Save log likelihoods of k-fold cross-validation for sdmTMB models.

sdmTMB_cv(
  formula,
  data,
  mesh_args,
  mesh = NULL,
  time = NULL,
  k_folds = 8,
  fold_ids = NULL,
  parallel = TRUE,
  use_initial_fit = FALSE,
  spde = deprecated(),
  ...
)

Arguments

formula

Model formula.

data

A data frame.

mesh_args

Arguments for make_mesh(). If supplied, the mesh will be reconstructed for each fold.

mesh

Output from make_mesh(). If supplied, the mesh will be constant across folds.

time

The name of the time column. Leave as NULL if this is only spatial data.

k_folds

Number of folds.

fold_ids

Optional vector containing user fold IDs. Can also be a single string, e.g. "fold_id" representing the name of the variable in data.

parallel

If TRUE and a future::plan() is supplied, will be run in parallel.

use_initial_fit

Fit the first fold and use those parameter values as starting values for subsequent folds? Can be faster with many folds.

spde

Depreciated. Use mesh instead.

...

All other arguments required to run sdmTMB() model with the exception of weights, which are used to define the folds.

Value

A list:

  • data: Original data plus columns for fold ID, CV predicted value, and CV log likelihood.

  • models: A list of models; one per fold.

  • fold_loglik: Sum of left-out log likelihoods per fold.

  • fold_elpd: Expected log predictive density per fold on left-out data.

  • sum_loglik: Sum of fold_loglik across all left-out data.

  • elpd: Expected log predictive density across all left-out data.

  • pdHess: Logical vector: Hessian was invertible each fold?

  • converged: Logical: all pdHess TRUE?

  • max_gradients: Max gradient per fold.

Details

Parallel processing can be used by setting a future::plan().

For example:

library(future)
plan(multisession)
# now use sdmTMB_cv() ...

Examples

mesh <- make_mesh(pcod, c("X", "Y"), cutoff = 25)

# Set parallel processing first if desired with the future package.
# See the Details section above.

m_cv <- sdmTMB_cv(
  density ~ 0 + depth_scaled + depth_scaled2,
  data = pcod, mesh = mesh,
  family = tweedie(link = "log"), k_folds = 2
)
#> Running fits with `future.apply()`.
#> Set a parallel `future::plan()` to use parallel processing.

