Fit a log-additive model over two time scales

Fits a log-additive model over two time scales. If covariates are included in the model, fitpgam() will fit a proportional hazards model, where the baseline hazard is a surface over the two time scales, where the effect of the time scales is additive on the log-scale. The model is described in Carollo et al. (2025).

Usage

fitpgam(
  data2ts = NULL,
  Y = NULL,
  R = NULL,
  Z = NULL,
  bins = NULL,
  Bbases_spec = list(),
  pord = 2,
  ridge = 1e-06,
  lrho = c(0, 0),
  optim_method = c("ucminf", "grid_search"),
  optim_criterion = c("aic", "bic"),
  control_algorithm = list(),
  par_gridsearch = list()
)

Arguments

data2ts

(optional) an object of class "data2ts" created by the function prepare_data(). Proving this input is the easiest way to use the function fitpgam(). 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 scale u. * midu A vector with the midpoints of the bins over u. * nu The number of bins over u. * bins_s A vector of bins extremes for the time scale s. * mids A vector with the midpoints of the bins over s. * ns The number of bins over s.

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 over u. Default is 10.

• min_u (optional) The lower limit of the domain of Bu. Default is min(bins_u).

• max_u (optional) The upper limit of the domain of Bu. Default is max(bins_u).

• nseg_s The number of segments for the B-splines over s. Default is 10.

• min_s (optional) The lower limit of the domain of Bs. Default is min(bins_s).

• max_s (optional) The upper limit of the domain of Bs. Default is max(bins_s).

pord

The order of the penalty. Default is 2.

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.

lrho

A vector of two elements if optim_method == "ucminf". Default is c(0,0). A list of two vectors of values for \(\log_{10}(\rho_u)\) and \(\log_{10}(\rho_s)\) if optim_method == "grid_search". In the latter case, if a list with two vectors is not provided, a default sequence of values is used for both \(\log_{10}(\rho_u)\) and \(\log_{10}(\rho_s)\).

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 of \(\log_{10}(\rho_u)\) and \(\log_{10}(\rho_s)\) values.

optim_criterion

The criterion to be used for optimization: "aic" (default) or "bic". BIC penalizes model complexity more strongly than AIC, so that its usage is recommended when a smoother fit is preferable (see also Camarda, 2012).

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 is 1e-5.

• verbose A Boolean. Default is FALSE. If TRUE monitors the iteration process.

• monitor_ev A Boolean. Default is FALSE. If TRUE monitors the evaluation of the model over the log_10(rho_s) values.

par_gridsearch

A list of parameters for the grid_search:

• plot_aic A Boolean. Default is FALSE. If TRUE, plot the AIC values over the grid of log_10(rho_u) and log_10(rho_s) values.

• plot_bic A Boolean. Default is FALSE. If TRUE, plot the BIC values over the grid of log_10(rho_u) and log_10(rho_s) values.

• return_aic A Boolean. Default is TRUE. Return the AIC values.

• return_bic A Boolean. Default is TRUE. Return the BIC values.

• col The color palette to be used for the AIC/BIC plot. Default is grDevices::gray.colors(n=10).

• plot_contour A Boolean. Default is TRUE. Adds white contour lines to the AIC/BIC plot.

• mark_optimal A Boolean. Default is TRUE. If the plot of the AIC or BIC values is returned, marks the optimal combination of log_10(rho_u) and log_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 haz2tsPGAM, that is a list with the following elements:

• optimal_model A list with :

  • alpha The vector of estimated P-splines coefficients of length \(c_u + c_s\).

  • SE_alpha The vector of estimated standard errors of the alpha coefficients, of dimension \(c_u + c_s\).

  • beta (if covariates) The vector of length \(p\) of estimated covariates coefficients.

  • se_beta The vector of length \(p\) of estimated Standard Errors for the beta coefficients.

  • eta0 (if covariates) The vector of values of the baseline linear predictor (log-hazard).

  • eta (if covariates) The vector of values of the baseline linear predictor (log-hazard) of length \(n_u * n_s\).

  • H The hat-matrix.

  • deviance The deviance.

  • ed The (total) effective dimension of the model.

  • aic The value of the AIC.

  • bic The value of the BIC.

  • Bbases a list with the B-spline bases Bu and Bs

• optimal_logrho A vector with the optimal values of \(\log_{10}(\rho_u)\) and \(\log_{10}(\rho_s)\).

• P_optimal The optimal penalty matrix P.

• EDu The effective dimensions along the u axis.

• EDs The effective dimensions along the s axis.

• AIC (if par_gridsearch$return_aic == TRUE) The matrix of AIC values.

• BIC (if par_gridsearch$return_bic == TRUE) The matrix of BIC values.

Details

The name P-GAM follows from the way this class of models is named in Eilers and Marx (2021) Practical Smoothing. The Joys of P-splines. In Carollo et al. (2025) this model is referred to as log-additive.

@references Carollo, A., Putter, H., Eilers, P. H. C., & Gampe, J. (2025). Analysis of Time-to-Event Data With Two Time Scales. An Application to Transitions out of Cohabitation. Sociological Methods & Research, 0(0). https://doi.org/10.1177/00491241251374193

