## 7 Variable Selection  
For machine learning methods, variable selection is termed feature selection, while, for non-machine learning methods, it is often called model selection. However, model selection often leads to the most parsimonious fitted model rather than the most accurate predictive model [6]. In this study, we use the term \"variable selection\" for both non-machine learning and machine learning methods to identify and develop the most accurate spatial predictive model(s). Variable selection is important for many predictive methods, although it is not required for all methods. For instance, classification and regression trees [97] and LIVES [98] are exempt from variable selection. However, as per all other methods, they assume that the predictive variables used are informative and not misleading because they treat each predictive variable as equally important. Thus, misleading predictive variables may considerably reduce predictive accuracy as discussed previously [98]. The variable selection procedure for machine learning methods and their hybrid methods is fundamentally different from the procedure for non-machine learning methods [47; 79; 99]. For geostatistical methods like IDW and OK, no variable selection is required, and it is really about the selection of appropriate values for relevant parameters, as discussed in Section 6. In this section, I focus on the following three methods: (1) GLM; (2) RF; and (3) GBM. This is because of their wide applications, robustness, or the recent developments in variable selection techniques for these methods. For GLM, there are many methods available in R for variable selection [100; 101; 102; 103]. These methods may include (1) _stepAIC_ or _step_; (2) _dropterm_, _drop1_, or _add1_; (3) _anova_; (4) _regsubsets_; and (5) _bestglm_[100; 102; 103]. The application of these methods for spatial predictive modeling can be seen in recent studies [6; 104]. Variables selected based on these methods may form the most parsimonious model, but the model may have low predictive accuracy or even be misleading [6; 104], with the exception that _bestglm_ is promising if cross-validation, instead of [PERSON]'s information criterion (AIC) or Bayesian information criterion (BIC), is used for information criteria [104]. Alternatively, the variable selection for GLM can also be based on variables selected by other method such as RF [71]. It was found that traditional variable selection methods are unsuitable for identifying GLM predictive models, and joint application of RF and AIC can select accuracy-improved predictive models [6]. This highlights the importance of differentiating variable selection for predictive modeling [6] from variable selection for hypothesis testing [99] or inferential modeling [19]. The common mistakes associated with incorrectly distinguishing data analytic types were briefly summarized and discussed previously [19]. For RF, variable selection methods may include (1) variable importance (VI) [78], (2) averaged variable importance (AVI) [79], (3) Boruta [105], (4) knowledge informed AVI (KIAVI) [6; 79], (5) recursive feature selection (RFE) [106], and (6) variable selection using RF (VSURF) [107]. Of these methods, KIAVI is recommended because it outperforms all other variable selection methods [6; 79; 104; 108]. For GBM, variables can be selected in terms of the relative influence [95; 108]. The recursive feature selection [106] can also be used for variable selection. Two concepts were proposed for variable selection: important and unimportant predictive variables based on the predictive accuracy [6; 79]. They were defined as follows:  
1. Important variable based on the predictive accuracy (IVPA). This refers to the variable for which exclusion during the variable selection process would reduce the accuracy of a predictive model based on cross-validation. It may be more appropriate to call it predictive accuracy boosting variable (PABV). 2. Unimportant variable based on the predictive accuracy (UVPA).