION 586 17287.067970 17287.063322
#> LO-REDUCTION 588 17287.067727 17287.063322
#> EXTENSION 590 17287.066896 17287.061580
#> LO-REDUCTION 592 17287.066709 17287.061580
#> LO-REDUCTION 594 17287.066510 17287.061580
#> EXTENSION 596 17287.065841 17287.057767
#> LO-REDUCTION 598 17287.064747 17287.057767
#> EXTENSION 600 17287.063788 17287.053859
#> LO-REDUCTION 602 17287.063322 17287.053859
#> LO-REDUCTION 604 17287.062792 17287.053859
#> LO-REDUCTION 606 17287.062126 17287.053859
#> EXTENSION 608 17287.061580 17287.050184
#> EXTENSION 610 17287.058435 17287.045782
#> LO-REDUCTION 612 17287.057767 17287.045782
#> LO-REDUCTION 614 17287.057359 17287.045782
#> EXTENSION 616 17287.057193 17287.037166
#> LO-REDUCTION 618 17287.053911 17287.037166
#> LO-REDUCTION 620 17287.053859 17287.037166
#> LO-REDUCTION 622 17287.050184 17287.037166
#> LO-REDUCTION 624 17287.048790 17287.037166
#> EXTENSION 626 17287.046966 17287.027006
#> LO-REDUCTION 628 17287.045782 17287.027006
#> EXTENSION 630 17287.041585 17287.015525
#> LO-REDUCTION 632 17287.037975 17287.015525
#> LO-REDUCTION 634 17287.037776 17287.015525
#> LO-REDUCTION 636 17287.037537 17287.015525
#> EXTENSION 638 17287.037166 17287.002045
#> LO-REDUCTION 640 17287.029130 17287.002045
#> LO-REDUCTION 642 17287.027006 17287.002045
#> EXTENSION 644 17287.021112 17286.982852
#> LO-REDUCTION 646 17287.020505 17286.982852
#> LO-REDUCTION 648 17287.020369 17286.982852
#> EXTENSION 650 17287.015525 17286.962921
#> LO-REDUCTION 652 17287.006234 17286.962921
#> LO-REDUCTION 654 17287.003316 17286.962921
#> LO-REDUCTION 656 17287.002045 17286.962921
#> LO-REDUCTION 658 17286.999773 17286.962921
#> EXTENSION 660 17286.994995 17286.933690
#> LO-REDUCTION 662 17286.982852 17286.933690
#> LO-REDUCTION 664 17286.977870 17286.933690
#> LO-REDUCTION 666 17286.975300 17286.933690
#> LO-REDUCTION 668 17286.974307 17286.933690
#> EXTENSION 670 17286.969127 17286.897589
#> LO-REDUCTION 672 17286.962921 17286.897589
#> LO-REDUCTION 674 17286.956414 17286.897589
#> EXTENSION 676 17286.943420 17286.853826
#> LO-REDUCTION 678 17286.937677 17286.853826
#> LO-REDUCTION 680 17286.935539 17286.853826
#> EXTENSION 682 17286.933690 17286.809961
#> LO-REDUCTION 684 17286.911841 17286.809961
#> LO-REDUCTION 686 17286.906427 17286.809961
#> EXTENSION 688 17286.897589 17286.764565
#> EXTENSION 690 17286.877846 17286.704552
#> LO-REDUCTION 692 17286.872431 17286.704552
#> EXTENSION 694 17286.853826 17286.604256
#> LO-REDUCTION 696 17286.822022 17286.604256
#> LO-REDUCTION 698 17286.811029 17286.604256
#> LO-REDUCTION 700 17286.809961 17286.604256
#> EXTENSION 702 17286.764565 17286.493497
#> LO-REDUCTION 704 17286.736274 17286.493497
#> EXTENSION 706 17286.704552 17286.355870
#> LO-REDUCTION 708 17286.657383 17286.355870
#> LO-REDUCTION 710 17286.628318 17286.355870
#> EXTENSION 712 17286.621506 17286.141094
#> LO-REDUCTION 714 17286.604256 17286.141094
#> LO-REDUCTION 716 17286.503365 17286.141094
#> LO-REDUCTION 718 17286.493497 17286.141094
#> EXTENSION 720 17286.414390 17285.877458
#> LO-REDUCTION 722 17286.366513 17285.877458
#> LO-REDUCTION 724 17286.355870 17285.877458
#> LO-REDUCTION 726 17286.251140 17285.877458
#> EXTENSION 728 17286.244105 17285.662233
#> EXTENSION 730 17286.223061 17285.393569