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
fitpgam(fakedata2ts,
  optim_method = "grid_search",
  lrho = list(seq(1, 1.5, .5), seq(1, 1.5, .5))
)
#> $optimal_model
#> $optimal_model$alpha
#>             [,1]
#>  [1,] -1.4303836
#>  [2,] -1.1469946
#>  [3,] -0.8649400
#>  [4,] -0.6043617
#>  [5,] -0.4144981
#>  [6,] -0.3752876
#>  [7,] -0.4934777
#>  [8,] -0.7614314
#>  [9,] -1.1284111
#> [10,] -1.5421670
#> [11,] -1.9660493
#> [12,] -2.3916751
#> [13,] -2.8174088
#> [14,] -1.3190372
#> [15,] -1.2876160
#> [16,] -1.2566445
#> [17,] -1.2327070
#> [18,] -1.2287427
#> [19,] -1.2444947
#> [20,] -1.2673619
#> [21,] -1.2735485
#> [22,] -1.2536638
#> [23,] -1.2126988
#> [24,] -1.1660924
#> [25,] -1.1201826
#> [26,] -1.0742958
#> 
#> $optimal_model$SE_alpha
#>  [1] 196.1230 196.1197 196.1180 196.1172 196.1169 196.1168 196.1168 196.1168
#>  [9] 196.1170 196.1178 196.1197 196.1232 196.1289 196.1184 196.1174 196.1169
#> [17] 196.1167 196.1166 196.1167 196.1167 196.1168 196.1171 196.1176 196.1186
#> [25] 196.1203 196.1228
#> 
#> $optimal_model$eta
#>             [,1]
#>   [1,] -2.316125
#>   [2,] -2.104420
#>   [3,] -1.911035
#>   [4,] -1.758950
#>   [5,] -1.680258
#>   [6,] -1.692167
#>   [7,] -1.795796
#>   [8,] -1.984773
#>   [9,] -2.239233
#>  [10,] -2.535714
#>  [11,] -2.853459
#>  [12,] -3.178377
#>  [13,] -3.505351
#>  [14,] -2.296584
#>  [15,] -2.084879
#>  [16,] -1.891494
#>  [17,] -1.739409
#>  [18,] -1.660717
#>  [19,] -1.672626
#>  [20,] -1.776255
#>  [21,] -1.965232
#>  [22,] -2.219692
#>  [23,] -2.516173
#>  [24,] -2.833918
#>  [25,] -3.158836
#>  [26,] -3.485810
#>  [27,] -2.280483
#>  [28,] -2.068778
#>  [29,] -1.875394
#>  [30,] -1.723308
#>  [31,] -1.644616
#>  [32,] -1.656525
#>  [33,] -1.760154
#>  [34,] -1.949131
#>  [35,] -2.203592
#>  [36,] -2.500073
#>  [37,] -2.817817
#>  [38,] -3.142735
#>  [39,] -3.469710
#>  [40,] -2.271261
#>  [41,] -2.059556
#>  [42,] -1.866171
#>  [43,] -1.714086
#>  [44,] -1.635394
#>  [45,] -1.647303
#>  [46,] -1.750932
#>  [47,] -1.939908
#>  [48,] -2.194369
#>  [49,] -2.490850
#>  [50,] -2.808595
#>  [51,] -3.133512
#>  [52,] -3.460487
#>  [53,] -2.270796
#>  [54,] -2.059091
#>  [55,] -1.865706
#>  [56,] -1.713621
#>  [57,] -1.634929
#>  [58,] -1.646838
#>  [59,] -1.750467
#>  [60,] -1.939444
#>  [61,] -2.193904
#>  [62,] -2.490385
#>  [63,] -2.808130
#>  [64,] -3.133048
#>  [65,] -3.460022
#>  [66,] -2.278485
#>  [67,] -2.066780
#>  [68,] -1.873395
#>  [69,] -1.721310
#>  [70,] -1.642617
#>  [71,] -1.654527
#>  [72,] -1.758155
#>  [73,] -1.947132
#>  [74,] -2.201593
#>  [75,] -2.498074
#>  [76,] -2.815818
#>  [77,] -3.140736
#>  [78,] -3.467711
#>  [79,] -2.291133
#>  [80,] -2.079428
#>  [81,] -1.886043
#>  [82,] -1.733958
#>  [83,] -1.655266
#>  [84,] -1.667175
#>  [85,] -1.770804
#>  [86,] -1.959780
#>  [87,] -2.214241
#>  [88,] -2.510722
#>  [89,] -2.828466
#>  [90,] -3.153384
#>  [91,] -3.480359
#>  [92,] -2.303349
#>  [93,] -2.091644
#>  [94,] -1.898259
#>  [95,] -1.746174
#>  [96,] -1.667482
#>  [97,] -1.679391
#>  [98,] -1.783020
#>  [99,] -1.971997
#> [100,] -2.226457
#> [101,] -2.522938
#> [102,] -2.840683
#> [103,] -3.165601
#> [104,] -3.492575
#> [105,] -2.308863
#> [106,] -2.097158
#> [107,] -1.903773
#> [108,] -1.751688
#> [109,] -1.672996
#> [110,] -1.684905
#> [111,] -1.788534
#> [112,] -1.977511
#> [113,] -2.231971
#> [114,] -2.528452
#> [115,] -2.846197
#> [116,] -3.171115
#> [117,] -3.498089
#> [118,] -2.304270
#> [119,] -2.092565
#> [120,] -1.899180
#> [121,] -1.747095
#> [122,] -1.668403
#> [123,] -1.680312
#> [124,] -1.783941
#> [125,] -1.972918
#> [126,] -2.227378
#> [127,] -2.523859
#> [128,] -2.841604
#> [129,] -3.166522
#> [130,] -3.493496
#> [131,] -2.288918
#> [132,] -2.077213
#> [133,] -1.883828
#> [134,] -1.731743
#> [135,] -1.653051
#> [136,] -1.664960
#> [137,] -1.768589
#> [138,] -1.957565
#> [139,] -2.212026
#> [140,] -2.508507
#> [141,] -2.826251
#> [142,] -3.151169
#> [143,] -3.478144
#> [144,] -2.264713
#> [145,] -2.053007
#> [146,] -1.859623
#> [147,] -1.707538
#> [148,] -1.628845
#> [149,] -1.640755
#> [150,] -1.744383
#> [151,] -1.933360
#> [152,] -2.187821
#> [153,] -2.484302
#> [154,] -2.802046
#> [155,] -3.126964
#> [156,] -3.453939
#> [157,] -2.235657
#> [158,] -2.023951
#> [159,] -1.830567
#> [160,] -1.678482
#> [161,] -1.599789
#> [162,] -1.611699
#> [163,] -1.715327
#> [164,] -1.904304
#> [165,] -2.158765
#> [166,] -2.455246
#> [167,] -2.772990
#> [168,] -3.097908
#> [169,] -3.424883
#> [170,] -2.204976
#> [171,] -1.993271
#> [172,] -1.799886
#> [173,] -1.647801
#> [174,] -1.569109
#> [175,] -1.581018
#> [176,] -1.684647
#> [177,] -1.873623
#> [178,] -2.128084
#> [179,] -2.424565
#> [180,] -2.742309
#> [181,] -3.067227
#> [182,] -3.394202
#> [183,] -2.174259
#> [184,] -1.962554
#> [185,] -1.769169
#> [186,] -1.617084
#> [187,] -1.538391
#> [188,] -1.550301
#> [189,] -1.653930
#> [190,] -1.842906
#> [191,] -2.097367
#> [192,] -2.393848
#> [193,] -2.711592
#> [194,] -3.036510
#> [195,] -3.363485
#> 
#> $optimal_model$H
#>                [,1]        [,2]         [,3]          [,4]         [,5]
#>  [1,]  0.0219220130  0.30887457  0.337826850  0.4163704893  0.201426941
#>  [2,]  0.0162785268  0.22936318  0.260960539  0.3524879665  0.196480446
#>  [3,]  0.0106652059  0.15027671  0.184282456  0.2881110238  0.191191856
#>  [4,]  0.0055371665  0.07802610  0.110633341  0.2157826665  0.180399438
#>  [5,]  0.0015377851  0.02167481  0.045681834  0.1289854131  0.154054399
#>  [6,] -0.0011839404 -0.01667625 -0.003963889  0.0429806800  0.104930863
#>  [7,] -0.0028210862 -0.03974578 -0.036582702 -0.0241471931  0.045520358
#>  [8,] -0.0037346793 -0.05262012 -0.056564253 -0.0720873122 -0.011660750
#>  [9,] -0.0042838558 -0.06035958 -0.069892011 -0.1089701459 -0.064875022
#> [10,] -0.0047062549 -0.06631259 -0.080741442 -0.1414477205 -0.115860585
#> [11,] -0.0051002202 -0.07186492 -0.090999446 -0.1728131435 -0.166149778
#> [12,] -0.0054887353 -0.07734044 -0.101138366 -0.2039415013 -0.216260110
#> [13,] -0.0058769114 -0.08281119 -0.111269882 -0.2350551152 -0.266359307
#> [14,]  0.0022745544  0.03204396  0.025198656  0.0593821517  0.127922291
#> [15,]  0.0022389247  0.03154304  0.027504017  0.0573555626  0.107495982
#> [16,]  0.0022026946  0.03103366  0.029800794  0.0553186970  0.087073487
#> [17,]  0.0021569897  0.03039079  0.031954860  0.0531667698  0.066763247
#> [18,]  0.0020842852  0.02936748  0.033651078  0.0508257882  0.046949109
#> [19,]  0.0019726969  0.02779623  0.034541815  0.0481402121  0.028192742
#> [20,]  0.0018293327  0.02577708  0.034434404  0.0444682275  0.010946990
#> [21,]  0.0016787759  0.02365628  0.033410360  0.0390866042 -0.004820501
#> [22,]  0.0015356971  0.02164057  0.031733733  0.0320398486 -0.019520210
#> [23,]  0.0013976565  0.01969568  0.029712838  0.0240594225 -0.033656620
#> [24,]  0.0012609519  0.01776957  0.027579120  0.0157845005 -0.047595799
#> [25,]  0.0011244664  0.01584654  0.025430284  0.0074712466 -0.061502917
#> [26,]  0.0009879881  0.01392361  0.023281076 -0.0008429166 -0.075409052
#>                [,6]         [,7]         [,8]        [,9]       [,10]
#>  [1,] -7.999463e-05 -0.142074162 -0.221612398 -0.22998748 -0.14388837
#>  [2,]  8.216264e-02 -0.074758305 -0.183414963 -0.20133412 -0.13205774
#>  [3,]  1.642373e-01 -0.007440543 -0.145096009 -0.17254144 -0.12015174
#>  [4,]  2.436085e-01  0.059907090 -0.104822162 -0.14150743 -0.10703309
#>  [5,]  3.116297e-01  0.125718735 -0.058952036 -0.10384151 -0.09014995
#>  [6,]  3.418811e-01  0.179987165 -0.002365801 -0.05179417 -0.06453246
#>  [7,]  3.079676e-01  0.201926215  0.066580814  0.02258988 -0.02419595