m_cv$fold_elpd
#> [1] -1.058983 -1.035476
m_cv$elpd
#> [1] -1.046859

m_cv$fold_loglik
#> [1] -3288.382 -3326.460
m_cv$sum_loglik
#> [1] -6614.843

head(m_cv$data)
#> # A tibble: 6 × 15
#>    year     X     Y depth density present   lat   lon depth_mean depth_sd
#>   <int> <dbl> <dbl> <dbl>   <dbl>   <dbl> <dbl> <dbl>      <dbl>    <dbl>
#> 1  2003  446. 5793.   201   113.        1  52.3 -130.       5.16    0.445
#> 2  2003  446. 5800.   212    41.7       1  52.3 -130.       5.16    0.445
#> 3  2003  449. 5802.   220     0         0  52.4 -130.       5.16    0.445
#> 4  2003  437. 5802.   197    15.7       1  52.4 -130.       5.16    0.445
#> 5  2003  421. 5771.   256     0         0  52.1 -130.       5.16    0.445
#> 6  2003  418. 5772.   293     0         0  52.1 -130.       5.16    0.445
#> # … with 5 more variables: depth_scaled <dbl>, depth_scaled2 <dbl>,
#> #   cv_fold <int>, cv_predicted <dbl>, cv_loglik <dbl>
m_cv$models[[1]]
#> Spatial model fit by ML ['sdmTMB']
#> Formula: density ~ 0 + depth_scaled + depth_scaled2
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#>  Mesh: 2L, 1L, 2L, 1L, 1L, 1L, 1L, NA, 3L, 2L, 1L, 1L, 3L, 3L, 2L, 1L, 
#>  Mesh: 1L, 1L, 2L, NA, 3L, 1L, 1L, 3L, 1L, 1L, 1L, 3L, 1L, 3L, 1L, 1L, 
#>  Mesh: 1L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 3L, 1L, 1L, 1L, 1L, 1L, 2L, 3L, 
#>  Mesh: 1L, 1L, 1L, 1L, 1L, 2L, 1L, 3L, 1L, 2L, 1L, 3L, 1L, 1L, 2L, 1L, 
#>  Mesh: 1L, 2L, 1L, 3L, 2L, 3L, 1L, 2L, 1L, 2L, 2L, NA, 3L, 3L, 2L, 1L, 
#>  Mesh: 3L, 1L, NA, 3L, 2L, 1L, 2L, 2L, 3L, 1L, 2L, 2L, 2L, 2L, 3L, 3L, 
#>  Mesh: 1L, 3L, 2L, 2L, 2L, 3L, 1L, 2L, 3L, 2L, 2L, 2L, 3L, 2L, 3L, 3L, 
#>  Mesh: 2L, NA, 3L, 2L, NA, 1L, 3L, 3L, 2L, 2L, 1L, 3L, 3L, 1L, 3L, 2L, 
#>  Mesh: 3L, 2L, 2L, 3L, 1L, 2L, 3L, 3L, 2L, 2L, 2L, 3L, 2L, 2L, 3L, 2L, 
#>  Mesh: 2L, 1L, 3L, 3L, 2L, 1L, 2L, 2L, 1L, 2L, 3L, 2L, 3L, 3L, 2L, 2L, 
#>  Mesh: 2L, 2L, 2L, 2L, 2L, 2L, 1L, 3L, 3L, 3L, NA, 1L, NA, 3L, 3L, 2L, 
#>  Mesh: 1L, 2L, 2L, 1L, 2L, 3L, 2L, 2L, 3L, 3L, 1L, 1L, 2L, 2L, 3L, 2L, 
#>  Mesh: 3L, 3L, 3L, 1L, 2L, 3L, 2L, 3L, 1L, 3L, 2L, 2L, 3L, 1L, 3L, 2L, 
#>  Mesh: 2L, 3L, 3L, 3L, 3L, 2L, NA, 2L, 3L, 2L, 2L, 2L, 1L, 3L, 3L, 1L, 
#>  Mesh: NA, 2L, NA, 3L, 2L, 3L, 2L, 1L, 3L, 1L, 3L, 3L, 3L, 3L, 1L, 3L, 
#>  Mesh: 3L, 2L, 3L, 3L, 1L, 2L, 3L, 3L, 1L, 3L, 2L, 2L, 3L, 2L, 2L), dim = c(91L, 
#>  Mesh: 3L)), vv = new("dgTMatrix", i = c(1L, 8L, 9L, 19L, 20L, 30L, 
#>  Mesh: 0L, 2L, 8L, 25L, 30L, 35L, 1L, 21L, 25L, 31L, 34L, 35L, 4L, 7L, 
#>  Mesh: 13L, 26L, 33L, 3L, 5L, 13L, 14L, 15L, 22L, 33L, 4L, 6L, 15L, 
#>  Mesh: 22L, 23L, 24L, 5L, 15L, 23L, 32L, 41L, 52L, 3L, 17L, 25L, 26L, 
