Fit and validate Generalized Boosted Regression models based on Ensembles of Small Models approach
Source:R/esm_gbm.R
esm_gbm.RdThis function constructs Generalized Boosted Regression using the Ensembles of Small Models (ESM) approach (Breiner et al., 2015, 2018).
Usage
esm_gbm(
data,
response,
predictors,
partition,
thr = NULL,
n_trees = 100,
n_minobsinnode = NULL,
shrinkage = 0.1
)Arguments
- data
data.frame. Database with the response (0,1) and predictors values.
- response
character. Column name with species absence-presence data (0,1)
- predictors
character. Vector with the column names of quantitative predictor variables (i.e. continuous variables). This can only construct models with continuous variables and does not allow categorical variables. Usage predictors = c("aet", "cwd", "tmin")
- partition
character. Column name with training and validation partition groups.
- thr
character. Threshold used to get binary suitability values (i.e. 0,1). It is useful for threshold-dependent performance metrics. It is possible to use more than one threshold type. It is necessary to provide a vector for this argument. The following threshold criteria are available:
equal_sens_spec: Threshold at which the sensitivity and specificity are equal.
max_sens_spec: Threshold at which the sum of the sensitivity and specificity is the highest (aka threshold that maximizes the TSS).
max_jaccard: The threshold at which the Jaccard index is the highest.
max_sorensen: The threshold at which the Sorensen index is highest.
max_fpb: The threshold at which FPB (F-measure on presence-background data) is highest.
sensitivity: Threshold based on a specified sensitivity value. Usage thr = c('sensitivity', sens='0.6') or thr = c('sensitivity'). 'sens' refers to sensitivity value. If a sensitivity value is not specified, the default value is 0.9.
In the case of use more than one threshold type it is necessary concatenate threshold types, e.g., thr=c('max_sens_spec', 'max_jaccard'), or thr=c('max_sens_spec', 'sensitivity', sens='0.8'), or thr=c('max_sens_spec', 'sensitivity'). Function will use all thresholds if no threshold is specified.
- n_trees
Integer specifying the total number of trees to fit. This is equivalent to the number of iterations and the number of basis functions in the additive expansion. Default is 100.
- n_minobsinnode
Integer specifying the minimum number of observations in the terminal nodes of the trees. Note that this is the actual number of observations, not the total weight. If n_minobsinnode is NULL, this parameter will assume a value equal to nrow(data)*0.5/4. Default is NULL.
- shrinkage
Numeric. This parameter applied to each tree in the expansion. Also known as the learning rate or step-size reduction; 0.001 to 0.1 usually works, but a smaller learning rate typically requires more trees. Default is 0.1.
Value
A list object with:
esm_model: A list with "gbm" class object from gbm package for each bivariate model. This object can be used for predicting ensembles of small models with
sdm_predictfunction.predictors: A tibble with variables use for modeling.
performance: Performance metrics (see
sdm_eval). Threshold dependent metrics are calculated based on the threshold specified in thr argument.performance_part: Performance metric for each replica and partition (see
sdm_eval).
Details
This method consists of creating bivariate models with all the pair-wise combinations of predictors and perform an ensemble based on the average of suitability weighted by Somers' D metric (D = 2 x (AUC -0.5)). ESM is recommended for modeling species with few occurrences. This function does not allow categorical variables because the use of these types of variables could be problematic when using with few occurrences. For further detail see Breiner et al. (2015, 2018).
