###### Abstract
The possible reason may be that most of the applications implicitly or explicitly consider the explanatory variables as mutually independent, which is often not the case in reality. In fact, the VNIR spectra of soil samples are the comprehensive representation of soil properties, and thus multicollinearity inevitably exists. As such, multicollinearity should be removed to obtain relatively independent variables when constructing a MARS model. The multicollinearity-removing strategy from PLS regression is verified to be beneficial by reducing the dimensionality, considering the high dimensionality and correlated representations [4; 18]. Therefore, this research proposes the utilization of partial least squares regression to remove multicollinearity and obtain extensive information on the explanatory variables; the resultant principal components (PCs) from the PLS regression are used as a replacement for the original explanatory variables to construct a MARS model, thereby overcoming the weakness of the available MARS model for prediction of soil properties. For simplicity, the entire process is referred to as the partial least squares-based multivariate adaptive regression spline (PLS-MARS) method herein. The proposed PLS-MARS method can effectively represent the nonlinear relationship between the data with local difference and numerous variables, as will be discussed in Section 3. The accuracy of the prediction model relies significantly on calibrated samples. Underrepresentation of calibrated samples will lead to a biased prediction model due to soil spatial heterogeneity. However, preceding studies (e.g., [8; 9; 11; 12]) focused exclusively on developing new prediction models for estimating soil properties, disregarding the influence of the calibration sets on the reliability of the prediction models. In particular, the calibration sets in most of these studies were selected randomly or from several available methods, such as the concentration gradient method (C method) [19; 20]. The prediction model may be biased if inappropriate calibration sets are adopted [3]. Hence, reasonable calibration sets should be selected before they are applied to construct prediction models. Accordingly, our newly developed multi-variable analysis method (i.e., regional multi-variable associate rule mining and Rank-Kennard-Stone (MVARC-R-KS) method) [3] was adopted to select calibration sets in the current study (see Subsection III-A for elaboration). The MVARC-R-KS method was used due to the following two reasons. (1) This method is effective in enhancing the accuracy of linear prediction methods, such as PLS regression ([PERSON], [PERSON], [PERSON] and [PERSON] [3]), thereby providing the confidence to extend it for nonlinear prediction methods (e.g., the proposed PLS-MARS method in this study). (2) The MVARC-R-KS method can consider multiple influential factors (e.g., chemical component, spectrograph information, and environmental factors) and select a representative calibration set, which makes the VNIR-spectrum-based SOM prediction model calibrated from such a calibration set as to be an extensively applicable one [3]. Three commonly used calibration set selection methods, namely, component concentration representative methods (e.g., the C method [19; 20]), spectrum representative methods (e.g., the Kennard-Stone (KS) method [21]), and component concentration and spectrum representative methods (e.g., the Rank-Kennard-Stone (Rank-KS) method [22]), are also utilized and compared with the MVARC-R-KS method to investigate their influences on the prediction models and further verify the effectiveness of the proposed method. To the best of our knowledge, such a systematic comparison of the influences of different calibration set selection methods on the performance of SOM prediction models, particularly nonlinear prediction models, such as the proposed PLS-MARS model herein, appears to be original. This comparison is expected to guide the calibration set selection for a specific prediction model in the future.