#>  Mesh: 30L, 33L, 0L, 1L, 9L, 10L, 12L, 35L, 0L, 8L, 10L, 20L, 44L, 53L, 
#>  Mesh: 8L, 9L, 11L, 12L, 45L, 53L, 10L, 12L, 45L, 46L, 47L, 48L, 49L, 
#>  Mesh: 8L, 10L, 11L, 21L, 35L, 49L, 3L, 4L, 14L, 26L, 29L, 51L, 4L, 
#>  Mesh: 13L, 22L, 36L, 51L, 4L, 5L, 6L, 16L, 32L, 33L, 15L, 17L, 27L, 
#>  Mesh: 32L, 33L, 7L, 16L, 19L, 27L, 30L, 33L, 19L, 27L, 28L, 42L, 56L, 
#>  Mesh: 0L, 17L, 18L, 20L, 27L, 28L, 30L, 0L, 9L, 19L, 28L, 44L, 2L, 
#>  Mesh: 12L, 31L, 35L, 49L, 54L, 4L, 5L, 14L, 24L, 36L, 5L, 6L, 24L, 
#>  Mesh: 38L, 39L, 40L, 41L, 5L, 22L, 23L, 36L, 37L, 38L, 1L, 2L, 7L, 
#>  Mesh: 26L, 30L, 34L, 3L, 7L, 13L, 25L, 29L, 34L, 16L, 17L, 18L, 19L, 
#>  Mesh: 32L, 42L, 18L, 19L, 20L, 43L, 44L, 56L, 13L, 26L, 34L, 51L, 55L, 
#>  Mesh: 0L, 1L, 7L, 17L, 19L, 25L, 2L, 21L, 34L, 50L, 54L, 6L, 15L, 16L, 
#>  Mesh: 27L, 42L, 52L, 3L, 4L, 7L, 15L, 16L, 17L, 2L, 25L, 26L, 29L, 
#>  Mesh: 31L, 50L, 55L, 1L, 2L, 8L, 12L, 21L, 14L, 22L, 24L, 37L, 51L, 
#>  Mesh: 24L, 36L, 38L, 23L, 24L, 37L, 39L, 23L, 38L, 40L, 23L, 39L, 41L, 
#>  Mesh: 6L, 23L, 40L, 52L, 18L, 27L, 32L, 52L, 56L, 28L, 44L, 56L, 9L, 
#>  Mesh: 20L, 28L, 43L, 53L, 10L, 11L, 46L, 53L, 11L, 45L, 47L, 11L, 46L, 
#>  Mesh: 48L, 11L, 47L, 49L, 11L, 12L, 21L, 48L, 54L, 31L, 34L, 54L, 55L, 
#>  Mesh: 13L, 14L, 29L, 36L, 55L, 6L, 32L, 41L, 42L, 9L, 10L, 44L, 45L, 
#>  Mesh: 21L, 31L, 49L, 50L, 29L, 34L, 50L, 51L, 18L, 28L, 42L, 43L), 
#>  Mesh:     j = c(0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 
#>  Mesh:     2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 
#>  Mesh:     4L, 4L, 5L, 5L, 5L, 5L, 5L, 5L, 6L, 6L, 6L, 6L, 6L, 6L, 7L, 
#>  Mesh:     7L, 7L, 7L, 7L, 7L, 8L, 8L, 8L, 8L, 8L, 8L, 9L, 9L, 9L, 9L, 
#>  Mesh:     9L, 9L, 10L, 10L, 10L, 10L, 10L, 10L, 11L, 11L, 11L, 11L, 
#>  Mesh:     11L, 11L, 11L, 12L, 12L, 12L, 12L, 12L, 12L, 13L, 13L, 13L, 
#>  Mesh:     13L, 13L, 13L, 14L, 14L, 14L, 14L, 14L, 15L, 15L, 15L, 15L, 
#>  Mesh:     15L, 15L, 16L, 16L, 16L, 16L, 16L, 17L, 17L, 17L, 17L, 17L, 
#>  Mesh:     17L, 18L, 18L, 18L, 18L, 18L, 19L, 19L, 19L, 19L, 19L, 19L, 
#>  Mesh:     19L, 20L, 20L, 20L, 20L, 20L, 21L, 21L, 21L, 21L, 21L, 21L, 
#>  Mesh:     22L, 22L, 22L, 22L, 22L, 23L, 23L, 23L, 23L, 23L, 23L, 23L, 
#>  Mesh:     24L, 24L, 24L, 24L, 24L, 24L, 25L, 25L, 25L, 25L, 25L, 25L, 
#>  Mesh:     26L, 26L, 26L, 26L, 26L, 26L, 27L, 27L, 27L, 27L, 27L, 27L, 
#>  Mesh:     28L, 28L, 28L, 28L, 28L, 28L, 29L, 29L, 29L, 29L, 29L, 30L, 
#>  Mesh:     30L, 30L, 30L, 30L, 30L, 31L, 31L, 31L, 31L, 31L, 32L, 32L, 
#>  Mesh:     32L, 32L, 32L, 32L, 33L, 33L, 33L, 33L, 33L, 33L, 34L, 34L, 