#>  [8,]  2.281943e-01  0.182882666  0.133188657  0.11507362  0.03463505
#>  [9,]  1.329991e-01  0.140270092  0.182198419  0.21023271  0.11101164
#> [10,]  3.647627e-02  0.090941897  0.218066847  0.29804871  0.19678241
#> [11,] -5.947194e-02  0.040564183  0.250656560  0.38221493  0.28286282
#> [12,] -1.551527e-01 -0.009921315  0.282627639  0.46549154  0.36824327
#> [13,] -2.508168e-01 -0.060413491  0.314560276  0.54871284  0.45358013
#> [14,] -8.058350e-02  0.058788290  0.089853251  0.06656911  0.08053671
#> [15,] -5.293387e-02  0.054760667  0.086521824  0.07280071  0.07791278
#> [16,] -2.524342e-02  0.050756327  0.083172396  0.07902038  0.07527408
#> [17,]  2.999628e-03  0.047071733  0.079553089  0.08505957  0.07241454
#> [18,]  3.240187e-02  0.044373982  0.075219039  0.09053962  0.06898703
#> [19,]  6.321611e-02  0.043563263  0.069718013  0.09480897  0.06493998
#> [20,]  9.593301e-02  0.045036144  0.062846404  0.09722050  0.06045085
#> [21,]  1.308014e-01  0.048672080  0.054781702  0.09762337  0.05571850
#> [22,]  1.674944e-01  0.053965560  0.045727066  0.09641471  0.05097098
#> [23,]  2.052409e-01  0.060221351  0.036017017  0.09421608  0.04632782
#> [24,]  2.433210e-01  0.066817537  0.026059192  0.09164839  0.04175339
#> [25,]  2.814360e-01  0.073459903  0.016068929  0.08902880  0.03719080
#> [26,]  3.195515e-01  0.080103398  0.006077927  0.08640788  0.03262856
#>              [,11]        [,12]         [,13]         [,14]        [,15]
#>  [1,] -0.037076519 -0.010929286 -7.750583e-04 -0.0004169035 -0.002765032
#>  [2,] -0.034811429 -0.010606151 -7.521721e-04  0.0001017901  0.004008768
#>  [3,] -0.032528464 -0.010278243 -7.289474e-04  0.0006185853  0.010756403
#>  [4,] -0.029957906 -0.009873543 -7.002776e-04  0.0011048387  0.017083054
#>  [5,] -0.026469381 -0.009215769 -6.536624e-04  0.0015047644  0.022196899
#>  [6,] -0.020779763 -0.007921081 -5.618809e-04  0.0017300855  0.025007258
#>  [7,] -0.011256158 -0.005449064 -3.866043e-04  0.0017046006  0.024754312
#>  [8,]  0.003790650 -0.001025165 -7.288112e-05  0.0014812022  0.022167491
#>  [9,]  0.025209254  0.006030743  4.275565e-04  0.0011864165  0.018840097
#> [10,]  0.051768385  0.015857062  1.124566e-03  0.0008898541  0.015625853
#> [11,]  0.080310943  0.027813253  1.972749e-03  0.0006233763  0.012883319
#> [12,]  0.109345814  0.040646034  2.883159e-03  0.0003721249  0.010366174
#> [13,]  0.138411259  0.053533302  3.797437e-03  0.0001218202  0.007863042
#> [14,]  0.027318133  0.009988021  7.084685e-04  0.0287028890  0.394935903
#> [15,]  0.025213269  0.008952107  6.349715e-04  0.0217513389  0.303212718
#> [16,]  0.023108587  0.007920409  5.617738e-04  0.0148570895  0.212052160
#> [17,]  0.021015319  0.006959556  4.936060e-04  0.0086400815  0.128103433
#> [18,]  0.018979388  0.006182324  4.384740e-04  0.0035779830  0.058178924
#> [19,]  0.017098506  0.005612551  3.980677e-04 -0.0003501282  0.002867541
#> [20,]  0.015464540  0.005220960  3.703061e-04 -0.0033747225 -0.040488725
#> [21,]  0.014074724  0.004962929  3.520210e-04 -0.0057730330 -0.075431739
#> [22,]  0.012866051  0.004789449  3.397343e-04 -0.0077963736 -0.105282046
#> [23,]  0.011771825  0.004662193  3.307266e-04 -0.0096380466 -0.132643194
#> [24,]  0.010723472  0.004551802  3.229152e-04 -0.0114193179 -0.159170851
#> [25,]  0.009682052  0.004443843  3.152763e-04 -0.0131915921 -0.185573625
#> [26,]  0.008640823  0.004335948  3.076419e-04 -0.0149636131 -0.211972866
#>             [,16]       [,17]        [,18]       [,19]         [,20]
#>  [1,]  0.01076172  0.04168284  0.089322483  0.10494303  0.0714850285
#>  [2,]  0.01892383  0.04212036  0.079369392  0.09074689  0.0663246279
#>  [3,]  0.02705859  0.04257571  0.069476351  0.07660600  0.0611328734
#>  [4,]  0.03475316  0.04331789  0.060549471  0.06335424  0.0554371254
#>  [5,]  0.04102232  0.04451314  0.053984898  0.05269252  0.0493419656
#>  [6,]  0.04497822  0.04606981  0.049641046  0.04606431  0.0453797692
#>  [7,]  0.04660392  0.04845859  0.047032188  0.04337873  0.0448871613
#>  [8,]  0.04618238  0.05103134  0.046424820  0.04378001  0.0473806508
#>  [9,]  0.04516857  0.05387702  0.046492855  0.04477715  0.0511593736
#> [10,]  0.04440723  0.05706129  0.046696437  0.04508425  0.0546036427
#> [11,]  0.04407851  0.05978687  0.046509809  0.04498471  0.0578266841
#> [12,]  0.04391643  0.06219124  0.046131354  0.04482975  0.0610338774
#> [13,]  0.04376470  0.06457563  0.045740970  0.04467136  0.0642400847
#> [14,]  0.53241708  0.21638309  0.003954793 -0.08444253 -0.1105786194
#> [15,]  0.43194499  0.20901964  0.040713908 -0.04092741 -0.0741447368
#> [16,]  0.33133060  0.20115760  0.077263475  0.00254096 -0.0376849314
#> [17,]  0.23059482  0.18607488  0.110147028  0.04503195 -0.0009519588
#> [18,]  0.13643485  0.15612861  0.130187039  0.08279273  0.0356567299
#> [19,]  0.05462711  0.11559250  0.130686082  0.10860470  0.0696044662
#> [20,] -0.01477302  0.07122031  0.115679359  0.11807893  0.0960695584
#> [21,] -0.07453243  0.02630009  0.092031747  0.11516262  0.1120408006
#> [22,] -0.12806266 -0.01801938  0.064323098  0.10561347  0.1202651863
#> [23,] -0.17839370 -0.06168088  0.035080618  0.09324498  0.1248731233
#> [24,] -0.22761167 -0.10502333  0.005446153  0.08004654  0.1283623013
#> [25,] -0.27665769 -0.14830559 -0.024231420  0.06673842  0.1316957827
#> [26,] -0.32569871 -0.19158582 -0.053909800  0.05342759  0.1350251749
#>              [,21]       [,22]       [,23]        [,24]         [,25]
#>  [1,]  0.063981055  0.03946214  0.04127076  0.032943444  0.0071046741
#>  [2,]  0.064100825  0.04515845  0.04661994  0.034932860  0.0073635881
#>  [3,]  0.064166483  0.05085076  0.05197729  0.036925134  0.0076231494
#>  [4,]  0.063361914  0.05647875  0.05746599  0.038963325  0.0078931150
#>  [5,]  0.061010985  0.06173899  0.06278627  0.040828144  0.0081377871
#>  [6,]  0.058609906  0.06603621  0.06642721  0.041608576  0.0082060023
#>  [7,]  0.057357623  0.06921284  0.06751316  0.040817635  0.0080417582
#>  [8,]  0.057047547  0.07127425  0.06649938  0.038804888  0.0076960895
#>  [9,]  0.056873141  0.07245765  0.06487740  0.036707829  0.0073589322
#> [10,]  0.056443263  0.07323145  0.06353062  0.035083236  0.0071223156
#> [11,]  0.056076443  0.07406204  0.06238198  0.033644868  0.0069225322
#> [12,]  0.055748177  0.07492500  0.06128720  0.032250057  0.0067310657
#> [13,]  0.055422303  0.07578997  0.06019577  0.030857948  0.0065401153
#> [14,] -0.130296275 -0.13707785 -0.12496550 -0.074138846 -0.0144694044
#> [15,] -0.098502261 -0.11041622 -0.10534058 -0.064217761 -0.0127163603
#> [16,] -0.066650231 -0.08368256 -0.08564579 -0.054254013 -0.0109548254
#> [17,] -0.033965173 -0.05585693 -0.06486422 -0.043617683 -0.0090584995
#> [18,]  0.000709507 -0.02497555 -0.04083397 -0.030904650 -0.0067391527
#> [19,]  0.037438804  0.01052926 -0.01131312 -0.014510087 -0.0036524305
#> [20,]  0.074235069  0.05083983  0.02514728  0.006864264  0.0005045241
#> [21,]  0.107166489  0.09431433  0.06872713  0.033903318  0.0059303323
#> [22,]  0.133684666  0.13767823  0.11807170  0.066480535  0.0126761010
#> [23,]  0.155805652  0.17855081  0.17019043  0.103402841  0.0205912137
#> [24,]  0.176439327  0.21786886  0.22245101  0.142434330  0.0292800389
#> [25,]  0.196859733  0.25692746  0.27455567  0.181785441  0.0382057735
#> [26,]  0.217274369  0.29597885  0.32665295  0.221140266  0.0471438157
#>               [,26]
#>  [1,]  2.223582e-04
#>  [2,]  2.270997e-04
#>  [3,]  2.318638e-04
#>  [4,]  2.369908e-04
#>  [5,]  2.416493e-04
#>  [6,]  2.421328e-04
#>  [7,]  2.378356e-04
#>  [8,]  2.297466e-04
#>  [9,]  2.224315e-04
