fit2ts()
fits a smooth hazard model with two time scales.
Three methods are implemented for the search of the optimal smoothing
parameters (and therefore optimal model): a numerical optimization of the
AIC or BIC of the model, a search for the minimum AIC or BIC of the
model over a grid of log_10
values for the smoothing parameters, and a
solution that uses a sparse mixed model representation of the P-spline model to
estimate the smoothing parameters.
Construction of the B-splines bases and of the penalty matrix is
incorporated within the function. If a matrix of covariates is provided,
the function will estimate a model with covariates.
Arguments
- data2ts
(optional) an object of class created by the function
prepare_data()
. Proving this input is the easiest way to use the functionfit2ts
. However, the user can also provide the input data together with a list of bins, as explained by the following parameters' descriptions.- Y
A matrix (or 3d-array) of event counts of dimension nu by ns (or nu by ns by n).
- R
A matrix (or 3d-array) of exposure times of dimension nu by ns (or nu by ns by n).
- Z
(optional) A regression matrix of covariates values of dimensions n by p.
- bins
a list with the specification for the bins. This is created by the function
prepare_data
. If a list prepared externally from such function if provided, it should contain the following elements: *bins_u
A vector of bins extremes for the time scaleu
. *midu
A vector with the midpoints of the bins overu
. *nu
The number of bins overu
. *bins_s
A vector of bins extremes for the time scales
. *mids
A vector with the midpoints of the bins overs
. *ns
The number of bins overs
.- Bbases_spec
A list with the specification for the B-splines basis with the following elements:
bdeg
The degree of the B-splines basis. Default is 3 (for cubic B-splines).nseg_u
The number of segments for the B-splines overu
. Default is 10.min_u
(optional) The lower limit of the domain ofBu
. Default ismin(bins_u)
.max_u
(optional) The upper limit of the domain ofBu
. Default ismax(bins_u)
.nseg_s
The number of segments for the B-splines overs
. Default is 10.min_s
(optional) The lower limit of the domain ofBs
. Default ismin(bins_s)
.max_s
(optional) The upper limit of the domain ofBs
. Default ismax(bins_s)
.
- pord
The order of the penalty. Default is 2.
- optim_method
The method to be used for optimization:
"ucminf"
(default) for the numerical optimization of the AIC (or BIC),"grid_search"
for a grid search of the minimum AIC (or BIC) over a grid oflog_10(rho_u)
andlog_10(rho_s)
values, or"LMMsolver"
to solve the model as sparse linear mixed model using the package LMMsolver.- optim_criterion
The criterion to be used for optimization:
"aic"
(default) or"bic"
. BIC penalized model complexity more strongly than AIC, so that its usage is recommended when a smoother fit is preferable (see also Camarda, 2012).- lrho
A vector of two elements if
optim_method == "ucminf"
. Default isc(0,0)
. A list of two vectors of values forlog_10(rho_u)
andlog_10(rho_s)
ifoptim_method == "grid_search"
. In the latter case, if a list with two vectors is not provided, a default sequence of values is used for bothlog_10(rho_u)
andlog_10(rho_s)
.- Wprior
An optional matrix of a-priori weights.
- ridge
A ridge penalty parameter: default is 0. This is useful when, in some cases the algorithm shows convergence problems. In this case, set to a small number, for example
1e-4
.- control_algorithm
A list with optional values for the parameters of the iterative processes:
maxiter
The maximum number of iteration for the IWSL algorithm. Default is 20.conv_crit
The convergence criteria, expressed as difference between estimates at iteration i and i+1. Default is1e-5
.verbose
A Boolean. Default isFALSE
. IfTRUE
monitors the iteration process.monitor_ev
A Boolean. Default isFALSE
. IfTRUE
monitors the evaluation of the model over thelog_10(rho_s)
values.
- par_gridsearch
A list of parameters for the grid_search:
plot_aic
A Boolean. Default isFALSE
. IfTRUE
, plot the AIC values over the grid oflog_10(rho_u)
andlog_10(rho_s)
values.plot_bic
A Boolean. Default isFALSE
. IfTRUE
, plot the BIC values over the grid oflog_10(rho_u)
andlog_10(rho_s)
values.return_aic
A Boolean. Default isTRUE
. Return the AIC values.return_bic
A Boolean. Default isTRUE
. Return the BIC values.col
The color palette to be used for the AIC/BIC plot. Default isgrDevices::gray.colors(n=10)
.plot_contour
A Boolean. Default isTRUE
. Adds white contour lines to the AIC/BIC plot.mark_optimal
A Boolean. Default isTRUE
. If the plot of the AIC or BIC values is returned, marks the optimal combination oflog_10(rho_u)
andlog_10(rho_s)
in the plot.main_aic
The title of the AIC plot. Default is"AIC grid"
.main_bic
The title of the BIC plot. Default is"BIC grid"
.
Value
An object of class haz2ts
, or of class haz2tsLMM
.
For objects of class haz2ts
this is
optimal_model
A list with :Alpha
The matrix of estimated P-splines coefficients of dimension \(c_u\) by \(c_s\).Cov_alpha
The variance-covariance matrix of theAlpha
coefficients, of dimension \(c_uc_s\) by \(c_uc_s\).beta
The vector of length p of estimated covariates coefficients (if model with covariates).Cov_beta
The variance-covariance matrix of thebeta
coefficients, of dimension \(p\) by \(p\) (if model with covariates).SE_beta
The vector of length \(p\) of estimated Standard Errors for thebeta
coefficients (if model with covariates)..Eta
orEta0
The matrix of values of the (baseline) linear predictor (log-hazard) of dimension \(n_u\) by \(n_s\).H
The hat-matrix.deviance
The deviance.ed
The effective dimension of the model.aic
The value of the AIC.bic
The value of the BIC.Bbases
a list with the B-spline basesBu
andBs
optimal_logrho
A vector with the optimal values oflog10(rho_u)
andlog10(rho_s)
.P_optimal
The optimal penalty matrix P.AIC
(ifpar_gridsearch$return_aic == TRUE
) The matrix of AIC values.BIC
(ifpar_gridsearch$return_bic == TRUE
) The matrix of BIC values.
Objects of class haz2tsLMM
have a slight different structure. They are
a list with:
optimal_model
an object of classLMMsolve
AIC_BIC
a list with, among other things, the AIC and BIC values and the ED of the modeln_events
the number of eventsnu
the number of bins over the u-axisns
the number of bins over the s-axiscu
the number of B-splines over the u-axiscs
the number of B-splines over the s-axiscovariates
an indicator for PH model
Details
Some functions from the R-package LMMsolver
are used here.
We refer the interested readers to https://biometris.github.io/LMMsolver/
for more details on LMMsolver
and its usage.