#>  Mesh:     34L, 34L, 34L, 34L, 34L, 35L, 35L, 35L, 35L, 35L, 36L, 36L, 
#>  Mesh:     36L, 36L, 36L, 37L, 37L, 37L, 38L, 38L, 38L, 38L, 39L, 39L, 
#>  Mesh:     39L, 40L, 40L, 40L, 41L, 41L, 41L, 41L, 42L, 42L, 42L, 42L, 
#>  Mesh:     42L, 43L, 43L, 43L, 44L, 44L, 44L, 44L, 44L, 45L, 45L, 45L, 
#>  Mesh:     45L, 46L, 46L, 46L, 47L, 47L, 47L, 48L, 48L, 48L, 49L, 49L, 
#>  Mesh:     49L, 49L, 49L, 50L, 50L, 50L, 50L, 51L, 51L, 51L, 51L, 51L, 
#>  Mesh:     52L, 52L, 52L, 52L, 53L, 53L, 53L, 53L, 54L, 54L, 54L, 54L, 
#>  Mesh:     55L, 55L, 55L, 55L, 56L, 56L, 56L, 56L), Dim = c(57L, 57L
#>  Mesh:     ), Dimnames = list(NULL, NULL), x = c(1, 1, 1, 1, 1, 1, 1, 
#>  Mesh:     1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
#>  Mesh:     1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
#>  Mesh:     1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
#>  Mesh:     1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
#>  Mesh:     1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
#>  Mesh:     1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
#>  Mesh:     1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
#>  Mesh:     1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
#>  Mesh:     1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
#>  Mesh:     1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
#>  Mesh:     1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
#>  Mesh:     1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
#>  Mesh:     1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
#>  Mesh:     1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
#>  Mesh:     1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
#>  Mesh:     1, 1), factors = list())), segm = list(bnd = structure(list(
#>  Mesh:     loc = NULL, idx = structure(c(37L, 38L, 39L, 40L, 41L, 42L, 
#>  Mesh:     53L, 43L, 57L, 44L, 45L, 54L, 46L, 47L, 48L, 49L, 50L, 55L, 
#>  Mesh:     51L, 56L, 52L, 38L, 39L, 40L, 41L, 42L, 53L, 43L, 57L, 44L, 
#>  Mesh:     45L, 54L, 46L, 47L, 48L, 49L, 50L, 55L, 51L, 56L, 52L, 37L
#>  Mesh:     ), dim = c(21L, 2L)), grp = structure(c(0L, 0L, 0L, 0L, 0L, 
#>  Mesh:     0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
#>  Mesh:     0L), dim = c(21L, 1L)), is.bnd = TRUE, crs = NULL), class = "inla.mesh.segment"), 
#>  Mesh:     int = structure(list(loc = NULL, idx = structure(integer(0), dim = c(0L, 
#>  Mesh:     2L)), grp = structure(integer(0), dim = 0:1), is.bnd = FALSE, 
#>  Mesh:         crs = NULL), class = "inla.mesh.segment")), idx = list(