#> [10,]  2.181220e-04
#> [11,]  2.148684e-04
#> [12,]  2.118472e-04
#> [13,]  2.088406e-04
#> [14,] -4.246353e-04
#> [15,] -3.772759e-04
#> [16,] -3.296638e-04
#> [17,] -2.780193e-04
#> [18,] -2.135726e-04
#> [19,] -1.255316e-04
#> [20,] -3.912290e-06
#> [21,]  1.585576e-04
#> [22,]  3.650651e-04
#> [23,]  6.130344e-04
#> [24,]  8.926858e-04
#> [25,]  1.186875e-03
#> [26,]  1.482179e-03
#> 
#> $optimal_model$deviance
#> [1] 32.39612
#> 
#> $optimal_model$ed
#> [1] 3.79551
#> 
#> $optimal_model$aic
#> [1] 39.98714
#> 
#> $optimal_model$bic
#> [1] 49.07529
#> 
#> $optimal_model$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
#>  [14,] 0.03884084 5.471856e-01 0.404490973 0.009482628 0.0000000000 0.000000000
#>  [15,] 0.00000000 1.009710e-01 0.644818692 0.253603399 0.0006068882 0.000000000
#>  [16,] 0.00000000 7.586102e-05 0.207859202 0.660977090 0.1310878471 0.000000000
#>  [17,] 0.00000000 0.000000e+00 0.004855105 0.353284782 0.5865574268 0.055302685
#>  [18,] 0.00000000 0.000000e+00 0.000000000 0.026020331 0.5028068578 0.454786831
#>  [19,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0758610226 0.619556972
#>  [20,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.166666667
#>  [21,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.002048248
#>  [22,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.000000000
#>  [23,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.000000000
#>  [24,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.000000000
#>  [25,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.000000000
#>  [26,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.000000000
#>  [27,] 0.03884084 5.471856e-01 0.404490973 0.009482628 0.0000000000 0.000000000
#>  [28,] 0.00000000 1.009710e-01 0.644818692 0.253603399 0.0006068882 0.000000000
#>  [29,] 0.00000000 7.586102e-05 0.207859202 0.660977090 0.1310878471 0.000000000
#>  [30,] 0.00000000 0.000000e+00 0.004855105 0.353284782 0.5865574268 0.055302685
#>  [31,] 0.00000000 0.000000e+00 0.000000000 0.026020331 0.5028068578 0.454786831
#>  [32,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0758610226 0.619556972
#>  [33,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.166666667
#>  [34,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.002048248
#>  [35,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.000000000
#>  [36,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.000000000
#>  [37,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.000000000
#>  [38,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.000000000
#>  [39,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.000000000
#>  [40,] 0.03884084 5.471856e-01 0.404490973 0.009482628 0.0000000000 0.000000000
#>  [41,] 0.00000000 1.009710e-01 0.644818692 0.253603399 0.0006068882 0.000000000
#>  [42,] 0.00000000 7.586102e-05 0.207859202 0.660977090 0.1310878471 0.000000000
#>  [43,] 0.00000000 0.000000e+00 0.004855105 0.353284782 0.5865574268 0.055302685
#>  [44,] 0.00000000 0.000000e+00 0.000000000 0.026020331 0.5028068578 0.454786831
#>  [45,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0758610226 0.619556972
#>  [46,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.166666667
#>  [47,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.002048248
#>  [48,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.000000000
#>  [49,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.000000000
#>  [50,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.000000000
#>  [51,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.000000000
#>  [52,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.000000000
#>  [53,] 0.03884084 5.471856e-01 0.404490973 0.009482628 0.0000000000 0.000000000
#>  [54,] 0.00000000 1.009710e-01 0.644818692 0.253603399 0.0006068882 0.000000000
#>  [55,] 0.00000000 7.586102e-05 0.207859202 0.660977090 0.1310878471 0.000000000
#>  [56,] 0.00000000 0.000000e+00 0.004855105 0.353284782 0.5865574268 0.055302685
#>  [57,] 0.00000000 0.000000e+00 0.000000000 0.026020331 0.5028068578 0.454786831
#>  [58,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0758610226 0.619556972
#>  [59,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.166666667
#>  [60,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.002048248
#>  [61,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.000000000
#>  [62,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.000000000
#>  [63,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.000000000
#>  [64,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.000000000
#>  [65,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.000000000
#>  [66,] 0.03884084 5.471856e-01 0.404490973 0.009482628 0.0000000000 0.000000000
#>  [67,] 0.00000000 1.009710e-01 0.644818692 0.253603399 0.0006068882 0.000000000
#>  [68,] 0.00000000 7.586102e-05 0.207859202 0.660977090 0.1310878471 0.000000000
#>  [69,] 0.00000000 0.000000e+00 0.004855105 0.353284782 0.5865574268 0.055302685
#>  [70,] 0.00000000 0.000000e+00 0.000000000 0.026020331 0.5028068578 0.454786831
#>  [71,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0758610226 0.619556972
#>  [72,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.166666667
#>  [73,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.002048248
#>  [74,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.000000000
#>  [75,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.000000000
#>  [76,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.000000000
#>  [77,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.000000000
#>  [78,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.000000000
#>  [79,] 0.03884084 5.471856e-01 0.404490973 0.009482628 0.0000000000 0.000000000
#>  [80,] 0.00000000 1.009710e-01 0.644818692 0.253603399 0.0006068882 0.000000000
#>  [81,] 0.00000000 7.586102e-05 0.207859202 0.660977090 0.1310878471 0.000000000
#>  [82,] 0.00000000 0.000000e+00 0.004855105 0.353284782 0.5865574268 0.055302685
#>  [83,] 0.00000000 0.000000e+00 0.000000000 0.026020331 0.5028068578 0.454786831
#>  [84,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0758610226 0.619556972
#>  [85,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.166666667
#>  [86,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.002048248
#>  [87,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.000000000
#>  [88,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.000000000
#>  [89,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.000000000
#>  [90,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.000000000
#>  [91,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.000000000
#>  [92,] 0.03884084 5.471856e-01 0.404490973 0.009482628 0.0000000000 0.000000000
#>  [93,] 0.00000000 1.009710e-01 0.644818692 0.253603399 0.0006068882 0.000000000
#>  [94,] 0.00000000 7.586102e-05 0.207859202 0.660977090 0.1310878471 0.000000000
#>  [95,] 0.00000000 0.000000e+00 0.004855105 0.353284782 0.5865574268 0.055302685
#>  [96,] 0.00000000 0.000000e+00 0.000000000 0.026020331 0.5028068578 0.454786831
#>  [97,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0758610226 0.619556972
#>  [98,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.166666667
#>  [99,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.002048248
#> [100,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.000000000
#> [101,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.000000000
#> [102,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.000000000
#> [103,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.000000000