#> LO-REDUCTION 732 17286.141094 17285.393569
#> LO-REDUCTION 734 17285.992524 17285.393569
#> LO-REDUCTION 736 17285.964793 17285.393569
#> EXTENSION 738 17285.889261 17284.967393
#> LO-REDUCTION 740 17285.877458 17284.967393
#> EXTENSION 742 17285.662233 17284.823201
#> EXTENSION 744 17285.587027 17284.571260
#> EXTENSION 746 17285.430175 17284.208648
#> LO-REDUCTION 748 17285.411444 17284.208648
#> LO-REDUCTION 750 17285.393569 17284.208648
#> LO-REDUCTION 752 17285.061522 17284.208648
#> LO-REDUCTION 754 17284.967393 17284.208648
#> LO-REDUCTION 756 17284.823201 17284.208648
#> LO-REDUCTION 758 17284.663334 17284.208648
#> EXTENSION 760 17284.571260 17284.082158
#> EXTENSION 762 17284.471298 17283.933635
#> REFLECTION 764 17284.370237 17283.918499
#> LO-REDUCTION 766 17284.326906 17283.918499
#> LO-REDUCTION 768 17284.242090 17283.918499
#> LO-REDUCTION 770 17284.232223 17283.918499
#> EXTENSION 772 17284.208648 17283.684327
#> HI-REDUCTION 774 17284.082158 17283.684327
#> LO-REDUCTION 776 17284.006206 17283.684327
#> LO-REDUCTION 778 17283.954602 17283.684327
#> LO-REDUCTION 780 17283.943643 17283.684327
#> EXTENSION 782 17283.941150 17283.629046
#> LO-REDUCTION 784 17283.933635 17283.629046
#> EXTENSION 786 17283.918499 17283.432835
#> LO-REDUCTION 788 17283.855866 17283.432835
#> LO-REDUCTION 790 17283.737787 17283.432835
#> EXTENSION 792 17283.707141 17283.177089
#> LO-REDUCTION 794 17283.691961 17283.177089
#> LO-REDUCTION 796 17283.684327 17283.177089
#> LO-REDUCTION 798 17283.629046 17283.177089
#> EXTENSION 800 17283.480788 17283.019801
#> EXTENSION 802 17283.464836 17282.857567
#> LO-REDUCTION 804 17283.432835 17282.857567
#> LO-REDUCTION 806 17283.427379 17282.857567
#> REFLECTION 808 17283.273719 17282.810344
#> LO-REDUCTION 810 17283.192011 17282.810344
#> EXTENSION 812 17283.177089 17282.773026
#> LO-REDUCTION 814 17283.100216 17282.773026
#> EXTENSION 816 17283.019801 17282.431349
#> LO-REDUCTION 818 17282.924383 17282.431349
#> LO-REDUCTION 820 17282.882981 17282.431349
#> LO-REDUCTION 822 17282.857567 17282.431349
#> LO-REDUCTION 824 17282.826993 17282.431349
#> EXTENSION 826 17282.810344 17282.134774
#> LO-REDUCTION 828 17282.773026 17282.134774
#> LO-REDUCTION 830 17282.673630 17282.134774
#> EXTENSION 832 17282.551561 17281.917158
#> LO-REDUCTION 834 17282.507799 17281.917158
#> LO-REDUCTION 836 17282.441034 17281.917158
#> EXTENSION 838 17282.431349 17281.805083
#> EXTENSION 840 17282.328334 17281.485386
#> LO-REDUCTION 842 17282.207399 17281.485386
#> EXTENSION 844 17282.134774 17281.177471
#> LO-REDUCTION 846 17281.971962 17281.177471
#> LO-REDUCTION 848 17281.930907 17281.177471
#> LO-REDUCTION 850 17281.917158 17281.177471
#> LO-REDUCTION 852 17281.805083 17281.177471
#> LO-REDUCTION 854 17281.637799 17281.177471
#> LO-REDUCTION 856 17281.542150 17281.177471
#> LO-REDUCTION 858 17281.485386 17281.177471
#> LO-REDUCTION 860 17281.450381 17281.177471
#> EXTENSION 862 17281.448390 17280.945651
#> LO-REDUCTION 864 17281.369614 17280.945651
#> LO-REDUCTION 866 17281.303934 17280.945651
#> EXTENSION 868 17281.250802 17280.800450
#> LO-REDUCTION 870 17281.238533 17280.800450
#> LO-REDUCTION 872 17281.223261 17280.800450
#> EXTENSION 874 17281.177471 17280.488585
#> LO-REDUCTION 876 17281.024470 17280.488585