#>  Mesh:     loc = c(1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 4L, 4L, 
#>  Mesh:     5L, 5L, 5L, 5L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 7L, 7L, 7L, 8L, 
#>  Mesh:     8L, 34L, 31L, 31L, 31L, 2L, 2L, 2L, 31L, 2L, 2L, 9L, 9L, 
#>  Mesh:     9L, 9L, 9L, 9L, 9L, 10L, 10L, 10L, 11L, 10L, 11L, 11L, 11L, 
#>  Mesh:     11L, 13L, 9L, 12L, 12L, 12L, 12L, 13L, 13L, 14L, 14L, 15L, 
#>  Mesh:     15L, 15L, 15L, 6L, 6L, 5L, 5L, 5L, 14L, 5L, 5L, 4L, 5L, 5L, 
#>  Mesh:     5L, 34L, 16L, 16L, 6L, 6L, 6L, 6L, 25L, 34L, 17L, 18L, 18L, 
#>  Mesh:     18L, 18L, 19L, 19L, 19L, 20L, 20L, 20L, 20L, 21L, 21L, 21L, 
#>  Mesh:     21L, 21L, 10L, 21L, 10L, 10L, 10L, 1L, 9L, 9L, 9L, 9L, 9L, 
#>  Mesh:     36L, 22L, 22L, 22L, 2L, 36L, 36L, 36L, 36L, 36L, 36L, 36L, 
#>  Mesh:     22L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 35L, 3L, 3L, 2L, 2L, 
#>  Mesh:     5L, 5L, 5L, 23L, 23L, 5L, 14L, 14L, 24L, 24L, 25L, 25L, 25L, 
#>  Mesh:     6L, 6L, 6L, 6L, 26L, 26L, 35L, 26L, 26L, 26L, 26L, 26L, 26L, 
#>  Mesh:     27L, 27L, 27L, 30L, 30L, 27L, 24L, 25L, 25L, 16L, 16L, 16L, 
#>  Mesh:     16L, 33L, 33L, 33L, 28L, 28L, 28L, 28L, 28L, 28L, 28L, 28L, 
#>  Mesh:     20L, 20L, 20L, 20L, 20L, 31L, 31L, 31L, 1L, 1L, 4L, 27L, 
#>  Mesh:     18L, 18L, 18L, 18L, 8L, 8L, 8L, 31L, 8L, 27L, 16L, 16L, 16L, 
#>  Mesh:     16L, 16L, 33L, 16L, 7L, 6L, 6L, 6L, 25L, 24L, 26L, 26L, 31L, 
#>  Mesh:     16L, 16L, 16L, 16L, 6L, 7L, 7L, 7L, 24L, 24L, 5L, 34L, 17L, 
#>  Mesh:     17L, 34L, 2L, 9L, 9L, 9L, 9L, 9L, 9L, 10L, 24L, 24L, 17L, 
#>  Mesh:     17L, 17L, 17L, 17L, 28L, 28L, 28L, 28L, 28L, 28L, 28L, 19L, 
#>  Mesh:     20L, 20L, 20L, 19L, 29L, 29L, 21L, 21L, 21L, 21L, 10L, 10L, 
#>  Mesh:     10L, 10L, 9L, 1L, 25L, 25L, 25L, 25L, 6L, 23L, 23L, 5L, 5L, 
#>  Mesh:     5L, 7L, 5L, 15L, 15L, 15L, 15L, 15L, 15L, 23L, 23L, 23L, 
#>  Mesh:     23L, 23L, 25L, 6L, 25L, 23L, 23L, 5L, 10L, 10L, 11L, 12L, 
#>  Mesh:     12L, 12L, 12L, 12L, 12L, 13L, 13L, 13L, 13L, 13L, 13L, 9L, 
#>  Mesh:     36L, 2L, 2L, 2L, 2L, 2L, 31L, 1L, 31L, 31L, 31L, 2L, 31L, 
#>  Mesh:     31L, 4L, 36L, 22L, 22L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 
#>  Mesh:     13L, 13L, 13L, 13L, 22L, 22L, 22L, 36L, 26L, 27L, 27L, 27L, 
#>  Mesh:     30L, 30L, 30L, 30L, 30L, 31L, 31L, 31L, 31L, 18L, 8L, 8L, 
#>  Mesh:     31L, 31L, 8L, 8L, 8L, 8L, 8L, 34L, 5L, 4L, 4L, 4L, 14L, 4L, 
#>  Mesh:     23L, 5L, 6L, 6L, 6L, 6L, 6L, 6L, 7L, 30L, 30L, 27L, 27L, 
#>  Mesh:     27L, 31L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L, 32L, 32L, 3L, 
#>  Mesh:     31L, 26L, 26L, 26L, 26L, 35L, 35L, 24L, 35L, 26L, 26L, 27L, 