#> [104,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.000000000
#> [105,] 0.03884084 5.471856e-01 0.404490973 0.009482628 0.0000000000 0.000000000
#> [106,] 0.00000000 1.009710e-01 0.644818692 0.253603399 0.0006068882 0.000000000
#> [107,] 0.00000000 7.586102e-05 0.207859202 0.660977090 0.1310878471 0.000000000
#> [108,] 0.00000000 0.000000e+00 0.004855105 0.353284782 0.5865574268 0.055302685
#> [109,] 0.00000000 0.000000e+00 0.000000000 0.026020331 0.5028068578 0.454786831
#> [110,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0758610226 0.619556972
#> [111,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.166666667
#> [112,] 0.00000000 0.000000e+00 0.000000000 0.000000000 0.0000000000 0.002048248
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#> [134,] 0.00000000 0.000000000 0.0000000000 0.000000000 0.000000000 0.000000e+00
#> [135,] 0.01638598 0.000000000 0.0000000000 0.000000000 0.000000000 0.000000e+00
#> [136,] 0.30253376 0.002048248 0.0000000000 0.000000000 0.000000000 0.000000e+00
#> [137,] 0.66666667 0.166666667 0.0000000000 0.000000000 0.000000000 0.000000e+00
#> [138,] 0.30253376 0.619556972 0.0758610226 0.000000000 0.000000000 0.000000e+00
#> [139,] 0.01638598 0.454786831 0.5028068578 0.026020331 0.000000000 0.000000e+00
#> [140,] 0.00000000 0.055302685 0.5865574268 0.353284782 0.004855105 0.000000e+00
#> [141,] 0.00000000 0.000000000 0.1310878471 0.660977090 0.207859202 7.586102e-05
#> [142,] 0.00000000 0.000000000 0.0006068882 0.253603399 0.644818692 1.009710e-01
#> [143,] 0.00000000 0.000000000 0.0000000000 0.009482628 0.404490973 5.471856e-01
#> [144,] 0.00000000 0.000000000 0.0000000000 0.000000000 0.000000000 0.000000e+00
#> [145,] 0.00000000 0.000000000 0.0000000000 0.000000000 0.000000000 0.000000e+00
#> [146,] 0.00000000 0.000000000 0.0000000000 0.000000000 0.000000000 0.000000e+00
#> [147,] 0.00000000 0.000000000 0.0000000000 0.000000000 0.000000000 0.000000e+00
#> [148,] 0.01638598 0.000000000 0.0000000000 0.000000000 0.000000000 0.000000e+00
#> [149,] 0.30253376 0.002048248 0.0000000000 0.000000000 0.000000000 0.000000e+00
#> [150,] 0.66666667 0.166666667 0.0000000000 0.000000000 0.000000000 0.000000e+00
#> [151,] 0.30253376 0.619556972 0.0758610226 0.000000000 0.000000000 0.000000e+00
#> [152,] 0.01638598 0.454786831 0.5028068578 0.026020331 0.000000000 0.000000e+00
#> [153,] 0.00000000 0.055302685 0.5865574268 0.353284782 0.004855105 0.000000e+00
#> [154,] 0.00000000 0.000000000 0.1310878471 0.660977090 0.207859202 7.586102e-05
#> [155,] 0.00000000 0.000000000 0.0006068882 0.253603399 0.644818692 1.009710e-01
#> [156,] 0.00000000 0.000000000 0.0000000000 0.009482628 0.404490973 5.471856e-01
#> [157,] 0.00000000 0.000000000 0.0000000000 0.000000000 0.000000000 0.000000e+00
#> [158,] 0.00000000 0.000000000 0.0000000000 0.000000000 0.000000000 0.000000e+00
#> [159,] 0.00000000 0.000000000 0.0000000000 0.000000000 0.000000000 0.000000e+00
#> [160,] 0.00000000 0.000000000 0.0000000000 0.000000000 0.000000000 0.000000e+00
#> [161,] 0.01638598 0.000000000 0.0000000000 0.000000000 0.000000000 0.000000e+00
#> [162,] 0.30253376 0.002048248 0.0000000000 0.000000000 0.000000000 0.000000e+00
#> [163,] 0.66666667 0.166666667 0.0000000000 0.000000000 0.000000000 0.000000e+00
#> [164,] 0.30253376 0.619556972 0.0758610226 0.000000000 0.000000000 0.000000e+00
#> [165,] 0.01638598 0.454786831 0.5028068578 0.026020331 0.000000000 0.000000e+00
#> [166,] 0.00000000 0.055302685 0.5865574268 0.353284782 0.004855105 0.000000e+00
#> [167,] 0.00000000 0.000000000 0.1310878471 0.660977090 0.207859202 7.586102e-05
#> [168,] 0.00000000 0.000000000 0.0006068882 0.253603399 0.644818692 1.009710e-01
#> [169,] 0.00000000 0.000000000 0.0000000000 0.009482628 0.404490973 5.471856e-01
#> [170,] 0.00000000 0.000000000 0.0000000000 0.000000000 0.000000000 0.000000e+00
#> [171,] 0.00000000 0.000000000 0.0000000000 0.000000000 0.000000000 0.000000e+00
#> [172,] 0.00000000 0.000000000 0.0000000000 0.000000000 0.000000000 0.000000e+00
#> [173,] 0.00000000 0.000000000 0.0000000000 0.000000000 0.000000000 0.000000e+00
#> [174,] 0.01638598 0.000000000 0.0000000000 0.000000000 0.000000000 0.000000e+00
#> [175,] 0.30253376 0.002048248 0.0000000000 0.000000000 0.000000000 0.000000e+00
#> [176,] 0.66666667 0.166666667 0.0000000000 0.000000000 0.000000000 0.000000e+00
#> [177,] 0.30253376 0.619556972 0.0758610226 0.000000000 0.000000000 0.000000e+00
#> [178,] 0.01638598 0.454786831 0.5028068578 0.026020331 0.000000000 0.000000e+00
#> [179,] 0.00000000 0.055302685 0.5865574268 0.353284782 0.004855105 0.000000e+00
#> [180,] 0.00000000 0.000000000 0.1310878471 0.660977090 0.207859202 7.586102e-05
#> [181,] 0.00000000 0.000000000 0.0006068882 0.253603399 0.644818692 1.009710e-01
#> [182,] 0.00000000 0.000000000 0.0000000000 0.009482628 0.404490973 5.471856e-01
#> [183,] 0.00000000 0.000000000 0.0000000000 0.000000000 0.000000000 0.000000e+00
#> [184,] 0.00000000 0.000000000 0.0000000000 0.000000000 0.000000000 0.000000e+00
#> [185,] 0.00000000 0.000000000 0.0000000000 0.000000000 0.000000000 0.000000e+00
#> [186,] 0.00000000 0.000000000 0.0000000000 0.000000000 0.000000000 0.000000e+00
#> [187,] 0.01638598 0.000000000 0.0000000000 0.000000000 0.000000000 0.000000e+00
#> [188,] 0.30253376 0.002048248 0.0000000000 0.000000000 0.000000000 0.000000e+00
#> [189,] 0.66666667 0.166666667 0.0000000000 0.000000000 0.000000000 0.000000e+00
#> [190,] 0.30253376 0.619556972 0.0758610226 0.000000000 0.000000000 0.000000e+00
#> [191,] 0.01638598 0.454786831 0.5028068578 0.026020331 0.000000000 0.000000e+00
#> [192,] 0.00000000 0.055302685 0.5865574268 0.353284782 0.004855105 0.000000e+00
#> [193,] 0.00000000 0.000000000 0.1310878471 0.660977090 0.207859202 7.586102e-05
#> [194,] 0.00000000 0.000000000 0.0006068882 0.253603399 0.644818692 1.009710e-01
#> [195,] 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
#>  [14,] 0.00000000
#>  [15,] 0.00000000
#>  [16,] 0.00000000
#>  [17,] 0.00000000
#>  [18,] 0.00000000
#>  [19,] 0.00000000
#>  [20,] 0.00000000
#>  [21,] 0.00000000
#>  [22,] 0.00000000
#>  [23,] 0.00000000
#>  [24,] 0.00000000
#>  [25,] 0.00000000
#>  [26,] 0.03884084
#>  [27,] 0.00000000
#>  [28,] 0.00000000
#>  [29,] 0.00000000
#>  [30,] 0.00000000
#>  [31,] 0.00000000
#>  [32,] 0.00000000
#>  [33,] 0.00000000
#>  [34,] 0.00000000
#>  [35,] 0.00000000
#>  [36,] 0.00000000
#>  [37,] 0.00000000
#>  [38,] 0.00000000
#>  [39,] 0.03884084
#>  [40,] 0.00000000
#>  [41,] 0.00000000
#>  [42,] 0.00000000
#>  [43,] 0.00000000
#>  [44,] 0.00000000
#>  [45,] 0.00000000
#>  [46,] 0.00000000
#>  [47,] 0.00000000
#>  [48,] 0.00000000
#>  [49,] 0.00000000
#>  [50,] 0.00000000
#>  [51,] 0.00000000
#>  [52,] 0.03884084
#>  [53,] 0.00000000
#>  [54,] 0.00000000
#>  [55,] 0.00000000
#>  [56,] 0.00000000
#>  [57,] 0.00000000
#>  [58,] 0.00000000
#>  [59,] 0.00000000
#>  [60,] 0.00000000
#>  [61,] 0.00000000
#>  [62,] 0.00000000
#>  [63,] 0.00000000
#>  [64,] 0.00000000
#>  [65,] 0.03884084
#>  [66,] 0.00000000
#>  [67,] 0.00000000
#>  [68,] 0.00000000
#>  [69,] 0.00000000
#>  [70,] 0.00000000
#>  [71,] 0.00000000
#>  [72,] 0.00000000
#>  [73,] 0.00000000
#>  [74,] 0.00000000
#>  [75,] 0.00000000
#>  [76,] 0.00000000
#>  [77,] 0.00000000
#>  [78,] 0.03884084
#>  [79,] 0.00000000
#>  [80,] 0.00000000
#>  [81,] 0.00000000
#>  [82,] 0.00000000
#>  [83,] 0.00000000
#>  [84,] 0.00000000
#>  [85,] 0.00000000
#>  [86,] 0.00000000
#>  [87,] 0.00000000
#>  [88,] 0.00000000
#>  [89,] 0.00000000
#>  [90,] 0.00000000
#>  [91,] 0.03884084
#>  [92,] 0.00000000
#>  [93,] 0.00000000
#>  [94,] 0.00000000
