SDMSelect: Cross-validation model selection and species distribution mapping

Covariates selection method

The model selection procedure will test different combinations of covariates with LM, GLM, GLM natural splines and GAM models, with different distributions (Gaussian, Gamma, Log-Normal, Tweedie; Binomial) and with different maximum degrees of freedom for GLM with polynoms or natural splines. The multiple k-fold cross-validation realised on the same folds for each model/submodel type allows their comparison using cross-validated RMSE or AUC. Covariates correlation can be tested prior to the selection procedure to avoid fitting models with correlated covariates. However, the cross-validation procedure is coupled with a forward stepwise procedure. This means that covariates are added to best models selected at the previous step. This obviously not choose a new covariate that add no predictive power to a model, thus avoiding selecting correlated covariates in the same model.
Models are ordered according to RMSE (or AUC for presence-absence). The cross-validation produces a distribution of (N*k) RMSE values for each model at each step. Models are ordered according to mean RMSE. RMSE distributions of model n°2 to n are then statistically (wilcoxon) compared to the best model. Models not statistically worse than the best model are retained for the next step. After the stepwise procedure, the best model among all is selected with the same method. Models not statistically worse are also identified.

Outputs

Outputs of the selection procedure are numerous, allowing for summary of the model selection and the comparison of the different models alltogether (GAM, GLM; Gaussian, Gamma, Log-Normal, Tweedie; Binomial). All output files and figures are stored in a common folder and are not showing up in the R session directly. The final model retained by the user can then be analysed (residual analysis, variance analysis, effect of covariates). For spatial data, maps of prediction can be produced.

Uncertainties

A particular attention has been given to assessment of uncertainty. Indeed, each prediction of a model is given with a standard error associated. This standard errors have been used to estimate possible minimum and maximum distributions of species (through estimations of quantiles).

Figure 2: Distribution of minimum (quantile 5%) and maximum (quantile 95%) of probabilities of presence

Concerning presence-absence data, the estimation of probability of presence is not enough. The balance between presences and absences in data may conduct to biased predictions. The best threshold value to classify a probability of presence in presence or absence is here explored in more details. Map of probability to be over the threshold value is calculated.

Figure 3: Comparison of predictions against observations in a presence-absence data model and thresholds values

Figure 4: Distribution of probabilities to be over the best threshold value separating presences from absences

Caution

This library relies on a lot of other R-packages, which means that any modifications of those may prevent this library to work correctly. As I continue to use it regularly, I may see if some updates broke some of my functions and would try to fix them.
There are new key libraries in R like dplyr, tidyr, ggplot2 that did not originally exist when I first created these R-scripts. I now try to implement them from time to time.

Remark

This library is not as complete as can be library(caret) in terms of model types available, however, as far as I know, caret model selection procedure is designed for a unique combination of model/distribution. Here, cross-validation outputs of each model/distribution are kept, and can then be compared all together with paired comparison. Moreover, not only the model with the best mean RMSE (or AUC) is retained, but also all other models giving predictions statistically as good as the best one. For biological purpose, knowing all models with the same predictive power may modify outputs interpretation. Another difference is that SDMSelect package is designed for predicting species distribution models, which means that some outputs are maps of species distributions as well as all maps of uncertainty that can be deduced from model outputs.

How to cite

Please give credit where credit is due and cite R and R packages when you use them for data analysis. To cite SDMSelect properly, call the R built-in command citation("SDMSelect"):

Sébastien Rochette. (2018, October 8). SDMSelect: A R-package for cross-validation model selection and species distribution mapping (Version v0.1.4). Zenodo. http://doi.org/10.5281/zenodo.894344

Examples

I plan to write a few other posts to better explain the different functions of this library but the two vignettes included in the package show the main ones. Vignettes have been created to show how to use the library for covariate selection on simple cases (vignette(package = "SDMSelect")).

• First case is covariate selection procedure for classical dataset (not geographical data, nor species distribution data): vignette("Covar_Selection", package = "SDMSelect"). You can read it on covar selection {pkgdown} page
  
• The second case is for spatial data of species occurence to produce predicted species distribution maps and maps of uncertainties: vignette("SDM_Selection", package = "SDMSelect"). You can read it on SDM selection {pkgdown} page

Note that most figures of the vignette are saved in “inst” so that model selection is not run during vignette building. However, code in the vignettes can be run on your own computer and should return the same outputs. You can also find the path of the complete vignettes to be run on your computer with: system.file("Covar_Selection", "Covar_Selection.Rmd", package = "SDMSelect") and system.file("SDM_Selection", "SDM_Selection.Rmd", package = "SDMSelect"). Open and click knit button if you are on Rstudio. (This may require 5-10 minutes depending on the number of cores of your system).

Main functions are listed in the library general help: ?SDMSelect.