References
Boer, Martin P. 2023. “Tensor Product P-Splines Using a Sparse Mixed Model Formulation.” Statistical Modelling 23 (5-6): 465–79. https://doi.org/10.1177/1471082X231178591. Carollo, Angela, Paul H. C. Eilers, Hein Putter, and Jutta Gampe. 2023. “Smooth Hazards with Multiple Time Scales.” arXiv Preprint: https://arxiv.org/abs/http://arxiv.org/abs/2305.09342v1
Examples
# Create some fake data - the bare minimum
id <- 1:20
u <- c(5.43, 3.25, 8.15, 5.53, 7.28, 6.61, 5.91, 4.94, 4.25, 3.86, 4.05, 6.86,
4.94, 4.46, 2.14, 7.56, 5.55, 7.60, 6.46, 4.96)
s <- c(0.44, 4.89, 0.92, 1.81, 2.02, 1.55, 3.16, 6.36, 0.66, 2.02, 1.22, 3.96,
7.07, 2.91, 3.38, 2.36, 1.74, 0.06, 5.76, 3.00)
ev <- c(1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1)#'
fakedata <- as.data.frame(cbind(id, u, s, ev))
fakedata2ts <- prepare_data(data = fakedata,
u = "u",
s_out = "s",
ev = "ev",
ds = .5)
#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> `s_in = NULL`. I will use `s_in = 0` for all observations.
# Fit a fake model - not optimal smoothing
fit2ts(fakedata2ts,
optim_method = "grid_search",
lrho = list(seq(1, 1.5, .5), seq(1, 1.5, .5)))
#> $optimal_model
#> $optimal_model$Alpha
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] -1.808081 -1.778454 -1.747655 -1.714188 -1.676995 -1.635863 -1.591420
#> [2,] -1.810935 -1.784563 -1.757348 -1.728088 -1.696004 -1.660774 -1.622757
#> [3,] -1.817510 -1.791949 -1.766135 -1.739834 -1.712879 -1.684530 -1.654272
#> [4,] -1.834424 -1.806477 -1.778659 -1.753044 -1.730798 -1.709777 -1.688428
#> [5,] -1.869347 -1.837880 -1.806883 -1.780993 -1.760493 -1.744151 -1.731201
#> [6,] -1.930121 -1.897808 -1.867242 -1.840892 -1.818780 -1.803498 -1.794386
#> [7,] -2.024095 -1.990602 -1.959814 -1.931692 -1.909264 -1.893425 -1.880286
#> [8,] -2.153502 -2.119333 -2.085794 -2.053752 -2.027618 -2.006188 -1.984643
#> [9,] -2.309822 -2.273154 -2.235742 -2.198121 -2.164026 -2.132498 -2.100128
#> [10,] -2.482343 -2.440158 -2.397205 -2.353126 -2.308713 -2.264372 -2.219740
#> [11,] -2.663203 -2.612061 -2.560195 -2.506952 -2.452358 -2.396920 -2.341158
#> [12,] -2.847376 -2.785381 -2.722831 -2.659233 -2.594571 -2.529106 -2.463244
#> [13,] -3.032281 -2.958842 -2.885174 -2.811032 -2.736301 -2.661030 -2.585416
#> [,8] [,9] [,10] [,11] [,12] [,13]
#> [1,] -1.544797 -1.497105 -1.449122 -1.401240 -1.353546 -1.305960
#> [2,] -1.583028 -1.542481 -1.501600 -1.460609 -1.419588 -1.378562
#> [3,] -1.622317 -1.589080 -1.555038 -1.520512 -1.485716 -1.450824
#> [4,] -1.665047 -1.638952 -1.610843 -1.581660 -1.552074 -1.522421
#> [5,] -1.715769 -1.695311 -1.670769 -1.644890 -1.619062 -1.593330
#> [6,] -1.782128 -1.762738 -1.737458 -1.712092 -1.687932 -1.663738
#> [7,] -1.864086 -1.842082 -1.815222 -1.787567 -1.760513 -1.733533
#> [8,] -1.960363 -1.932365 -1.901225 -1.868580 -1.835641 -1.802749
#> [9,] -2.065660 -2.029052 -1.990645 -1.951147 -1.911221 -1.871208
#> [10,] -2.174388 -2.128266 -2.081438 -2.034069 -1.986385 -1.938584
#> [11,] -2.285289 -2.229362 -2.173361 -2.117260 -2.061067 -2.004826
#> [12,] -2.397341 -2.331597 -2.266068 -2.200714 -2.135465 -2.070252
#> [13,] -2.509740 -2.434257 -2.359111 -2.284312 -2.209765 -2.135328
#>
#> $optimal_model$Cov_Alpha
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 5.761239861 4.62991556 3.545485255 2.53087680 1.595555474
#> [2,] 4.629915557 3.81896830 2.989514151 2.18496871 1.426807208
#> [3,] 3.545485255 2.98951415 2.428364416 1.83827864 1.258705549
#> [4,] 2.530876803 2.18496871 1.838278643 1.48187314 1.088301679
#> [5,] 1.595555474 1.42680721 1.258705549 1.08830168 0.904070823
#> [6,] 0.737683068 0.72195298 0.707258365 0.69327885 0.675694085
#> [7,] -0.054796528 0.06584269 0.187495089 0.31111994 0.436178293
#> [8,] -0.799926293 -0.55317336 -0.305602595 -0.05557394 0.198728358
#> [9,] -1.516474711 -1.14887847 -0.780728455 -0.40997615 -0.033094964
#> [10,] -2.219729628 -1.73315275 -1.246306028 -0.75684495 -0.259818193
#> [11,] -2.919324024 -2.31379949 -1.708287692 -1.10018220 -0.483216556
#> [12,] -3.619250348 -2.89428203 -2.169602044 -1.44234394 -0.704954646
#> [13,] -4.320040440 -3.47529136 -2.631101741 -1.78434080 -0.926169984
#> [14,] 4.431231358 3.57196388 2.740264773 1.95822010 1.237215125
#> [15,] 3.568103531 2.93545792 2.301694713 1.68617228 1.105272580
#> [16,] 2.734131637 2.29908537 1.860033535 1.41274264 0.973146587
#> [17,] 1.951041165 1.68186643 1.410721192 1.13137410 0.837043454
#> [18,] 1.230976932 1.10089689 0.970341332 0.83583899 0.689404088
#> [19,] 0.575635450 0.56387704 0.552352016 0.53984453 0.521977097
#> [20,] -0.024389926 0.06756953 0.160030107 0.25317083 0.345724255
#> [21,] -0.584377114 -0.39786823 -0.210806956 -0.02214658 0.169083457
#> [22,] -1.120383111 -0.84424745 -0.567606975 -0.28881908 -0.005204729
#> [23,] -1.645388548 -1.28153260 -0.917257785 -0.55044952 -0.176984513
#> [24,] -2.167566825 -1.71621438 -1.264538415 -0.80999766 -0.347136397
#> [25,] -2.689495583 -2.15048477 -1.611244849 -1.06881902 -0.516457514
#> [26,] -3.211863931 -2.58502830 -1.958055912 -1.32757449 -0.685547458
#> [27,] 3.118001444 2.51985217 1.936672080 1.38580337 0.878665422
#> [28,] 2.513658885 2.06381371 1.619611789 1.18985071 0.784806191
#> [29,] 1.926828465 1.61542198 1.303199194 0.99295732 0.690227437
#> [30,] 1.374497953 1.18312096 0.989861235 0.79235415 0.591599274
#> [31,] 0.869289967 0.77831518 0.686154022 0.58991282 0.486144249
#> [32,] 0.415283449 0.40784786 0.399967041 0.38992792 0.374341455
#> [33,] 0.006216073 0.06991864 0.133652512 0.19695044 0.258200905