#>  [95,] 0.00000000
#>  [96,] 0.00000000
#>  [97,] 0.00000000
#>  [98,] 0.00000000
#>  [99,] 0.00000000
#> [100,] 0.00000000
#> [101,] 0.00000000
#> [102,] 0.00000000
#> [103,] 0.00000000
#> [104,] 0.03884084
#> [105,] 0.00000000
#> [106,] 0.00000000
#> [107,] 0.00000000
#> [108,] 0.00000000
#> [109,] 0.00000000
#> [110,] 0.00000000
#> [111,] 0.00000000
#> [112,] 0.00000000
#> [113,] 0.00000000
#> [114,] 0.00000000
#> [115,] 0.00000000
#> [116,] 0.00000000
#> [117,] 0.03884084
#> [118,] 0.00000000
#> [119,] 0.00000000
#> [120,] 0.00000000
#> [121,] 0.00000000
#> [122,] 0.00000000
#> [123,] 0.00000000
#> [124,] 0.00000000
#> [125,] 0.00000000
#> [126,] 0.00000000
#> [127,] 0.00000000
#> [128,] 0.00000000
#> [129,] 0.00000000
#> [130,] 0.03884084
#> [131,] 0.00000000
#> [132,] 0.00000000
#> [133,] 0.00000000
#> [134,] 0.00000000
#> [135,] 0.00000000
#> [136,] 0.00000000
#> [137,] 0.00000000
#> [138,] 0.00000000
#> [139,] 0.00000000
#> [140,] 0.00000000
#> [141,] 0.00000000
#> [142,] 0.00000000
#> [143,] 0.03884084
#> [144,] 0.00000000
#> [145,] 0.00000000
#> [146,] 0.00000000
#> [147,] 0.00000000
#> [148,] 0.00000000
#> [149,] 0.00000000
#> [150,] 0.00000000
#> [151,] 0.00000000
#> [152,] 0.00000000
#> [153,] 0.00000000
#> [154,] 0.00000000
#> [155,] 0.00000000
#> [156,] 0.03884084
#> [157,] 0.00000000
#> [158,] 0.00000000
#> [159,] 0.00000000
#> [160,] 0.00000000
#> [161,] 0.00000000
#> [162,] 0.00000000
#> [163,] 0.00000000
#> [164,] 0.00000000
#> [165,] 0.00000000
#> [166,] 0.00000000
#> [167,] 0.00000000
#> [168,] 0.00000000
#> [169,] 0.03884084
#> [170,] 0.00000000
#> [171,] 0.00000000
#> [172,] 0.00000000
#> [173,] 0.00000000
#> [174,] 0.00000000
#> [175,] 0.00000000
#> [176,] 0.00000000
#> [177,] 0.00000000
#> [178,] 0.00000000
#> [179,] 0.00000000
#> [180,] 0.00000000
#> [181,] 0.00000000
#> [182,] 0.03884084
#> [183,] 0.00000000
#> [184,] 0.00000000
#> [185,] 0.00000000
#> [186,] 0.00000000
#> [187,] 0.00000000
#> [188,] 0.00000000
#> [189,] 0.00000000
#> [190,] 0.00000000
#> [191,] 0.00000000
#> [192,] 0.00000000
#> [193,] 0.00000000
#> [194,] 0.00000000
#> [195,] 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 2.39 2.89
#>  [16] 3.39 3.89 4.39 4.89 5.39 5.89 6.39 6.89 7.39 7.89 8.39 2.39 2.89 3.39 3.89
#>  [31] 4.39 4.89 5.39 5.89 6.39 6.89 7.39 7.89 8.39 2.39 2.89 3.39 3.89 4.39 4.89
#>  [46] 5.39 5.89 6.39 6.89 7.39 7.89 8.39 2.39 2.89 3.39 3.89 4.39 4.89 5.39 5.89
#>  [61] 6.39 6.89 7.39 7.89 8.39 2.39 2.89 3.39 3.89 4.39 4.89 5.39 5.89 6.39 6.89
#>  [76] 7.39 7.89 8.39 2.39 2.89 3.39 3.89 4.39 4.89 5.39 5.89 6.39 6.89 7.39 7.89
#>  [91] 8.39 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 2.39
#> [106] 2.89 3.39 3.89 4.39 4.89 5.39 5.89 6.39 6.89 7.39 7.89 8.39 2.39 2.89 3.39
#> [121] 3.89 4.39 4.89 5.39 5.89 6.39 6.89 7.39 7.89 8.39 2.39 2.89 3.39 3.89 4.39
#> [136] 4.89 5.39 5.89 6.39 6.89 7.39 7.89 8.39 2.39 2.89 3.39 3.89 4.39 4.89 5.39
#> [151] 5.89 6.39 6.89 7.39 7.89 8.39 2.39 2.89 3.39 3.89 4.39 4.89 5.39 5.89 6.39
#> [166] 6.89 7.39 7.89 8.39 2.39 2.89 3.39 3.89 4.39 4.89 5.39 5.89 6.39 6.89 7.39
#> [181] 7.89 8.39 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,] 0.04938272 0.57407407 0.37037037 0.00617284 0.00000000 0.00000000
#>   [3,] 0.04938272 0.57407407 0.37037037 0.00617284 0.00000000 0.00000000
#>   [4,] 0.04938272 0.57407407 0.37037037 0.00617284 0.00000000 0.00000000
#>   [5,] 0.04938272 0.57407407 0.37037037 0.00617284 0.00000000 0.00000000
#>   [6,] 0.04938272 0.57407407 0.37037037 0.00617284 0.00000000 0.00000000
#>   [7,] 0.04938272 0.57407407 0.37037037 0.00617284 0.00000000 0.00000000
#>   [8,] 0.04938272 0.57407407 0.37037037 0.00617284 0.00000000 0.00000000
#>   [9,] 0.04938272 0.57407407 0.37037037 0.00617284 0.00000000 0.00000000
#>  [10,] 0.04938272 0.57407407 0.37037037 0.00617284 0.00000000 0.00000000
#>  [11,] 0.04938272 0.57407407 0.37037037 0.00617284 0.00000000 0.00000000
#>  [12,] 0.04938272 0.57407407 0.37037037 0.00617284 0.00000000 0.00000000
#>  [13,] 0.04938272 0.57407407 0.37037037 0.00617284 0.00000000 0.00000000
#>  [14,] 0.00000000 0.16666667 0.66666667 0.16666667 0.00000000 0.00000000
#>  [15,] 0.00000000 0.16666667 0.66666667 0.16666667 0.00000000 0.00000000
#>  [16,] 0.00000000 0.16666667 0.66666667 0.16666667 0.00000000 0.00000000
#>  [17,] 0.00000000 0.16666667 0.66666667 0.16666667 0.00000000 0.00000000
#>  [18,] 0.00000000 0.16666667 0.66666667 0.16666667 0.00000000 0.00000000
#>  [19,] 0.00000000 0.16666667 0.66666667 0.16666667 0.00000000 0.00000000
#>  [20,] 0.00000000 0.16666667 0.66666667 0.16666667 0.00000000 0.00000000
#>  [21,] 0.00000000 0.16666667 0.66666667 0.16666667 0.00000000 0.00000000
#>  [22,] 0.00000000 0.16666667 0.66666667 0.16666667 0.00000000 0.00000000
#>  [23,] 0.00000000 0.16666667 0.66666667 0.16666667 0.00000000 0.00000000
#>  [24,] 0.00000000 0.16666667 0.66666667 0.16666667 0.00000000 0.00000000
#>  [25,] 0.00000000 0.16666667 0.66666667 0.16666667 0.00000000 0.00000000
#>  [26,] 0.00000000 0.16666667 0.66666667 0.16666667 0.00000000 0.00000000
#>  [27,] 0.00000000 0.00617284 0.37037037 0.57407407 0.04938272 0.00000000
#>  [28,] 0.00000000 0.00617284 0.37037037 0.57407407 0.04938272 0.00000000
#>  [29,] 0.00000000 0.00617284 0.37037037 0.57407407 0.04938272 0.00000000
#>  [30,] 0.00000000 0.00617284 0.37037037 0.57407407 0.04938272 0.00000000
#>  [31,] 0.00000000 0.00617284 0.37037037 0.57407407 0.04938272 0.00000000
#>  [32,] 0.00000000 0.00617284 0.37037037 0.57407407 0.04938272 0.00000000
#>  [33,] 0.00000000 0.00617284 0.37037037 0.57407407 0.04938272 0.00000000
#>  [34,] 0.00000000 0.00617284 0.37037037 0.57407407 0.04938272 0.00000000
#>  [35,] 0.00000000 0.00617284 0.37037037 0.57407407 0.04938272 0.00000000
#>  [36,] 0.00000000 0.00617284 0.37037037 0.57407407 0.04938272 0.00000000
#>  [37,] 0.00000000 0.00617284 0.37037037 0.57407407 0.04938272 0.00000000
#>  [38,] 0.00000000 0.00617284 0.37037037 0.57407407 0.04938272 0.00000000
#>  [39,] 0.00000000 0.00617284 0.37037037 0.57407407 0.04938272 0.00000000
#>  [40,] 0.00000000 0.00000000 0.04938272 0.57407407 0.37037037 0.00617284
#>  [41,] 0.00000000 0.00000000 0.04938272 0.57407407 0.37037037 0.00617284
#>  [42,] 0.00000000 0.00000000 0.04938272 0.57407407 0.37037037 0.00617284
#>  [43,] 0.00000000 0.00000000 0.04938272 0.57407407 0.37037037 0.00617284
#>  [44,] 0.00000000 0.00000000 0.04938272 0.57407407 0.37037037 0.00617284
#>  [45,] 0.00000000 0.00000000 0.04938272 0.57407407 0.37037037 0.00617284
#>  [46,] 0.00000000 0.00000000 0.04938272 0.57407407 0.37037037 0.00617284
#>  [47,] 0.00000000 0.00000000 0.04938272 0.57407407 0.37037037 0.00617284
#>  [48,] 0.00000000 0.00000000 0.04938272 0.57407407 0.37037037 0.00617284
#>  [49,] 0.00000000 0.00000000 0.04938272 0.57407407 0.37037037 0.00617284
#>  [50,] 0.00000000 0.00000000 0.04938272 0.57407407 0.37037037 0.00617284
#>  [51,] 0.00000000 0.00000000 0.04938272 0.57407407 0.37037037 0.00617284
#>  [52,] 0.00000000 0.00000000 0.04938272 0.57407407 0.37037037 0.00617284
#>  [53,] 0.00000000 0.00000000 0.00000000 0.16666667 0.66666667 0.16666667
#>  [54,] 0.00000000 0.00000000 0.00000000 0.16666667 0.66666667 0.16666667
#>  [55,] 0.00000000 0.00000000 0.00000000 0.16666667 0.66666667 0.16666667
#>  [56,] 0.00000000 0.00000000 0.00000000 0.16666667 0.66666667 0.16666667
#>  [57,] 0.00000000 0.00000000 0.00000000 0.16666667 0.66666667 0.16666667
#>  [58,] 0.00000000 0.00000000 0.00000000 0.16666667 0.66666667 0.16666667
#>  [59,] 0.00000000 0.00000000 0.00000000 0.16666667 0.66666667 0.16666667
#>  [60,] 0.00000000 0.00000000 0.00000000 0.16666667 0.66666667 0.16666667