#>  Mesh:     8L, 8L, 8L, 8L, 8L, 8L, 27L, 4L, 4L, 4L, 5L, 20L, 20L, 20L, 
#>  Mesh:     20L, 20L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 33L, 
#>  Mesh:     33L, 33L, 16L, 24L, 24L, 33L, 33L, 33L, 33L, 33L, 33L, 33L, 
#>  Mesh:     33L, 17L, 28L, 28L, 28L, 28L, 28L, 19L, 19L, 19L, 19L, 20L, 
#>  Mesh:     20L, 20L, 20L, 19L, 19L, 20L, 20L, 20L, 20L, 18L, 18L, 28L, 
#>  Mesh:     16L, 16L, 33L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 6L, 7L, 
#>  Mesh:     7L, 7L, 7L, 7L, 7L, 7L, 16L, 18L, 18L, 18L, 20L, 20L, 20L, 
#>  Mesh:     20L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 
#>  Mesh:     1L, 1L, 1L, 1L, 1L, 1L, 31L, 34L, 18L, 8L, 8L, 8L, 8L, 8L, 
#>  Mesh:     5L, 5L, 5L, 6L, 6L, 6L, 6L, 6L, 6L, 7L, 25L, 25L, 25L, 23L, 
#>  Mesh:     23L, 23L, 23L, 23L, 5L, 22L, 22L, 22L, 22L, 22L, 22L, 22L, 
#>  Mesh:     22L, 22L, 13L, 28L, 28L, 28L, 17L, 17L, 17L, 17L, 33L, 13L, 
#>  Mesh:     12L, 12L, 12L, 12L, 12L, 12L, 13L, 13L, 11L, 11L, 11L, 11L, 
#>  Mesh:     10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 
#>  Mesh:     9L, 9L, 10L, 1L, 9L, 13L, 9L, 9L, 9L, 36L, 36L, 36L, 36L, 
#>  Mesh:     9L, 9L, 2L, 4L, 4L, 4L, 4L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 
#>  Mesh:     16L, 5L, 34L, 34L, 34L, 34L, 34L, 8L, 31L, 31L, 2L, 2L, 2L, 
#>  Mesh:     2L, 2L, 36L, 36L, 22L, 3L, 3L, 3L, 35L, 26L, 26L, 8L, 26L, 
#>  Mesh:     26L, 26L, 26L, 27L, 27L, 27L, 23L, 15L, 15L, 15L, 15L, 15L, 
#>  Mesh:     27L, 27L, 27L, 30L, 14L, 27L, 14L, 14L, 14L, 14L, 27L, 4L, 
#>  Mesh:     9L, 9L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 31L, 31L, 31L, 31L, 
#>  Mesh:     31L, 31L, 20L, 20L, 20L, 20L, 20L, 20L, 20L, 18L, 18L, 18L, 
#>  Mesh:     18L, 8L, 4L, 4L, 4L, 4L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 23L, 
#>  Mesh:     23L, 34L, 34L, 4L, 4L, 4L, 8L, 18L, 8L, 31L, 31L, 26L, 26L, 
#>  Mesh:     8L, 8L, 8L, 26L, 2L, 2L, 2L, 2L, 9L, 9L, 9L, 9L, 9L, 9L, 
#>  Mesh:     9L, 11L, 11L, 10L, 10L, 10L, 10L, 11L, 11L, 13L, 13L, 13L, 
#>  Mesh:     4L, 14L, 14L, 14L, 14L, 14L, 14L, 15L, 15L, 15L, 25L, 25L, 
#>  Mesh:     25L, 25L, 6L, 6L, 23L, 15L, 15L, 15L, 15L, 15L, 15L, 2L, 
#>  Mesh:     2L, 2L, 31L, 31L, 31L, 31L, 31L, 26L, 2L, 11L, 12L, 12L, 
#>  Mesh:     13L, 23L, 22L, 22L, 3L, 3L, 3L, 32L, 22L, 3L, 35L, 26L, 26L, 
#>  Mesh:     26L, 35L, 27L, 27L, 27L, 14L, 23L, 23L, 13L, 13L, 13L, 13L, 
#>  Mesh:     13L, 13L, 13L, 13L, 13L, 22L, 22L, 22L, 13L, 36L, 36L, 36L, 
#>  Mesh:     36L, 36L, 36L, 36L, 36L, 36L, 36L, 36L, 24L, 24L, 24L, 24L, 
#>  Mesh:     24L, 24L, 24L, 7L, 7L, 33L, 33L, 33L, 33L, 33L, 33L, 33L, 