#> [34,] -0.369838702 -0.24310581 -0.116068549 0.01177907 0.140696776
#> [35,] -0.725929800 -0.54079362 -0.355192880 -0.16786540 0.023077248
#> [36,] -1.072653478 -0.83114712 -0.589067984 -0.34451709 -0.094169434
#> [37,] -1.416812055 -1.11943354 -0.821392677 -0.52020528 -0.211209672
#> [38,] -1.760118860 -1.40702216 -1.053178342 -0.69553696 -0.328143426
#> [39,] -2.103409783 -1.69459507 -1.284948807 -0.87085857 -0.445089435
#> [40,] 1.828892951 1.47919957 1.137170972 0.81419854 0.519684765
#> [41,] 1.473257745 1.20741250 0.947472948 0.69863547 0.466628048
#> [42,] 1.127680918 0.94341295 0.760676999 0.58305970 0.412739722
#> [43,] 0.803792695 0.69254324 0.580405537 0.46756041 0.356146382
#> [44,] 0.512109860 0.46156858 0.409769516 0.35505823 0.296944052
#> [45,] 0.257413246 0.25528018 0.252309103 0.24687639 0.237131711
#> [46,] 0.037020145 0.07338003 0.109418869 0.14431788 0.176673329
#> [47,] -0.157021485 -0.08917721 -0.021224756 0.04693850 0.115153449
#> [48,] -0.334144588 -0.23920496 -0.143814857 -0.04702286 0.052413468
#> [49,] -0.502389783 -0.38264589 -0.262160676 -0.13921160 -0.011194349
#> [50,] -0.667376992 -0.52372786 -0.379069879 -0.23095432 -0.075470257
#> [51,] -0.830981414 -0.66383561 -0.495422667 -0.32258969 -0.140155872
#> [52,] -0.994199343 -0.80368575 -0.611649281 -0.41424021 -0.205022445
#> [53,] 0.565365433 0.45292147 0.343794207 0.24410682 0.160166100
#> [54,] 0.448874896 0.36535435 0.285735880 0.21336641 0.151191670
#> [55,] 0.337415662 0.28303917 0.230789182 0.18330400 0.141630455
#> [56,] 0.237873851 0.20992094 0.182013114 0.15520497 0.130944151
#> [57,] 0.157376218 0.14968820 0.141100677 0.13103561 0.120097837
#> [58,] 0.100538390 0.10541551 0.109396701 0.11132461 0.110604343
#> [59,] 0.067551878 0.07779994 0.087558512 0.09599415 0.102238060
#> [60,] 0.054473326 0.06434824 0.074229247 0.08402197 0.093474779
#> [61,] 0.055946848 0.06133472 0.067209255 0.07432879 0.083500798
#> [62,] 0.066671911 0.06497707 0.064220619 0.06601685 0.072374703
#> [63,] 0.081849312 0.07175351 0.063028074 0.05812424 0.060274537
#> [64,] 0.098822853 0.07974051 0.062449697 0.05022188 0.047501433
#> [65,] 0.116313871 0.08805867 0.062012182 0.04225844 0.034443718
#> [66,] -0.674519235 -0.55870849 -0.442484987 -0.32387247 -0.199806786
#> [67,] -0.561068395 -0.46501067 -0.367367565 -0.26664075 -0.161736287
#> [68,] -0.445868434 -0.36865321 -0.289975278 -0.20846994 -0.123842542
#> [69,] -0.325997431 -0.26737202 -0.208364379 -0.14809503 -0.085976266
#> [70,] -0.197980484 -0.15971459 -0.121944333 -0.08471166 -0.047401328
#> [71,] -0.057526114 -0.04337289 -0.029943700 -0.01788757 -0.007157143
#> [72,] 0.097104982 0.08266173 0.067754913 0.05177382 0.034381011
#> [73,] 0.265412434 0.21808892 0.170794248 0.12345344 0.075942370
#> [74,] 0.446072788 0.36218531 0.278895509 0.19691819 0.116840533
#> [75,] 0.636495282 0.51325365 0.391191694 0.27190985 0.156974812
#> [76,] 0.832286356 0.66810240 0.505674249 0.34751092 0.196264074
#> [77,] 1.030153223 0.82434295 0.620856578 0.42310961 0.234865305
#> [78,] 1.228564470 0.98092396 0.736171331 0.49862404 0.273158287
#> [79,] -1.894358912 -1.55713397 -1.221722200 -0.88938855 -0.559989449
#> [80,] -1.559705326 -1.28671556 -1.014220596 -0.74274359 -0.472755388
#> [81,] -1.225081342 -1.01531698 -0.805328019 -0.59513410 -0.385274099
#> [82,] -0.890697045 -0.74258987 -0.594378666 -0.44587473 -0.297262904
#> [83,] -0.556488628 -0.46907689 -0.381979906 -0.29522267 -0.208613520
#> [84,] -0.218614483 -0.19269907 -0.167277775 -0.14266863 -0.118702653
#> [85,] 0.124997716 0.08736131 0.049428474 0.01089445 -0.028246517
#> [86,] 0.476360217 0.37245320 0.268724552 0.16528431 0.062202533
#> [87,] 0.837678892 0.66446328 0.492046752 0.32125152 0.152602884
#> [88,] 1.208571324 0.96333927 0.719586314 0.47900857 0.242879532
#> [89,] 1.585001688 1.26614096 0.949454670 0.63757918 0.332695752
#> [90,] 1.963628302 1.57043508 1.180110691 0.79624985 0.422005356
#> [91,] 2.342823428 1.87509119 1.410919369 0.95486253 0.511060496
#> [92,] -3.098257301 -2.54460052 -1.994661512 -1.45236552 -0.920068876
#> [93,] -2.549873768 -2.10211591 -1.656666504 -1.21609143 -0.782389676
#> [94,] -2.002514688 -1.65969372 -1.318039586 -0.97904887 -0.644233863
#> [95,] -1.458394880 -1.21846864 -0.979126379 -0.74111860 -0.505385564
#> [96,] -0.919682240 -0.78028732 -0.641324831 -0.50316751 -0.366180965
#> [97,] -0.383795224 -0.34376011 -0.304068355 -0.26494779 -0.226419951
#> [98,] 0.150715439 0.09133022 0.031873624 -0.02769206 -0.087273125
#> [99,] 0.687498665 0.52750909 0.367946391 0.20919315 0.051467561
#> [100,] 1.231423730 0.96865390 0.706974741 0.44743892 0.190588910
#> [101,] 1.783537778 1.41572452 1.049755660 0.68753114 0.330148597
#> [102,] 2.340497805 1.86626145 1.394658616 0.92852966 0.469691868
#> [103,] 2.899554570 2.31825550 1.740387213 1.16976644 0.609013815
#> [104,] 3.459189570 2.77063374 2.086305626 1.41100652 0.748187056
#> [105,] -4.290280530 -3.52364028 -2.762468446 -2.01301905 -1.279801909
#> [106,] -3.533956746 -2.91303845 -2.296059567 -1.68755602 -1.091057066
#> [107,] -2.779419390 -2.30330632 -1.829731829 -1.36172214 -0.901874415
#> [108,] -2.029797988 -1.69636121 -1.364399225 -1.03573166 -0.712099655
#> [109,] -1.287925243 -1.09432108 -0.901514336 -0.71044915 -0.522093104
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#> [,16] [,17] [,18] [,19] [,20]
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#> [14,] 2.160805946 1.540739160 9.725666e-01 0.457935021 -0.010556959
#> [15,] 1.816326448 1.327622216 8.702552e-01 0.449463829 0.062426854