#>  [61,] 0.00000000 0.00000000 0.00000000 0.16666667 0.66666667 0.16666667
#>  [62,] 0.00000000 0.00000000 0.00000000 0.16666667 0.66666667 0.16666667
#>  [63,] 0.00000000 0.00000000 0.00000000 0.16666667 0.66666667 0.16666667
#>  [64,] 0.00000000 0.00000000 0.00000000 0.16666667 0.66666667 0.16666667
#>  [65,] 0.00000000 0.00000000 0.00000000 0.16666667 0.66666667 0.16666667
#>  [66,] 0.00000000 0.00000000 0.00000000 0.00617284 0.37037037 0.57407407
#>  [67,] 0.00000000 0.00000000 0.00000000 0.00617284 0.37037037 0.57407407
#>  [68,] 0.00000000 0.00000000 0.00000000 0.00617284 0.37037037 0.57407407
#>  [69,] 0.00000000 0.00000000 0.00000000 0.00617284 0.37037037 0.57407407
#>  [70,] 0.00000000 0.00000000 0.00000000 0.00617284 0.37037037 0.57407407
#>  [71,] 0.00000000 0.00000000 0.00000000 0.00617284 0.37037037 0.57407407
#>  [72,] 0.00000000 0.00000000 0.00000000 0.00617284 0.37037037 0.57407407
#>  [73,] 0.00000000 0.00000000 0.00000000 0.00617284 0.37037037 0.57407407
#>  [74,] 0.00000000 0.00000000 0.00000000 0.00617284 0.37037037 0.57407407
#>  [75,] 0.00000000 0.00000000 0.00000000 0.00617284 0.37037037 0.57407407
#>  [76,] 0.00000000 0.00000000 0.00000000 0.00617284 0.37037037 0.57407407
#>  [77,] 0.00000000 0.00000000 0.00000000 0.00617284 0.37037037 0.57407407
#>  [78,] 0.00000000 0.00000000 0.00000000 0.00617284 0.37037037 0.57407407
#>  [79,] 0.00000000 0.00000000 0.00000000 0.00000000 0.04938272 0.57407407
#>  [80,] 0.00000000 0.00000000 0.00000000 0.00000000 0.04938272 0.57407407
#>  [81,] 0.00000000 0.00000000 0.00000000 0.00000000 0.04938272 0.57407407
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#> [166,] 0.00000000 0.00000000 0.04938272 0.57407407 0.37037037 0.00617284
#> [167,] 0.00000000 0.00000000 0.04938272 0.57407407 0.37037037 0.00617284
#> [168,] 0.00000000 0.00000000 0.04938272 0.57407407 0.37037037 0.00617284
#> [169,] 0.00000000 0.00000000 0.04938272 0.57407407 0.37037037 0.00617284
#> [170,] 0.00000000 0.00000000 0.00000000 0.16666667 0.66666667 0.16666667
#> [171,] 0.00000000 0.00000000 0.00000000 0.16666667 0.66666667 0.16666667
#> [172,] 0.00000000 0.00000000 0.00000000 0.16666667 0.66666667 0.16666667
#> [173,] 0.00000000 0.00000000 0.00000000 0.16666667 0.66666667 0.16666667
#> [174,] 0.00000000 0.00000000 0.00000000 0.16666667 0.66666667 0.16666667
#> [175,] 0.00000000 0.00000000 0.00000000 0.16666667 0.66666667 0.16666667
#> [176,] 0.00000000 0.00000000 0.00000000 0.16666667 0.66666667 0.16666667
#> [177,] 0.00000000 0.00000000 0.00000000 0.16666667 0.66666667 0.16666667
#> [178,] 0.00000000 0.00000000 0.00000000 0.16666667 0.66666667 0.16666667
#> [179,] 0.00000000 0.00000000 0.00000000 0.16666667 0.66666667 0.16666667
#> [180,] 0.00000000 0.00000000 0.00000000 0.16666667 0.66666667 0.16666667
#> [181,] 0.00000000 0.00000000 0.00000000 0.16666667 0.66666667 0.16666667
#> [182,] 0.00000000 0.00000000 0.00000000 0.16666667 0.66666667 0.16666667
#> [183,] 0.00000000 0.00000000 0.00000000 0.00617284 0.37037037 0.57407407
#> [184,] 0.00000000 0.00000000 0.00000000 0.00617284 0.37037037 0.57407407
#> [185,] 0.00000000 0.00000000 0.00000000 0.00617284 0.37037037 0.57407407
#> [186,] 0.00000000 0.00000000 0.00000000 0.00617284 0.37037037 0.57407407
#> [187,] 0.00000000 0.00000000 0.00000000 0.00617284 0.37037037 0.57407407
#> [188,] 0.00000000 0.00000000 0.00000000 0.00617284 0.37037037 0.57407407
#> [189,] 0.00000000 0.00000000 0.00000000 0.00617284 0.37037037 0.57407407
#> [190,] 0.00000000 0.00000000 0.00000000 0.00617284 0.37037037 0.57407407
#> [191,] 0.00000000 0.00000000 0.00000000 0.00617284 0.37037037 0.57407407
#> [192,] 0.00000000 0.00000000 0.00000000 0.00617284 0.37037037 0.57407407
#> [193,] 0.00000000 0.00000000 0.00000000 0.00617284 0.37037037 0.57407407
#> [194,] 0.00000000 0.00000000 0.00000000 0.00617284 0.37037037 0.57407407
#> [195,] 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,] 0.00000000
#>  [16,] 0.00000000
#>  [17,] 0.00000000
#>  [18,] 0.00000000
#>  [19,] 0.00000000
#>  [20,] 0.00000000
#>  [21,] 0.00000000
#>  [22,] 0.00000000
#>  [23,] 0.00000000
#>  [24,] 0.00000000
#>  [25,] 0.00000000
#>  [26,] 0.00000000
#>  [27,] 0.00000000
#>  [28,] 0.00000000
#>  [29,] 0.00000000
#>  [30,] 0.00000000
#>  [31,] 0.00000000
#>  [32,] 0.00000000
#>  [33,] 0.00000000
#>  [34,] 0.00000000
#>  [35,] 0.00000000
#>  [36,] 0.00000000
#>  [37,] 0.00000000
#>  [38,] 0.00000000
#>  [39,] 0.00000000
#>  [40,] 0.00000000
#>  [41,] 0.00000000
#>  [42,] 0.00000000
#>  [43,] 0.00000000
#>  [44,] 0.00000000
#>  [45,] 0.00000000
#>  [46,] 0.00000000
#>  [47,] 0.00000000
#>  [48,] 0.00000000
#>  [49,] 0.00000000
#>  [50,] 0.00000000
#>  [51,] 0.00000000
#>  [52,] 0.00000000
#>  [53,] 0.00000000
#>  [54,] 0.00000000
#>  [55,] 0.00000000
#>  [56,] 0.00000000
#>  [57,] 0.00000000
#>  [58,] 0.00000000
#>  [59,] 0.00000000
#>  [60,] 0.00000000
#>  [61,] 0.00000000
#>  [62,] 0.00000000
#>  [63,] 0.00000000
#>  [64,] 0.00000000
#>  [65,] 0.00000000
#>  [66,] 0.00000000
#>  [67,] 0.00000000
#>  [68,] 0.00000000
#>  [69,] 0.00000000
#>  [70,] 0.00000000
#>  [71,] 0.00000000
#>  [72,] 0.00000000
#>  [73,] 0.00000000
#>  [74,] 0.00000000
#>  [75,] 0.00000000
#>  [76,] 0.00000000
#>  [77,] 0.00000000
#>  [78,] 0.00000000
#>  [79,] 0.00000000
#>  [80,] 0.00000000
#>  [81,] 0.00000000
#>  [82,] 0.00000000
#>  [83,] 0.00000000
#>  [84,] 0.00000000
#>  [85,] 0.00000000
#>  [86,] 0.00000000
#>  [87,] 0.00000000
#>  [88,] 0.00000000
#>  [89,] 0.00000000
#>  [90,] 0.00000000
#>  [91,] 0.00000000
#>  [92,] 0.00000000
#>  [93,] 0.00000000
#>  [94,] 0.00000000
#>  [95,] 0.00000000
#>  [96,] 0.00000000
#>  [97,] 0.00000000
#>  [98,] 0.00000000
#>  [99,] 0.00000000
#> [100,] 0.00000000
#> [101,] 0.00000000
#> [102,] 0.00000000
#> [103,] 0.00000000
#> [104,] 0.00000000
#> [105,] 0.00000000
#> [106,] 0.00000000
#> [107,] 0.00000000
#> [108,] 0.00000000
#> [109,] 0.00000000
#> [110,] 0.00000000
#> [111,] 0.00000000
#> [112,] 0.00000000
#> [113,] 0.00000000
#> [114,] 0.00000000
#> [115,] 0.00000000
#> [116,] 0.00000000
#> [117,] 0.00000000
#> [118,] 0.00000000
#> [119,] 0.00000000
#> [120,] 0.00000000
#> [121,] 0.00000000
#> [122,] 0.00000000
#> [123,] 0.00000000
#> [124,] 0.00000000
#> [125,] 0.00000000
#> [126,] 0.00000000
#> [127,] 0.00000000
#> [128,] 0.00000000
#> [129,] 0.00000000
#> [130,] 0.00000000
#> [131,] 0.00000000
#> [132,] 0.00000000
#> [133,] 0.00000000
#> [134,] 0.00000000
#> [135,] 0.00000000
#> [136,] 0.00000000
#> [137,] 0.00000000
#> [138,] 0.00000000
#> [139,] 0.00000000
#> [140,] 0.00000000
#> [141,] 0.00000000
#> [142,] 0.00000000
#> [143,] 0.00000000
#> [144,] 0.00000000
#> [145,] 0.00000000
#> [146,] 0.00000000
#> [147,] 0.00000000
#> [148,] 0.00000000
#> [149,] 0.00000000
#> [150,] 0.00000000
#> [151,] 0.00000000
#> [152,] 0.00000000
#> [153,] 0.00000000
#> [154,] 0.00000000
#> [155,] 0.00000000
#> [156,] 0.00000000
#> [157,] 0.00000000
#> [158,] 0.00000000
#> [159,] 0.00000000
#> [160,] 0.00000000
#> [161,] 0.00000000
#> [162,] 0.00000000
#> [163,] 0.00000000
#> [164,] 0.00000000
#> [165,] 0.00000000
#> [166,] 0.00000000
#> [167,] 0.00000000
#> [168,] 0.00000000
#> [169,] 0.00000000
#> [170,] 0.00000000
#> [171,] 0.00000000
#> [172,] 0.00000000
#> [173,] 0.00000000
#> [174,] 0.00000000
#> [175,] 0.00000000
#> [176,] 0.00000000
#> [177,] 0.00000000
#> [178,] 0.00000000
#> [179,] 0.00000000
#> [180,] 0.00000000
#> [181,] 0.00000000
#> [182,] 0.00000000
#> [183,] 0.04938272
#> [184,] 0.04938272
#> [185,] 0.04938272
#> [186,] 0.04938272
#> [187,] 0.04938272
#> [188,] 0.04938272
#> [189,] 0.04938272