References
Breiner, F. T., Guisan, A., Bergamini, A., & Nobis, M. P. (2015). Overcoming limitations of modelling rare species by using ensembles of small models. Methods in Ecology and Evolution, 6(10), 1210-218. https://doi.org/10.1111/2041-210X.12403
Breiner, F. T., Nobis, M. P., Bergamini, A., & Guisan, A. (2018). Optimizing ensembles of small models for predicting the distribution of species with few occurrences. Methods in Ecology and Evolution, 9(4), 802-808. https://doi.org/10.1111/2041-210X.12957
Examples
# \donttest{
data("abies")
require(dplyr)
# Using k-fold partition method
set.seed(10)
abies2 <- abies %>%
na.omit() %>%
group_by(pr_ab) %>%
dplyr::slice_sample(n = 10) %>%
group_by()
abies2 <- part_random(
data = abies2,
pr_ab = "pr_ab",
method = c(method = "rep_kfold", folds = 3, replicates = 5)
)
abies2
#> # A tibble: 20 × 18
#> id pr_ab x y aet cwd tmin ppt_djf ppt_jja pH awc
#> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 12040 0 -308909. 384248. 573. 332. 4.84 521. 48.8 5.63 0.108
#> 2 10361 0 -254286. 417158. 260. 469. 2.93 151. 15.1 6.20 0.0950
#> 3 9402 0 -286979. 386206. 587. 376. 6.45 333. 15.7 5.5 0.160
#> 4 9815 0 -291849. 445595. 443. 455. 4.39 332. 19.1 6 0.0700
#> 5 10524 0 -256658. 184438. 355. 568. 5.87 303. 10.6 5.20 0.0800
#> 6 8860 0 121343. -164170. 354. 733. 3.97 182. 9.83 0 0
#> 7 6431 0 107903. -122968. 461. 578. 4.87 161. 7.66 5.90 0.0900
#> 8 11730 0 -333903. 431238. 561. 364. 6.73 387. 25.2 5.80 0.130
#> 9 808 0 -150163. 357180. 339. 564. 2.64 220. 15.3 6.40 0.100
#> 10 11054 0 -293663. 340981. 477. 396. 3.89 332. 26.4 4.60 0.0634
#> 11 2960 1 -49273. 181752. 512. 275. 0.920 319. 17.3 5.92 0.0900
#> 12 3065 1 126907. -198892. 322. 544. 0.700 203. 10.6 5.60 0.110
#> 13 5527 1 116751. -181089. 261. 537. 0.363 178. 7.43 0 0
#> 14 4035 1 -31777. 115940. 394. 440. 2.07 298. 11.2 6.01 0.0769
#> 15 4081 1 -5158. 90159. 301. 502. 0.703 203. 14.6 6.11 0.0633
#> 16 3087 1 102151. -143976. 299. 425. -2.08 205. 13.4 3.88 0.110
#> 17 3495 1 -19586. 89803. 438. 419. 2.13 189. 15.2 6.19 0.0959
#> 18 4441 1 49405. -60502. 362. 582. 2.42 218. 7.84 5.64 0.0786
#> 19 301 1 -132516. 270845. 367. 196. -2.56 422. 26.3 6.70 0.0300
#> 20 3162 1 59905. -53634. 319. 626. 1.99 212. 4.50 4.51 0.0396
#> # ℹ 7 more variables: depth <dbl>, landform <fct>, .part1 <int>, .part2 <int>,
#> # .part3 <int>, .part4 <int>, .part5 <int>
# Without threshold specification and with kfold
esm_gbm_t1 <- esm_gbm(
data = abies2,
response = "pr_ab",
predictors = c("aet", "cwd", "tmin", "ppt_djf", "ppt_jja", "pH", "awc", "depth"),
partition = ".part",
thr = NULL,
n_trees = 100,
n_minobsinnode = NULL,
shrinkage = 0.1
)
#>
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esm_gbm_t1$esm_model # bivariate model
#> $`0.328240740740741`
#> gbm::gbm(formula = formula1, distribution = "bernoulli", data = data,
#> n.trees = n_trees, n.minobsinnode = n_minobsinnode, shrinkage = shrinkage)
#> A gradient boosted model with bernoulli loss function.
#> 100 iterations were performed.
#> There were 2 predictors of which 2 had non-zero influence.
#>
#> $`0.992592592592593`
#> gbm::gbm(formula = formula1, distribution = "bernoulli", data = data,
#> n.trees = n_trees, n.minobsinnode = n_minobsinnode, shrinkage = shrinkage)
#> A gradient boosted model with bernoulli loss function.
#> 100 iterations were performed.
#> There were 2 predictors of which 2 had non-zero influence.
#>
#> $`0.287037037037037`
#> gbm::gbm(formula = formula1, distribution = "bernoulli", data = data,
#> n.trees = n_trees, n.minobsinnode = n_minobsinnode, shrinkage = shrinkage)
#> A gradient boosted model with bernoulli loss function.
#> 100 iterations were performed.
#> There were 2 predictors of which 2 had non-zero influence.
#>
#> $`0.0240740740740741`
#> gbm::gbm(formula = formula1, distribution = "bernoulli", data = data,
#> n.trees = n_trees, n.minobsinnode = n_minobsinnode, shrinkage = shrinkage)
#> A gradient boosted model with bernoulli loss function.
#> 100 iterations were performed.
#> There were 2 predictors of which 2 had non-zero influence.
#>
#> $`0.103240740740741`
#> gbm::gbm(formula = formula1, distribution = "bernoulli", data = data,
#> n.trees = n_trees, n.minobsinnode = n_minobsinnode, shrinkage = shrinkage)
#> A gradient boosted model with bernoulli loss function.
#> 100 iterations were performed.
#> There were 2 predictors of which 2 had non-zero influence.
#>
#> $`0.658333333333333`
#> gbm::gbm(formula = formula1, distribution = "bernoulli", data = data,
#> n.trees = n_trees, n.minobsinnode = n_minobsinnode, shrinkage = shrinkage)
#> A gradient boosted model with bernoulli loss function.
#> 100 iterations were performed.
#> There were 2 predictors of which 2 had non-zero influence.