#> [16,] 1.472363580 1.114688416 7.679486e-01 0.441081832 0.135541214
#> [17,] 1.114688416 0.898724170 6.636776e-01 0.431678879 0.208590498
#> [18,] 0.767948649 0.663677580 5.532941e-01 0.419058753 0.280852941
#> [19,] 0.441081832 0.431678879 4.190588e-01 0.398236171 0.350146558
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#> [27,] 1.588739071 1.131054469 7.143027e-01 0.340158697 0.003117099
#> [28,] 1.333528879 0.974643460 6.405062e-01 0.335479403 0.057379786
#> [29,] 1.078205323 0.818745940 5.669260e-01 0.330778522 0.111499756
#> [30,] 0.817500485 0.659694064 4.917066e-01 0.324965222 0.165026976
#> [31,] 0.565378688 0.491091436 4.107837e-01 0.316362312 0.217502571
#> [32,] 0.330278822 0.324757517 3.164233e-01 0.300337961 0.267416941
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#> [40,] 1.018912726 0.722462318 4.562740e-01 0.222171990 0.016425485
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#> [44,] 0.367395628 0.322584083 2.730161e-01 0.216870335 0.157017602
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#> [71,] 0.017053119 0.026989993 3.494703e-02 0.040642616 0.044312867
#> [72,] 0.057231338 0.054971112 5.162938e-02 0.046718290 0.040027950
#> [73,] 0.103339223 0.085348228 6.774057e-02 0.050553032 0.033514611
#> [74,] 0.154306766 0.117859699 8.350567e-02 0.052178617 0.024281776
#> [75,] 0.208723637 0.151946858 9.911174e-02 0.052193542 0.012647558
#> [76,] 0.264795426 0.186679274 1.144324e-01 0.051143855 -0.000539753
#> [77,] 0.321381341 0.221494422 1.294367e-01 0.049450724 -0.014569169
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#> [86,] 0.169076539 0.111436852 5.433385e-02 -0.002115811 -0.057927852
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#> [88,] 0.436484125 0.294785571 1.571197e-01 0.024901401 -0.101305349
#> [89,] 0.573701722 0.388060347 2.083933e-01 0.036966114 -0.125003429
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#> [100,] 0.449037067 0.287872487 1.291749e-01 -0.026614314 -0.179763122
#> [101,] 0.665496513 0.438573183 2.159271e-01 -0.001523650 -0.214068080
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#> [103,] 1.102437651 0.741870913 3.894641e-01 0.047361194 -0.284345543
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#> [115,] 1.194608765 0.792747164 3.974147e-01 0.009411097 -0.372721042
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#> [127,] 1.126804576 0.728516163 3.353959e-01 -0.052527046 -0.437314485
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#> [152,] 1.048220359 0.636596635 2.296456e-01 -0.173299937 -0.575033297
#> [153,] 1.590589685 1.020213502 4.562225e-01 -0.102235344 -0.659162890
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#> [,21] [,22] [,23] [,24] [,25]
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#> [11,] 1.1728857492 1.748078353 2.353567934 2.974262228 3.589808399
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#> [,41] [,42] [,43] [,44] [,45]
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#> [57,] 0.259054616 0.237298653 2.151185e-01 1.879942e-01 0.147607908
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#> [59,] 0.020491989 0.047992272 7.603098e-02 1.047719e-01 0.133116467
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#> [67,] 0.604430937 0.462967698 3.287507e-01 2.068915e-01 0.098818833
#> [68,] 0.464315834 0.373478018 2.808031e-01 1.902785e-01 0.106001375
#> [69,] 0.331228158 0.281989329 2.296065e-01 1.722071e-01 0.112991923
#> [70,] 0.210716632 0.192792419 1.734671e-01 1.492854e-01 0.117905694
#> [71,] 0.104428233 0.110099062 1.156025e-01 1.191012e-01 0.117071827
#> [72,] 0.011495521 0.035776541 6.038231e-02 8.508915e-02 0.108415735
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#> [79,] 0.587745412 0.432260678 2.914549e-01 1.680322e-01 0.060644844
#> [80,] 0.474097567 0.360447436 2.535195e-01 1.559522e-01 0.068378505
#> [81,] 0.363113580 0.288239690 2.146683e-01 1.433931e-01 0.076020084
#> [82,] 0.257988736 0.216664631 1.737201e-01 1.289599e-01 0.082834083
#> [83,] 0.162330275 0.147420682 1.309360e-01 1.110002e-01 0.087203536
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#> [93,] 0.344489653 0.258158578 1.779237e-01 1.046041e-01 0.037719663
#> [94,] 0.262121568 0.204195846 1.489098e-01 9.608931e-02 0.045478846
#> [95,] 0.184347972 0.151686085 1.189489e-01 8.595199e-02 0.052119180
#> [96,] 0.113370830 0.101473600 8.852853e-02 7.363970e-02 0.056601511
#> [97,] 0.049984590 0.054209238 5.762210e-02 5.915604e-02 0.058181016
#> [98,] -0.005971602 0.010704574 2.708512e-02 4.274493e-02 0.057162153
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#> [106,] 0.215499265 0.156301263 1.022280e-01 5.288650e-02 0.006729469
#> [107,] 0.161297714 0.121027441 8.376860e-02 4.873634e-02 0.014515855
#> [108,] 0.110257108 0.087188295 6.512190e-02 4.352149e-02 0.021276897
#> [109,] 0.063631845 0.055222503 4.656631e-02 3.713539e-02 0.026489963
#> [110,] 0.021893906 0.025210923 2.797528e-02 2.962464e-02 0.030010576
#> [111,] -0.015063990 -0.002626550 9.457772e-03 2.100218e-02 0.032068133
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#> [119,] 0.087025019 0.054825601 2.656875e-02 9.220459e-04 -0.024570435
#> [120,] 0.060470060 0.038374813 1.914553e-02 1.507917e-03 -0.016689203
#> [121,] 0.035629678 0.022970922 1.192150e-02 1.608386e-03 -0.009490011
#> [122,] 0.013091117 0.008783217 5.000965e-03 1.266081e-03 -0.003133357
#> [123,] -0.006938168 -0.004325323 -1.763753e-03 5.133885e-04 0.002472065
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#> [126,] -0.054276197 -0.038299729 -2.240376e-02 -5.187121e-03 0.015183851