#> [190,] 0.04938272
#> [191,] 0.04938272
#> [192,] 0.04938272
#> [193,] 0.04938272
#> [194,] 0.04938272
#> [195,] 0.04938272
#> attr(,"x")
#>   [1] 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.75 0.75
#>  [16] 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 1.25 1.25 1.25 1.25
#>  [31] 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.75 1.75 1.75 1.75 1.75 1.75
#>  [46] 1.75 1.75 1.75 1.75 1.75 1.75 1.75 2.25 2.25 2.25 2.25 2.25 2.25 2.25 2.25
#>  [61] 2.25 2.25 2.25 2.25 2.25 2.75 2.75 2.75 2.75 2.75 2.75 2.75 2.75 2.75 2.75
#>  [76] 2.75 2.75 2.75 3.25 3.25 3.25 3.25 3.25 3.25 3.25 3.25 3.25 3.25 3.25 3.25
#>  [91] 3.25 3.75 3.75 3.75 3.75 3.75 3.75 3.75 3.75 3.75 3.75 3.75 3.75 3.75 4.25
#> [106] 4.25 4.25 4.25 4.25 4.25 4.25 4.25 4.25 4.25 4.25 4.25 4.25 4.75 4.75 4.75
#> [121] 4.75 4.75 4.75 4.75 4.75 4.75 4.75 4.75 4.75 4.75 5.25 5.25 5.25 5.25 5.25
#> [136] 5.25 5.25 5.25 5.25 5.25 5.25 5.25 5.25 5.75 5.75 5.75 5.75 5.75 5.75 5.75
#> [151] 5.75 5.75 5.75 5.75 5.75 5.75 6.25 6.25 6.25 6.25 6.25 6.25 6.25 6.25 6.25
#> [166] 6.25 6.25 6.25 6.25 6.75 6.75 6.75 6.75 6.75 6.75 6.75 6.75 6.75 6.75 6.75
#> [181] 6.75 6.75 7.25 7.25 7.25 7.25 7.25 7.25 7.25 7.25 7.25 7.25 7.25 7.25 7.25
#> attr(,"xl")
#> [1] 0
#> attr(,"xr")
#> [1] 7.5
#> attr(,"nseg")
#> [1] 10
#> attr(,"bdeg")
#> [1] 3
#> attr(,"type")
#> [1] "bbase"
#> 
#> 
#> 
#> $optimal_logrho
#> [1] 1.0 1.5
#> 
#> $P_optimal
#>       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
#>  [1,]   10  -20   10    0    0    0    0    0    0     0     0     0     0
#>  [2,]  -20   50  -40   10    0    0    0    0    0     0     0     0     0
#>  [3,]   10  -40   60  -40   10    0    0    0    0     0     0     0     0
#>  [4,]    0   10  -40   60  -40   10    0    0    0     0     0     0     0
#>  [5,]    0    0   10  -40   60  -40   10    0    0     0     0     0     0
#>  [6,]    0    0    0   10  -40   60  -40   10    0     0     0     0     0
#>  [7,]    0    0    0    0   10  -40   60  -40   10     0     0     0     0
#>  [8,]    0    0    0    0    0   10  -40   60  -40    10     0     0     0
#>  [9,]    0    0    0    0    0    0   10  -40   60   -40    10     0     0
#> [10,]    0    0    0    0    0    0    0   10  -40    60   -40    10     0
#> [11,]    0    0    0    0    0    0    0    0   10   -40    60   -40    10
#> [12,]    0    0    0    0    0    0    0    0    0    10   -40    50   -20
#> [13,]    0    0    0    0    0    0    0    0    0     0    10   -20    10
#> [14,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#> [15,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#> [16,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#> [17,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#> [18,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#> [19,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#> [20,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#> [21,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#> [22,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#> [23,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#> [24,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#> [25,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#> [26,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#>           [,14]      [,15]      [,16]      [,17]      [,18]      [,19]
#>  [1,]   0.00000    0.00000    0.00000    0.00000    0.00000    0.00000
#>  [2,]   0.00000    0.00000    0.00000    0.00000    0.00000    0.00000
#>  [3,]   0.00000    0.00000    0.00000    0.00000    0.00000    0.00000
#>  [4,]   0.00000    0.00000    0.00000    0.00000    0.00000    0.00000
#>  [5,]   0.00000    0.00000    0.00000    0.00000    0.00000    0.00000
#>  [6,]   0.00000    0.00000    0.00000    0.00000    0.00000    0.00000
#>  [7,]   0.00000    0.00000    0.00000    0.00000    0.00000    0.00000
#>  [8,]   0.00000    0.00000    0.00000    0.00000    0.00000    0.00000
#>  [9,]   0.00000    0.00000    0.00000    0.00000    0.00000    0.00000
#> [10,]   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
#> [12,]   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
#> [14,]  31.62278  -63.24555   31.62278    0.00000    0.00000    0.00000
#> [15,] -63.24555  158.11388 -126.49111   31.62278    0.00000    0.00000
#> [16,]  31.62278 -126.49111  189.73666 -126.49111   31.62278    0.00000
#> [17,]   0.00000   31.62278 -126.49111  189.73666 -126.49111   31.62278
#> [18,]   0.00000    0.00000   31.62278 -126.49111  189.73666 -126.49111
#> [19,]   0.00000    0.00000    0.00000   31.62278 -126.49111  189.73666
#> [20,]   0.00000    0.00000    0.00000    0.00000   31.62278 -126.49111
#> [21,]   0.00000    0.00000    0.00000    0.00000    0.00000   31.62278
#> [22,]   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
#> [24,]   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
#> [26,]   0.00000    0.00000    0.00000    0.00000    0.00000    0.00000
#>            [,20]      [,21]      [,22]      [,23]      [,24]      [,25]
#>  [1,]    0.00000    0.00000    0.00000    0.00000    0.00000    0.00000
#>  [2,]    0.00000    0.00000    0.00000    0.00000    0.00000    0.00000
#>  [3,]    0.00000    0.00000    0.00000    0.00000    0.00000    0.00000
#>  [4,]    0.00000    0.00000    0.00000    0.00000    0.00000    0.00000
#>  [5,]    0.00000    0.00000    0.00000    0.00000    0.00000    0.00000
#>  [6,]    0.00000    0.00000    0.00000    0.00000    0.00000    0.00000
#>  [7,]    0.00000    0.00000    0.00000    0.00000    0.00000    0.00000
#>  [8,]    0.00000    0.00000    0.00000    0.00000    0.00000    0.00000
#>  [9,]    0.00000    0.00000    0.00000    0.00000    0.00000    0.00000
#> [10,]    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
#> [12,]    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
#> [14,]    0.00000    0.00000    0.00000    0.00000    0.00000    0.00000
#> [15,]    0.00000    0.00000    0.00000    0.00000    0.00000    0.00000
#> [16,]    0.00000    0.00000    0.00000    0.00000    0.00000    0.00000
#> [17,]    0.00000    0.00000    0.00000    0.00000    0.00000    0.00000
#> [18,]   31.62278    0.00000    0.00000    0.00000    0.00000    0.00000
#> [19,] -126.49111   31.62278    0.00000    0.00000    0.00000    0.00000
#> [20,]  189.73666 -126.49111   31.62278    0.00000    0.00000    0.00000
#> [21,] -126.49111  189.73666 -126.49111   31.62278    0.00000    0.00000
#> [22,]   31.62278 -126.49111  189.73666 -126.49111   31.62278    0.00000
#> [23,]    0.00000   31.62278 -126.49111  189.73666 -126.49111   31.62278
#> [24,]    0.00000    0.00000   31.62278 -126.49111  189.73666 -126.49111
#> [25,]    0.00000    0.00000    0.00000   31.62278 -126.49111  158.11388
#> [26,]    0.00000    0.00000    0.00000    0.00000   31.62278  -63.24555
#>           [,26]
#>  [1,]   0.00000
#>  [2,]   0.00000
#>  [3,]   0.00000
#>  [4,]   0.00000
#>  [5,]   0.00000
#>  [6,]   0.00000
#>  [7,]   0.00000
#>  [8,]   0.00000
#>  [9,]   0.00000
#> [10,]   0.00000
#> [11,]   0.00000
#> [12,]   0.00000
#> [13,]   0.00000
#> [14,]   0.00000
#> [15,]   0.00000
#> [16,]   0.00000
#> [17,]   0.00000
#> [18,]   0.00000
#> [19,]   0.00000
#> [20,]   0.00000
#> [21,]   0.00000
#> [22,]   0.00000
#> [23,]   0.00000
#> [24,]  31.62278
#> [25,] -63.24555
#> [26,]  31.62278
#> 
#> $EDu
#> [1] 2.01417
#> 
#> $EDs
#> [1] 1.78134
#> 
#> $AIC
#>          [,1]     [,2]
#> [1,] 40.43535 39.98714
#> [2,] 41.06590 40.61831
#> 
#> $BIC
#>          [,1]     [,2]
#> [1,] 50.38838 49.07529
#> [2,] 50.38888 49.07476
#> 
#> attr(,"class")
#> [1] "haz2tsPGAM"