#>
#> $`0.985185185185185`
#> gbm::gbm(formula = formula1, distribution = "bernoulli", data = data,
#> n.trees = n_trees, n.minobsinnode = n_minobsinnode, shrinkage = shrinkage)
#> A gradient boosted model with bernoulli loss function.
#> 100 iterations were performed.
#> There were 2 predictors of which 2 had non-zero influence.
#>
#> $`0.353703703703704`
#> gbm::gbm(formula = formula1, distribution = "bernoulli", data = data,
#> n.trees = n_trees, n.minobsinnode = n_minobsinnode, shrinkage = shrinkage)
#> A gradient boosted model with bernoulli loss function.
#> 100 iterations were performed.
#> There were 2 predictors of which 2 had non-zero influence.
#>
#> $`0.375925925925926`
#> gbm::gbm(formula = formula1, distribution = "bernoulli", data = data,
#> n.trees = n_trees, n.minobsinnode = n_minobsinnode, shrinkage = shrinkage)
#> A gradient boosted model with bernoulli loss function.
#> 100 iterations were performed.
#> There were 2 predictors of which 2 had non-zero influence.
#>
#> $`0.600462962962963`
#> gbm::gbm(formula = formula1, distribution = "bernoulli", data = data,
#> n.trees = n_trees, n.minobsinnode = n_minobsinnode, shrinkage = shrinkage)
#> A gradient boosted model with bernoulli loss function.
#> 100 iterations were performed.
#> There were 2 predictors of which 2 had non-zero influence.
#>
#> $`0.992592592592593`
#> gbm::gbm(formula = formula1, distribution = "bernoulli", data = data,
#> n.trees = n_trees, n.minobsinnode = n_minobsinnode, shrinkage = shrinkage)
#> A gradient boosted model with bernoulli loss function.
#> 100 iterations were performed.
#> There were 2 predictors of which 2 had non-zero influence.
#>
#> $`1`
#> gbm::gbm(formula = formula1, distribution = "bernoulli", data = data,
#> n.trees = n_trees, n.minobsinnode = n_minobsinnode, shrinkage = shrinkage)
#> A gradient boosted model with bernoulli loss function.
#> 100 iterations were performed.
#> There were 2 predictors of which 2 had non-zero influence.
#>
#> $`1`
#> gbm::gbm(formula = formula1, distribution = "bernoulli", data = data,
#> n.trees = n_trees, n.minobsinnode = n_minobsinnode, shrinkage = shrinkage)
#> A gradient boosted model with bernoulli loss function.
#> 100 iterations were performed.
#> There were 2 predictors of which 2 had non-zero influence.
#>
#> $`0.992592592592593`
#> gbm::gbm(formula = formula1, distribution = "bernoulli", data = data,
#> n.trees = n_trees, n.minobsinnode = n_minobsinnode, shrinkage = shrinkage)
#> A gradient boosted model with bernoulli loss function.
#> 100 iterations were performed.
#> There were 2 predictors of which 2 had non-zero influence.
#>
#> $`1`
#> gbm::gbm(formula = formula1, distribution = "bernoulli", data = data,
#> n.trees = n_trees, n.minobsinnode = n_minobsinnode, shrinkage = shrinkage)
#> A gradient boosted model with bernoulli loss function.
#> 100 iterations were performed.
#> There were 2 predictors of which 2 had non-zero influence.
#>
#> $`0.0958333333333334`
#> gbm::gbm(formula = formula1, distribution = "bernoulli", data = data,
#> n.trees = n_trees, n.minobsinnode = n_minobsinnode, shrinkage = shrinkage)
#> A gradient boosted model with bernoulli loss function.
#> 100 iterations were performed.
#> There were 2 predictors of which 2 had non-zero influence.
#>
#> $`0.0273148148148148`
#> gbm::gbm(formula = formula1, distribution = "bernoulli", data = data,
#> n.trees = n_trees, n.minobsinnode = n_minobsinnode, shrinkage = shrinkage)
#> A gradient boosted model with bernoulli loss function.
#> 100 iterations were performed.
#> There were 2 predictors of which 2 had non-zero influence.
#>
#> $`0.19537037037037`
#> gbm::gbm(formula = formula1, distribution = "bernoulli", data = data,
#> n.trees = n_trees, n.minobsinnode = n_minobsinnode, shrinkage = shrinkage)
#> A gradient boosted model with bernoulli loss function.
#> 100 iterations were performed.
#> There were 2 predictors of which 2 had non-zero influence.
#>
#> $`0.622222222222222`
#> gbm::gbm(formula = formula1, distribution = "bernoulli", data = data,
#> n.trees = n_trees, n.minobsinnode = n_minobsinnode, shrinkage = shrinkage)
#> A gradient boosted model with bernoulli loss function.
#> 100 iterations were performed.
#> There were 2 predictors of which 2 had non-zero influence.