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#> [,56] [,57] [,58] [,59] [,60]
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#> [110,] 0.049013650 0.009051199 -0.030915413 0.596859606 0.54859695
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#> [138,] 1.440309823 1.705604116 1.970815370 -1.414590838 -1.07029777
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#> [127,] 8.573223805 10.611982619 1.265009e+01 14.68727017
#> [128,] 10.654495441 13.286506140 1.592401e+01 18.56308065
#> [129,] 12.739535317 15.972385119 1.921706e+01 22.46774232
#> [130,] 14.824829484 18.661457849 2.251819e+01 26.38277910
#> [131,] -10.993199449 -14.351586831 -1.770276e+01 -21.05164843
#> [132,] -8.696058537 -11.437186739 -1.417228e+01 -16.90540859
#> [133,] -6.397878194 -8.521455009 -1.064017e+01 -12.75726326
#> [134,] -4.096025885 -5.600909573 -7.102135e+00 -8.60207401
#> [135,] -1.785593106 -2.668944074 -3.549907e+00 -4.42993959
#> [136,] 0.540745050 0.284384777 2.899313e-02 -0.22587025
#> [137,] 2.891313273 3.270889758 3.649743e+00 4.02862515
#> [138,] 5.267038094 6.296044551 7.322263e+00 8.34783359
#> [139,] 7.663288974 9.359411895 1.105062e+01 12.74027729
#> [140,] 10.071312693 12.453125549 1.482979e+01 17.20408806
#> [141,] 12.482427358 15.563256252 1.864520e+01 21.72575078
#> [142,] 14.891733709 18.678918635 2.247974e+01 26.28554912
#> [143,] 17.299601360 21.794465329 2.632089e+01 30.86154787
#> [144,] -12.605695356 -16.456442131 -2.029892e+01 -24.13879239
#> [145,] -9.971240403 -13.116701757 -1.625508e+01 -19.39119021
#> [146,] -7.334043308 -9.773604206 -1.220728e+01 -14.63899584
#> [147,] -4.689161140 -6.420893816 -8.147942e+00 -9.87334889
#> [148,] -2.030198033 -3.050143328 -4.066651e+00 -5.08184088
#> [149,] 0.649560487 0.348072122 4.864375e-02 -0.24981985
#> [150,] 3.355343778 3.782502462 4.210040e+00 4.63810685
#> [151,] 6.086212249 7.256755653 8.425359e+00 9.59386852
#> [152,] 8.834183238 10.768076090 1.269655e+01 14.62389413
#> [153,] 11.584632503 14.306736146 1.701879e+01 19.72793869
#> [154,] 14.321552734 17.855743501 2.137957e+01 24.89822203
#> [155,] 17.050217348 21.396764501 2.575920e+01 30.11911304
#> [156,] 19.776492075 24.933296908 3.013718e+01 35.36699251
#> [157,] -14.219623903 -18.563029699 -2.289711e+01 -27.22827466
#> [158,] -11.247267790 -14.797311323 -1.833923e+01 -21.87855944
#> [159,] -8.270381273 -11.026115038 -1.377493e+01 -16.52144986
#> [160,] -5.281760175 -7.240501669 -9.193517e+00 -11.14453102
#> [161,] -2.273653722 -3.430388455 -4.582605e+00 -5.73310666
#> [162,] 0.759993185 0.413117113 6.946228e-02 -0.27277379
#> [163,] 3.821595708 4.295885182 4.771834e+00 5.24885690
#> [164,] 6.908407970 8.219450655 9.529930e+00 10.84099376
#> [165,] 10.010636477 12.179730647 1.434442e+01 16.50881838
#> [166,] 13.108932552 16.166368493 1.921129e+01 22.25406434
#> [167,] 16.166368493 20.159551169 2.412042e+01 28.07433083
#> [168,] 19.211294033 24.120423206 2.905057e+01 33.96002281
#> [169,] 22.254064336 28.074330829 3.396002e+01 39.89004232
#>
#> $optimal_model$deviance
#> [1] 34.45564
#>
#> $optimal_model$Eta
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] -1.778551 -1.760495 -1.741830 -1.722388 -1.702017 -1.680592 -1.658093
#> [2,] -1.786083 -1.768456 -1.750839 -1.733267 -1.715598 -1.697546 -1.678890
#> [3,] -1.798317 -1.780091 -1.762709 -1.746439 -1.731141 -1.716340 -1.701644
#> [4,] -1.819980 -1.800719 -1.783089 -1.767399 -1.753535 -1.741127 -1.729831
#> [5,] -1.856663 -1.836869 -1.818952 -1.803144 -1.789556 -1.778275 -1.769092
#> [6,] -1.911684 -1.891752 -1.873467 -1.857165 -1.843252 -1.832080 -1.823291
#> [7,] -1.986314 -1.965837 -1.946683 -1.929548 -1.914961 -1.902968 -1.892728
#> [8,] -2.080672 -2.058896 -2.038053 -2.019115 -2.002585 -1.988137 -1.974658
#> [9,] -2.191019 -2.167326 -2.144058 -2.122194 -2.102170 -2.083572 -2.065381
#> [10,] -2.312181 -2.285993 -2.259730 -2.234054 -2.209296 -2.185237 -2.161273
#> [11,] -2.439286 -2.409767 -2.379842 -2.349744 -2.319661 -2.289629 -2.259520
#> [12,] -2.568825 -2.534872 -2.500388 -2.465401 -2.430013 -2.394346 -2.358493
#> [13,] -2.699209 -2.660071 -2.620444 -2.580305 -2.539708 -2.498759 -2.457582
#> [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,] -1.634622 -1.610383 -1.585582 -1.560392 -1.534953 -1.509355 -1.483661
#> [2,] -1.659501 -1.639338 -1.618439 -1.596910 -1.574903 -1.552561 -1.530000
#> [3,] -1.686594 -1.670702 -1.653714 -1.635628 -1.616655 -1.597086 -1.577177
#> [4,] -1.718818 -1.706887 -1.693348 -1.678041 -1.661275 -1.643646 -1.625657
#> [5,] -1.760803 -1.751485 -1.740021 -1.726104 -1.710175 -1.693286 -1.676241
#> [6,] -1.815459 -1.806483 -1.795137 -1.781069 -1.764779 -1.747543 -1.730304
#> [7,] -1.882859 -1.871803 -1.858640 -1.843115 -1.825630 -1.807191 -1.788582
#> [8,] -1.960978 -1.946160 -1.929687 -1.911445 -1.891698 -1.871045 -1.850009
#> [9,] -2.046722 -2.027081 -2.006241 -1.984193 -1.961099 -1.937271 -1.913016
#> [10,] -2.136896 -2.111837 -2.086025 -2.059482 -2.032297 -2.004622 -1.976619
#> [11,] -2.229188 -2.198530 -2.167522 -2.136170 -2.104504 -2.072579 -2.040456
#> [12,] -2.322504 -2.286400 -2.250193 -2.213890 -2.177497 -2.141019 -2.104467
#> [13,] -2.416285 -2.374947 -2.333617 -2.292319 -2.251059 -2.209833 -2.168629
#> [,15]
#> [1,] -1.457909
#> [2,] -1.507309
#> [3,] -1.557107
#> [4,] -1.607594
#> [5,] -1.659359
#> [6,] -1.713368
#> [7,] -1.770128
#> [8,] -1.828902
#> [9,] -1.888577
#> [10,] -1.948436
#> [11,] -2.008206
#> [12,] -2.067858
#> [13,] -2.127438
#>
#> $optimal_model$H