#>  Mesh:     33L, 17L, 17L, 28L, 28L, 28L, 28L, 28L, 28L, 28L, 28L, 28L, 
#>  Mesh:     28L, 19L, 20L, 20L, 17L, 17L, 33L, 33L, 33L, 33L, 33L, 33L, 
#>  Mesh:     16L, 16L, 16L, 19L, 20L, 20L, 29L, 29L, 21L, 21L, 21L, 21L, 
#>  Mesh:     21L, 21L, 10L, 21L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 9L, 
#>  Mesh:     9L, 9L, 9L, 16L, 7L, 16L, 16L, 16L, 7L, 6L, 6L, 6L, 6L, 6L, 
#>  Mesh:     24L, 24L, 24L, 17L, 17L, 34L, 28L, 28L, 28L, 19L, 19L, 19L, 
#>  Mesh:     19L, 19L, 29L, 20L, 20L, 24L, 24L, 20L, 20L, 18L, 19L, 19L, 
#>  Mesh:     28L, 28L, 19L, 19L, 19L, 29L, 21L, 21L, 21L, 21L, 21L, 20L, 
#>  Mesh:     20L, 20L, 20L, 20L, 10L, 21L, 10L, 21L, 21L, 1L, 1L, 1L, 
#>  Mesh:     1L, 1L, 2L, 28L, 28L, 28L, 28L, 28L, 28L, 28L, 28L, 28L, 
#>  Mesh:     28L, 17L, 17L, 17L, 17L, 33L, 33L, 33L, 33L, 33L, 33L, 33L, 
#>  Mesh:     33L, 16L, 16L, 24L, 24L, 24L, 7L, 7L, 7L, 16L, 16L, 16L, 
#>  Mesh:     17L, 17L, 17L, 17L, 18L, 17L, 18L, 18L, 18L, 18L, 18L, 31L, 
#>  Mesh:     31L, 31L, 1L, 31L, 31L, 31L, 31L, 1L, 1L, 1L, 9L, 11L, 11L, 
#>  Mesh:     11L, 23L, 26L, 26L, 26L, 26L, 26L, 35L, 35L, 27L, 8L, 22L, 
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#>  Data: 2009L, 2009L, 2009L, 2009L, 2009L, 2009L, 2009L, 2011L, 2011L, 
#>  Data: 2011L, 2011L, 2011L, 2011L, 2011L, 2011L, 2011L, 2011L, 2011L, 
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#>  Data: 2011L, 2011L, 2011L, 2011L, 2011L, 2011L, 2013L, 2013L, 2013L, 
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#>  Data: 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 
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#>  Data: 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 
#>  Data: 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 
#>  Data: 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 
#>  Data: 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 
#>  Data: 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 
#>  Data: 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 
#>  Data: 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 
#>  Data: 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 
#>  Data: 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 
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#>  Data: 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 
#>  Data: 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 
#>  Data: 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 
#>  Data: 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 2017L, 
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