#>
#> $`0.53287037037037`
#> gbm::gbm(formula = formula1, distribution = "bernoulli", data = data,
#> n.trees = n_trees, n.minobsinnode = n_minobsinnode, shrinkage = shrinkage)
#> A gradient boosted model with bernoulli loss function.
#> 100 iterations were performed.
#> There were 2 predictors of which 2 had non-zero influence.
#>
#> $`0.548148148148148`
#> gbm::gbm(formula = formula1, distribution = "bernoulli", data = data,
#> n.trees = n_trees, n.minobsinnode = n_minobsinnode, shrinkage = shrinkage)
#> A gradient boosted model with bernoulli loss function.
#> 100 iterations were performed.
#> There were 2 predictors of which 2 had non-zero influence.
#>
#> $`0.593981481481481`
#> gbm::gbm(formula = formula1, distribution = "bernoulli", data = data,
#> n.trees = n_trees, n.minobsinnode = n_minobsinnode, shrinkage = shrinkage)
#> A gradient boosted model with bernoulli loss function.
#> 100 iterations were performed.
#> There were 2 predictors of which 2 had non-zero influence.
#>
esm_gbm_t1$predictors
#> # A tibble: 1 × 8
#> c1 c2 c3 c4 c5 c6 c7 c8
#> <chr> <chr> <chr> <chr> <chr> <chr> <chr> <chr>
#> 1 aet cwd tmin ppt_djf ppt_jja pH awc depth
esm_gbm_t1$performance
#> # A tibble: 7 × 33
#> model threshold thr_value n_presences n_absences TPR_mean TPR_sd TNR_mean
#> <chr> <chr> <dbl> <int> <int> <dbl> <dbl> <dbl>
#> 1 esm_gbm equal_sens_… 0.586 10 10 0.944 0.116 0.944
#> 2 esm_gbm lpt 0.292 10 10 1 0 0.944
#> 3 esm_gbm max_fpb 0.310 10 10 1 0 0.944
#> 4 esm_gbm max_jaccard 0.310 10 10 1 0 0.944
#> 5 esm_gbm max_sens_sp… 0.370 10 10 0.944 0.116 1
#> 6 esm_gbm max_sorensen 0.310 10 10 1 0 0.944
#> 7 esm_gbm sensitivity 0.590 10 10 1 0 0.944
#> # ℹ 25 more variables: TNR_sd <dbl>, W_TPR_TNR_mean <dbl>, W_TPR_TNR_sd <dbl>,
#> # SORENSEN_mean <dbl>, SORENSEN_sd <dbl>, JACCARD_mean <dbl>,
#> # JACCARD_sd <dbl>, FPB_mean <dbl>, FPB_sd <dbl>, OR_mean <dbl>, OR_sd <dbl>,
#> # TSS_mean <dbl>, TSS_sd <dbl>, KAPPA_mean <dbl>, KAPPA_sd <dbl>,
#> # MCC_mean <dbl>, MCC_sd <dbl>, AUC_mean <dbl>, AUC_sd <dbl>,
#> # BOYCE_mean <dbl>, BOYCE_sd <dbl>, CRPS_mean <dbl>, CRPS_sd <dbl>,
#> # IMAE_mean <dbl>, IMAE_sd <dbl>
esm_gbm_t1$performance_part
#> # A tibble: 105 × 21
#> model replicates part threshold thr_value n_presences n_absences TPR TNR
#> <chr> <chr> <chr> <chr> <dbl> <int> <int> <dbl> <dbl>
#> 1 esm_… .part1 1 max_sore… 0.310 4 4 1 0.75
#> 2 esm_… .part1 1 max_jacc… 0.310 4 4 1 0.75
#> 3 esm_… .part1 1 max_fpb 0.310 4 4 1 0.75
#> 4 esm_… .part1 1 max_sens… 0.622 4 4 0.75 1
#> 5 esm_… .part1 1 equal_se… 0.332 4 4 0.75 0.75
#> 6 esm_… .part1 1 lpt 0.310 4 4 1 0.75
#> 7 esm_… .part1 1 sensitiv… 0.310 4 4 1 0.75
#> 8 esm_… .part1 2 max_sore… 0.587 3 3 1 0.667
#> 9 esm_… .part1 2 max_jacc… 0.587 3 3 1 0.667
#> 10 esm_… .part1 2 max_fpb 0.587 3 3 1 0.667
#> # ℹ 95 more rows
#> # ℹ 12 more variables: W_TPR_TNR <dbl>, SORENSEN <dbl>, JACCARD <dbl>,
#> # FPB <dbl>, OR <dbl>, TSS <dbl>, KAPPA <dbl>, MCC <dbl>, AUC <dbl>,
#> # BOYCE <dbl>, CRPS <dbl>, IMAE <dbl>
# }