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 0.13798396 0.09718468 0.07105068 0.06001527 0.064696812 0.08595856
#> [2,] 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000 0.00000000
#> [3,] 0.06427998 0.04554938 0.03346541 0.02805869 0.029439633 0.03780771
#> [4,] 0.08587846 0.06180666 0.03323531 0.01938154 0.000790924 0.00000000
#> [5,] 0.05974780 0.02903024 0.01682527 0.01421012 0.014029211 0.01329355
#> [6,] 0.07143929 0.05355587 0.04182638 0.03569660 0.034735722 0.03864328
#> [7,] 0.06765455 0.03517543 0.02756848 0.01311544 0.000000000 0.00000000
#> [8,] 0.02764152 0.02036130 0.01578645 0.01383136 0.014456664 0.01766521
#> [9,] 0.07036295 0.05105152 0.03913943 0.01907478 0.018922460 0.02444899
#> [10,] 0.04528476 0.03264168 0.02491845 0.02230198 0.025052479 0.03349969
#> [11,] 0.12160464 0.08284423 0.06342261 0.05725951 0.024832391 0.00000000
#> [12,] 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000 0.00000000
#> [13,] 0.08557854 0.05286541 0.00000000 0.00000000 0.000000000 0.00000000
#> [,7] [,8] [,9] [,10] [,11] [,12]
#> [1,] 0.094985700 0.00000000 0.00000000 0.00000000 0.0000000 0.00000000
#> [2,] 0.000000000 0.00000000 0.00000000 0.00000000 0.0000000 0.00000000
#> [3,] 0.053511590 0.07702785 0.10897466 0.11710349 0.0000000 0.00000000
#> [4,] 0.000000000 0.00000000 0.00000000 0.00000000 0.0000000 0.00000000
#> [5,] 0.000000000 0.00000000 0.00000000 0.00000000 0.0000000 0.00000000
#> [6,] 0.031594344 0.04077417 0.05360899 0.07066494 0.0926698 0.12045290
#> [7,] 0.000000000 0.00000000 0.00000000 0.00000000 0.0000000 0.00000000
#> [8,] 0.007535853 0.00000000 0.00000000 0.00000000 0.0000000 0.00000000
#> [9,] 0.034152429 0.04835064 0.06745321 0.09198736 0.1225575 0.08310682
#> [10,] 0.048086663 0.06380846 0.00000000 0.00000000 0.0000000 0.00000000
#> [11,] 0.000000000 0.00000000 0.00000000 0.00000000 0.0000000 0.00000000
#> [12,] 0.000000000 0.00000000 0.00000000 0.00000000 0.0000000 0.00000000
#> [13,] 0.000000000 0.00000000 0.00000000 0.00000000 0.0000000 0.00000000
#> [,13] [,14] [,15]
#> [1,] 0.0000000 0.00000000 0.00000000
#> [2,] 0.0000000 0.00000000 0.00000000
#> [3,] 0.0000000 0.00000000 0.00000000
#> [4,] 0.0000000 0.00000000 0.00000000
#> [5,] 0.0000000 0.00000000 0.00000000
#> [6,] 0.1332194 0.09846327 0.01732486
#> [7,] 0.0000000 0.00000000 0.00000000
#> [8,] 0.0000000 0.00000000 0.00000000
#> [9,] 0.0000000 0.00000000 0.00000000
#> [10,] 0.0000000 0.00000000 0.00000000
#> [11,] 0.0000000 0.00000000 0.00000000
#> [12,] 0.0000000 0.00000000 0.00000000
#> [13,] 0.0000000 0.00000000 0.00000000
#>
#> $optimal_model$ed
#> [1] 4.205395
#>
#> $optimal_model$aic
#> [1] 42.86643
#>
#> $optimal_model$bic
#> [1] 52.93603
#>
#> $optimal_model$Bbases
#> $optimal_model$Bbases$Bu
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 0.03884084 5.471856e-01 0.404490973 0.009482628 0.0000000000 0.000000000
#> [2,] 0.00000000 1.009710e-01 0.644818692 0.253603399 0.0006068882 0.000000000
#> [3,] 0.00000000 7.586102e-05 0.207859202 0.660977090 0.1310878471 0.000000000
#> [4,] 0.00000000 0.000000e+00 0.004855105 0.353284782 0.5865574268 0.055302685
#> [5,] 0.00000000 0.000000e+00 0.000000000 0.026020331 0.5028068578 0.454786831
#> [6,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0758610226 0.619556972
#> [7,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.166666667
#> [8,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.002048248
#> [9,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.000000000
#> [10,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.000000000
#> [11,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.000000000
#> [12,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.000000000
#> [13,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.000000000
#> [,7] [,8] [,9] [,10] [,11] [,12]
#> [1,] 0.00000000 0.000000000 0.0000000000 0.000000000 0.000000000 0.000000e+00
#> [2,] 0.00000000 0.000000000 0.0000000000 0.000000000 0.000000000 0.000000e+00
#> [3,] 0.00000000 0.000000000 0.0000000000 0.000000000 0.000000000 0.000000e+00
#> [4,] 0.00000000 0.000000000 0.0000000000 0.000000000 0.000000000 0.000000e+00
#> [5,] 0.01638598 0.000000000 0.0000000000 0.000000000 0.000000000 0.000000e+00
#> [6,] 0.30253376 0.002048248 0.0000000000 0.000000000 0.000000000 0.000000e+00
#> [7,] 0.66666667 0.166666667 0.0000000000 0.000000000 0.000000000 0.000000e+00
#> [8,] 0.30253376 0.619556972 0.0758610226 0.000000000 0.000000000 0.000000e+00
#> [9,] 0.01638598 0.454786831 0.5028068578 0.026020331 0.000000000 0.000000e+00
#> [10,] 0.00000000 0.055302685 0.5865574268 0.353284782 0.004855105 0.000000e+00
#> [11,] 0.00000000 0.000000000 0.1310878471 0.660977090 0.207859202 7.586102e-05
#> [12,] 0.00000000 0.000000000 0.0006068882 0.253603399 0.644818692 1.009710e-01
#> [13,] 0.00000000 0.000000000 0.0000000000 0.009482628 0.404490973 5.471856e-01
#> [,13]
#> [1,] 0.00000000
#> [2,] 0.00000000
#> [3,] 0.00000000
#> [4,] 0.00000000
#> [5,] 0.00000000
#> [6,] 0.00000000
#> [7,] 0.00000000
#> [8,] 0.00000000
#> [9,] 0.00000000
#> [10,] 0.00000000
#> [11,] 0.00000000
#> [12,] 0.00000000
#> [13,] 0.03884084
#> attr(,"x")
#> [1] 2.39 2.89 3.39 3.89 4.39 4.89 5.39 5.89 6.39 6.89 7.39 7.89 8.39
#> attr(,"xl")
#> [1] 2.14
#> attr(,"xr")
#> [1] 8.64
#> attr(,"nseg")
#> [1] 10
#> attr(,"bdeg")
#> [1] 3
#> attr(,"type")
#> [1] "bbase"
#>
#> $optimal_model$Bbases$Bs
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 0.04938272 0.57407407 0.37037037 0.00617284 0.00000000 0.00000000
#> [2,] 0.00000000 0.16666667 0.66666667 0.16666667 0.00000000 0.00000000