#> LO-REDUCTION 878 17280.950337 17280.488585
#> LO-REDUCTION 880 17280.945651 17280.488585
#> LO-REDUCTION 882 17280.939912 17280.488585
#> LO-REDUCTION 884 17280.816046 17280.488585
#> LO-REDUCTION 886 17280.800450 17280.488585
#> REFLECTION 888 17280.738456 17280.447101
#> REFLECTION 890 17280.664631 17280.390325
#> LO-REDUCTION 892 17280.577249 17280.390325
#> LO-REDUCTION 894 17280.566783 17280.390325
#> LO-REDUCTION 896 17280.538991 17280.390325
#> LO-REDUCTION 898 17280.511395 17280.390325
#> LO-REDUCTION 900 17280.488585 17280.390325
#> LO-REDUCTION 902 17280.459344 17280.390325
#> LO-REDUCTION 904 17280.447101 17280.390325
#> REFLECTION 906 17280.446459 17280.382631
#> LO-REDUCTION 908 17280.422497 17280.382631
#> LO-REDUCTION 910 17280.420917 17280.381469
#> LO-REDUCTION 912 17280.406656 17280.381469
#> LO-REDUCTION 914 17280.406429 17280.381469
#> LO-REDUCTION 916 17280.394455 17280.379401
#> LO-REDUCTION 918 17280.390325 17280.379401
#> HI-REDUCTION 920 17280.388261 17280.379401
#> REFLECTION 922 17280.387657 17280.375301
#> LO-REDUCTION 924 17280.387214 17280.375301
#> REFLECTION 926 17280.382631 17280.374067
#> HI-REDUCTION 928 17280.382496 17280.374067
#> REFLECTION 930 17280.381469 17280.373924
#> LO-REDUCTION 932 17280.379656 17280.373924
#> HI-REDUCTION 934 17280.379401 17280.373924
#> LO-REDUCTION 936 17280.377978 17280.373666
#> REFLECTION 938 17280.377712 17280.372196
#> EXTENSION 940 17280.375615 17280.367543
#> LO-REDUCTION 942 17280.375301 17280.367543
#> LO-REDUCTION 944 17280.374265 17280.367543
#> LO-REDUCTION 946 17280.374067 17280.367543
#> LO-REDUCTION 948 17280.373924 17280.367543
#> REFLECTION 950 17280.373666 17280.366638
#> REFLECTION 952 17280.372196 17280.366393
#> LO-REDUCTION 954 17280.370941 17280.366393
#> EXTENSION 956 17280.369039 17280.360078
#> LO-REDUCTION 958 17280.368943 17280.360078
#> LO-REDUCTION 960 17280.368258 17280.360078
#> LO-REDUCTION 962 17280.367543 17280.360078
#> LO-REDUCTION 964 17280.366638 17280.360078
#> LO-REDUCTION 966 17280.366395 17280.360078
#> EXTENSION 968 17280.366393 17280.358415
#> EXTENSION 970 17280.364882 17280.356231
#> EXTENSION 972 17280.364704 17280.352703
#> EXTENSION 974 17280.361998 17280.350130
#> EXTENSION 976 17280.360738 17280.346336
#> LO-REDUCTION 978 17280.360395 17280.346336
#> LO-REDUCTION 980 17280.360078 17280.346336
#> REFLECTION 982 17280.358415 17280.344675
#> LO-REDUCTION 984 17280.356231 17280.344675
#> LO-REDUCTION 986 17280.352703 17280.344675
#> LO-REDUCTION 988 17280.350130 17280.344675
#> LO-REDUCTION 990 17280.349130 17280.344675
#> EXTENSION 992 17280.348501 17280.341423
#> LO-REDUCTION 994 17280.347252 17280.341423
#> LO-REDUCTION 996 17280.346336 17280.341423
#> LO-REDUCTION 998 17280.346022 17280.341423
#> LO-REDUCTION 1000 17280.345873 17280.341423
#> Exiting from Nelder Mead minimizer
#> 1002 function evaluations used
# extract results
# regression coefficient vector
res2$beta
#> [1] -2.64077894 0.62582753 -0.08293688 0.53247068 -0.12437312 -0.16298836
#> [7] -1.10550227
# check likelihood
-ll(res2$beta)
#> [1] -17280.34
# number of calls to log lik function
# since optim does not return the number of
# iterations
res2$iter
#> function gradient
#> 1002 NA
# optim does not calculated working weights
head(res2$weights)
#> [1] 1
# }