#> [3,] 0.00000000 0.00617284 0.37037037 0.57407407 0.04938272 0.00000000
#> [4,] 0.00000000 0.00000000 0.04938272 0.57407407 0.37037037 0.00617284
#> [5,] 0.00000000 0.00000000 0.00000000 0.16666667 0.66666667 0.16666667
#> [6,] 0.00000000 0.00000000 0.00000000 0.00617284 0.37037037 0.57407407
#> [7,] 0.00000000 0.00000000 0.00000000 0.00000000 0.04938272 0.57407407
#> [8,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.16666667
#> [9,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00617284
#> [10,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [11,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [12,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [13,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [14,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [15,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [,7] [,8] [,9] [,10] [,11] [,12]
#> [1,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [2,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [3,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [4,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [5,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [6,] 0.04938272 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [7,] 0.37037037 0.00617284 0.00000000 0.00000000 0.00000000 0.00000000
#> [8,] 0.66666667 0.16666667 0.00000000 0.00000000 0.00000000 0.00000000
#> [9,] 0.37037037 0.57407407 0.04938272 0.00000000 0.00000000 0.00000000
#> [10,] 0.04938272 0.57407407 0.37037037 0.00617284 0.00000000 0.00000000
#> [11,] 0.00000000 0.16666667 0.66666667 0.16666667 0.00000000 0.00000000
#> [12,] 0.00000000 0.00617284 0.37037037 0.57407407 0.04938272 0.00000000
#> [13,] 0.00000000 0.00000000 0.04938272 0.57407407 0.37037037 0.00617284
#> [14,] 0.00000000 0.00000000 0.00000000 0.16666667 0.66666667 0.16666667
#> [15,] 0.00000000 0.00000000 0.00000000 0.00617284 0.37037037 0.57407407
#> [,13]
#> [1,] 0.00000000
#> [2,] 0.00000000
#> [3,] 0.00000000
#> [4,] 0.00000000
#> [5,] 0.00000000
#> [6,] 0.00000000
#> [7,] 0.00000000
#> [8,] 0.00000000
#> [9,] 0.00000000
#> [10,] 0.00000000
#> [11,] 0.00000000
#> [12,] 0.00000000
#> [13,] 0.00000000
#> [14,] 0.00000000
#> [15,] 0.04938272
#> attr(,"x")
#> [1] 0.25 0.75 1.25 1.75 2.25 2.75 3.25 3.75 4.25 4.75 5.25 5.75 6.25 6.75 7.25
#> attr(,"xl")
#> [1] 0
#> attr(,"xr")
#> [1] 7.5
#> attr(,"nseg")
#> [1] 10
#> attr(,"bdeg")
#> [1] 3
#> attr(,"type")
#> [1] "bbase"
#>
#>
#> $optimal_model$nevents
#> [1] 8
#>
#>
#> $optimal_logrho
#> [1] 1.0 1.5
#>
#> $P_optimal
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 41.62278 -20.00000 10.00000 0.00000 0.00000 0.00000 0.00000
#> [2,] -20.00000 81.62278 -40.00000 10.00000 0.00000 0.00000 0.00000
#> [3,] 10.00000 -40.00000 91.62278 -40.00000 10.00000 0.00000 0.00000
#> [4,] 0.00000 10.00000 -40.00000 91.62278 -40.00000 10.00000 0.00000
#> [5,] 0.00000 0.00000 10.00000 -40.00000 91.62278 -40.00000 10.00000
#> [6,] 0.00000 0.00000 0.00000 10.00000 -40.00000 91.62278 -40.00000
#> [7,] 0.00000 0.00000 0.00000 0.00000 10.00000 -40.00000 91.62278
#> [8,] 0.00000 0.00000 0.00000 0.00000 0.00000 10.00000 -40.00000
#> [9,] 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 10.00000
#> [10,] 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
#> [11,] 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
#> [12,] 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
#> [13,] 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
#> [14,] -63.24555 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
#> [15,] 0.00000 -63.24555 0.00000 0.00000 0.00000 0.00000 0.00000
#> [16,] 0.00000 0.00000 -63.24555 0.00000 0.00000 0.00000 0.00000
#> [17,] 0.00000 0.00000 0.00000 -63.24555 0.00000 0.00000 0.00000
#> [18,] 0.00000 0.00000 0.00000 0.00000 -63.24555 0.00000 0.00000
#> [19,] 0.00000 0.00000 0.00000 0.00000 0.00000 -63.24555 0.00000
#> [20,] 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 -63.24555
#> [21,] 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
#> [22,] 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
#> [23,] 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
#> [24,] 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
#> [25,] 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
#> [26,] 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
#> [27,] 31.62278 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
#> [28,] 0.00000 31.62278 0.00000 0.00000 0.00000 0.00000 0.00000
#> [29,] 0.00000 0.00000 31.62278 0.00000 0.00000 0.00000 0.00000
#> [30,] 0.00000 0.00000 0.00000 31.62278 0.00000 0.00000 0.00000
#> [31,] 0.00000 0.00000 0.00000 0.00000 31.62278 0.00000 0.00000
#> [32,] 0.00000 0.00000 0.00000 0.00000 0.00000 31.62278 0.00000
#> [33,] 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 31.62278
#> [34,] 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
#> [35,] 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
#> [36,] 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
#> [37,] 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
#> [38,] 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
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#> [36,] 0.00000 0.00000 0.00000 0.00000
#> [37,] 0.00000 0.00000 0.00000 0.00000
#> [38,] 0.00000 0.00000 0.00000 0.00000
#> [39,] 0.00000 0.00000 0.00000 0.00000
#> [40,] 0.00000 0.00000 0.00000 0.00000
#> [41,] 0.00000 0.00000 0.00000 0.00000
#> [42,] 0.00000 0.00000 0.00000 0.00000
#> [43,] 0.00000 0.00000 0.00000 0.00000
#> [44,] 0.00000 0.00000 0.00000 0.00000
#> [45,] 0.00000 0.00000 0.00000 0.00000
#> [46,] 0.00000 0.00000 0.00000 0.00000
#> [47,] 0.00000 0.00000 0.00000 0.00000
#> [48,] 0.00000 0.00000 0.00000 0.00000
#> [49,] 0.00000 0.00000 0.00000 0.00000
#> [50,] 0.00000 0.00000 0.00000 0.00000
#> [51,] 0.00000 0.00000 0.00000 0.00000
#> [52,] 0.00000 0.00000 0.00000 0.00000
#> [53,] 0.00000 0.00000 0.00000 0.00000
#> [54,] 0.00000 0.00000 0.00000 0.00000
#> [55,] 0.00000 0.00000 0.00000 0.00000
#> [56,] 0.00000 0.00000 0.00000 0.00000
#> [57,] 0.00000 0.00000 0.00000 0.00000
#> [58,] 0.00000 0.00000 0.00000 0.00000
#> [59,] 0.00000 0.00000 0.00000 0.00000
#> [60,] 0.00000 0.00000 0.00000 0.00000
#> [61,] 0.00000 0.00000 0.00000 0.00000
#> [62,] 0.00000 0.00000 0.00000 0.00000
#> [63,] 0.00000 0.00000 0.00000 0.00000
#> [64,] 0.00000 0.00000 0.00000 0.00000
#> [65,] 0.00000 0.00000 0.00000 0.00000
#> [66,] 0.00000 0.00000 0.00000 0.00000
#> [67,] 0.00000 0.00000 0.00000 0.00000
#> [68,] 0.00000 0.00000 0.00000 0.00000
#> [69,] 0.00000 0.00000 0.00000 0.00000
#> [70,] 0.00000 0.00000 0.00000 0.00000
#> [71,] 0.00000 0.00000 0.00000 0.00000
#> [72,] 0.00000 0.00000 0.00000 0.00000
#> [73,] 0.00000 0.00000 0.00000 0.00000
#> [74,] 0.00000 0.00000 0.00000 0.00000
#> [75,] 0.00000 0.00000 0.00000 0.00000
#> [76,] 0.00000 0.00000 0.00000 0.00000
#> [77,] 0.00000 0.00000 0.00000 0.00000
#> [78,] 0.00000 0.00000 0.00000 0.00000
#> [79,] 0.00000 0.00000 0.00000 0.00000
#> [80,] 0.00000 0.00000 0.00000 0.00000
#> [81,] 0.00000 0.00000 0.00000 0.00000
#> [82,] 0.00000 0.00000 0.00000 0.00000
#> [83,] 0.00000 0.00000 0.00000 0.00000
#> [84,] 0.00000 0.00000 0.00000 0.00000
#> [85,] 0.00000 0.00000 0.00000 0.00000
#> [86,] 0.00000 0.00000 0.00000 0.00000
#> [87,] 0.00000 0.00000 0.00000 0.00000
#> [88,] 0.00000 0.00000 0.00000 0.00000
#> [89,] 0.00000 0.00000 0.00000 0.00000
#> [90,] 0.00000 0.00000 0.00000 0.00000
#> [91,] 0.00000 0.00000 0.00000 0.00000
#> [92,] 0.00000 0.00000 0.00000 0.00000
#> [93,] 0.00000 0.00000 0.00000 0.00000
#> [94,] 0.00000 0.00000 0.00000 0.00000
#> [95,] 0.00000 0.00000 0.00000 0.00000
#> [96,] 0.00000 0.00000 0.00000 0.00000
#> [97,] 0.00000 0.00000 0.00000 0.00000
#> [98,] 0.00000 0.00000 0.00000 0.00000
#> [99,] 0.00000 0.00000 0.00000 0.00000
#> [100,] 0.00000 0.00000 0.00000 0.00000
#> [101,] 0.00000 0.00000 0.00000 0.00000
#> [102,] 0.00000 0.00000 0.00000 0.00000
#> [103,] 0.00000 0.00000 0.00000 0.00000
#> [104,] 0.00000 0.00000 0.00000 0.00000
#> [105,] 0.00000 0.00000 0.00000 0.00000
#> [106,] 0.00000 0.00000 0.00000 0.00000
#> [107,] 0.00000 0.00000 0.00000 0.00000
#> [108,] 0.00000 0.00000 0.00000 0.00000
#> [109,] 0.00000 0.00000 0.00000 0.00000
#> [110,] 0.00000 0.00000 0.00000 0.00000
#> [111,] 0.00000 0.00000 0.00000 0.00000
#> [112,] 0.00000 0.00000 0.00000 0.00000
#> [113,] 0.00000 0.00000 0.00000 0.00000
#> [114,] 0.00000 0.00000 0.00000 0.00000
#> [115,] 0.00000 0.00000 0.00000 0.00000
#> [116,] 0.00000 0.00000 0.00000 0.00000
#> [117,] 0.00000 0.00000 0.00000 0.00000
#> [118,] 0.00000 0.00000 0.00000 0.00000
#> [119,] 0.00000 0.00000 0.00000 0.00000
#> [120,] 0.00000 0.00000 0.00000 0.00000
#> [121,] 0.00000 0.00000 0.00000 0.00000
#> [122,] 0.00000 0.00000 0.00000 0.00000
#> [123,] 0.00000 0.00000 0.00000 0.00000
#> [124,] 0.00000 0.00000 0.00000 0.00000
#> [125,] 0.00000 0.00000 0.00000 0.00000
#> [126,] 0.00000 0.00000 0.00000 0.00000
#> [127,] 0.00000 0.00000 0.00000 0.00000
#> [128,] 0.00000 0.00000 0.00000 0.00000
#> [129,] 0.00000 0.00000 0.00000 0.00000
#> [130,] 0.00000 0.00000 0.00000 0.00000
#> [131,] 0.00000 0.00000 0.00000 0.00000
#> [132,] 0.00000 0.00000 0.00000 0.00000
#> [133,] 0.00000 0.00000 0.00000 0.00000
#> [134,] 0.00000 0.00000 0.00000 0.00000
#> [135,] 0.00000 0.00000 0.00000 0.00000
#> [136,] 0.00000 0.00000 0.00000 0.00000
#> [137,] 0.00000 0.00000 0.00000 0.00000
#> [138,] 0.00000 0.00000 0.00000 0.00000
#> [139,] 0.00000 0.00000 0.00000 0.00000
#> [140,] 31.62278 0.00000 0.00000 0.00000
#> [141,] 0.00000 31.62278 0.00000 0.00000
#> [142,] 0.00000 0.00000 31.62278 0.00000
#> [143,] 0.00000 0.00000 0.00000 31.62278
#> [144,] 0.00000 0.00000 0.00000 0.00000
#> [145,] 0.00000 0.00000 0.00000 0.00000
#> [146,] 0.00000 0.00000 0.00000 0.00000
#> [147,] 0.00000 0.00000 0.00000 0.00000
#> [148,] 0.00000 0.00000 0.00000 0.00000
#> [149,] 0.00000 0.00000 0.00000 0.00000
#> [150,] 0.00000 0.00000 0.00000 0.00000
#> [151,] 0.00000 0.00000 0.00000 0.00000
#> [152,] 0.00000 0.00000 0.00000 0.00000
#> [153,] -63.24555 0.00000 0.00000 0.00000
#> [154,] 0.00000 -63.24555 0.00000 0.00000
#> [155,] 0.00000 0.00000 -63.24555 0.00000
#> [156,] 0.00000 0.00000 0.00000 -63.24555
#> [157,] 0.00000 0.00000 0.00000 0.00000
#> [158,] 0.00000 0.00000 0.00000 0.00000
#> [159,] 0.00000 0.00000 0.00000 0.00000
#> [160,] 0.00000 0.00000 0.00000 0.00000
#> [161,] 0.00000 0.00000 0.00000 0.00000
#> [162,] 0.00000 0.00000 0.00000 0.00000
#> [163,] 0.00000 0.00000 0.00000 0.00000
#> [164,] 10.00000 0.00000 0.00000 0.00000
#> [165,] -40.00000 10.00000 0.00000 0.00000
#> [166,] 91.62278 -40.00000 10.00000 0.00000
#> [167,] -40.00000 91.62278 -40.00000 10.00000
#> [168,] 10.00000 -40.00000 81.62278 -20.00000
#> [169,] 0.00000 10.00000 -20.00000 41.62278
#>
#> $AIC
#> [,1] [,2]
#> [1,] 42.98039 42.86643
#> [2,] 43.10964 43.01909
#>
#> $BIC
#> [,1] [,2]
#> [1,] 53.29606 52.93603
#> [2,] 53.13726 52.84690
#>
#> attr(,"class")
#> [1] "haz2ts"
# For more examples please check the vignettes!!! Running more complicated examples
# here would imply longer running times...