Multivariate Adaptive Regression Spline Modeling in SAS

Surface longwave net radiation (LWNR) is a vital component in the surface radiation budget. Major progress has been made in the estimations of clear-sky LWNR. However, the estimation of cloudy-sky LWNR remains a significant challenge. In this paper, a linear model (LM) and a multivariate adaptive regression spline (MARS) model were developed to estimate the cloudy-sky LWNR from a satellite-derived surface shortwave net radiation product. Spatially and temporally matched satellite data and ground-measured LWNR, which was collected at 24 sites from four networks, were used to build and validate the linear and MARS models. The effects of land cover, climate type, and surface elevation on the estimate of LWNR were also analyzed. The MARS model, incorporating the normalized difference vegetation index (NDVI) and surface elevation (H) as the inputs, had the best performance. The determination coefficient, BIAS, and root mean square error (RMSE) were 0.51, 0.01 W/m2, and 26.10 W/m2, respectively. The developed model, when combined with freely distributed Global LAnd Surface Satellite (GLASS) products, showed promise for producing surface LWNR and all-sky surface net radiation.

The current study investigates an improved version of Least Square Support Vector Machines integrated with a Bat Algorithm (LSSVM-BA) for modeling the dissolved oxygen (DO) concentration in rivers. The LSSVM-BA model results are compared with those obtained using M5 Tree and Multivariate Adaptive Regression Spline (MARS) models to show the efficacy of this novel integrated model. The river water quality data at three monitoring stations located in the USA are considered for the simulation of DO concentration. Eight input combinations of four water quality parameters, namely, water temperature, discharge, pH, and specific conductance, are used to simulate the DO concentration. The results revealed the superiority of the LSSVM-BA model over the M5 Tree and MARS models in the prediction of river DO. The accuracy of the LSSVM-BA model compared with those of the M5 Tree and MARS models is found to increase by 20% and 42%, respectively, in terms of the root-mean-square error. All the predictive models are found to perform best when all the four water quality variables are used as input, which indicates that it is possible to supply more information to the predictive model by way of incorporation of all the water quality variables.

Application of least square support vector machine and multivariate adaptive regression spline models in long term prediction of river water pollution

Driven pile is widely used as an effective and convenient structural component to transfer superstructure loads to deep stiffer soils. Nevertheless, during the design process of piles, due to the intrinsic complexity as well as various design variables, the internal stress state related to pile drivability remains unclear, which makes the analysis imprecise. Thus, the development of an accurate predictive model becomes emergent. This paper presents a practical approach to assess pile drivability in relation to the prediction of Maximum compressive stresses and Blow per foot using a series of machine learning algorithms. A database of more than 4000 piles is employed to construct random forest regression (RFR) and multivariate adaptive regression splines (MARS) models. The 10-fold cross-validation method and Lasso regularisation are adapted to obtain the model of superior generalisation ability and better persuasive results. Lastly, the results of RFR and MARS models were compared and evaluated in accordance with the goodness of fit, running time and interpretability. The results show that the RFR model performs better than the MARS in terms of fitting and operational efficiency, but is short of interpretability.

A Multivariate Adaptive Regression Splines model for determining horizontal wall deflection envelope for braced excavations in clays

Axisymmetric solutions for the bearing capacity of ring foundation resting on anisotropic and heterogenous clays are presented in this paper using finite element analysis (FEA). The NGI-ADP model in PLAXIS FEA, a widely used anisotropic soil model, is adopted to study the stability responses of ring foundations, with special consideration given to the effects of increasing undrained shear strength with the depth. Numerical results are formulated in terms of a dimensionless stability number (bearing capacity ratio) that is a function of three dimensionless input parameters: namely, the ratio of inner and outer radius, the increasing strength gradient ratio, and the anisotropic shear strength ratio. The influence of each dimensionless input parameter on the bearing capacity ratio is investigated using design charts and failure mechanisms, and they are scored by relative importance indexes in multivariate adaptive regression splines (MARS) model—a machine learning approach. A highly accurate equation generated from the MARS model is proposed as an effective tool for engineering practitioners.

The treatment of childhood myopia often involves the use of topical atropine, which has been demonstrated to be effective in decelerating the progression of myopia. It is crucial to monitor intraocular pressure (IOP) to ensure the safety of topical atropine. This study aims to identify the optimal machine learning IOP-monitoring module and establish a precise baseline IOP as a clinical safety reference for atropine medication. Data from 1545 eyes of 1171 children receiving atropine for myopia were retrospectively analyzed. Nineteen variables including patient demographics, medical history, refractive error, and IOP measurements were considered. The data were analyzed using a multivariate adaptive regression spline (MARS) model to analyze the impact of different factors on the End IOP. The MARS model identified age, baseline IOP, End Spherical, duration of previous atropine treatment, and duration of current atropine treatment as the five most significant factors influencing the End IOP. The outcomes revealed that the baseline IOP had the most significant effect on final IOP, exhibiting a notable knot at 14 mmHg. When the baseline IOP was equal to or exceeded 14 mmHg, there was a positive correlation between atropine use and End IOP, suggesting that atropine may increase the End IOP in children with a baseline IOP greater than 14 mmHg. MARS model demonstrates a better ability to capture nonlinearity than classic multiple linear regression for predicting End IOP. It is crucial to acknowledge that administrating atropine may elevate intraocular pressure when the baseline IOP exceeds 14 mmHg. These findings offer valuable insights into factors affecting IOP in children undergoing atropine treatment for myopia, enabling clinicians to make informed decisions regarding treatment options.

In the paper, the response surface modeling approach is applied to study the effectiveness of different grounding schemes implemented for mitigation of single-line-to-ground faults in a simulation of a notional Medium Voltage DC shipboard power system. Multivariate adaptive regression splines (MARS) models are used for preliminary exploration of the functional relationships between the input parameters and response variables. Using the constructed MARS models, Sobol’ total sensitivity indices were computed for the models to study possible differences in the sensitivities of the response variables for the different grounding schemes. For final analyses, and for response surface models for which the MARS models show significant prediction error, Gaussian process models are used to account for prediction variance.

This study predicts the strength of rotary brace damper by analyzing a new set of probabilistic models using the usual method of multiple linear regressions (MLR) and advanced machine-learning methods of multivariate adaptive regression splines (MARS), Rotary brace damper can be easily assembled with high energy-dissipation capability. To investigate the behavior of this damper in structures, a steel frame is modeled with this device subjected to monotonic and cyclic loading. Several response parameters are considered, and the performance of damper in reducing each response is evaluated. MLR and MARS methods were used to predict the strength of this damper. Displacement was determined to be the most effective parameter of damper strength, whereas the thickness did not exhibit any effect. Adding thickness parameter as inputs to MARS and MLR models did not increase the accuracies of the models in predicting the strength of this damper. The MARS model with a root mean square error (RMSE) of 0.127 and mean absolute error (MAE) of 0.090 performed better than the MLR model with an RMSE of 0.221 and MAE of 0.181.

The precise forecasting of daily solar radiation (DSR) is receiving prominent attention among thriving solar energy studies. In this study, three standalone models, including gene expression programing (GEP), multivariate adaptive regression splines (MARS), and self-adaptive MARS (SaMARS), were evaluated to forecast DSR. A SaMARS model was classified as MARS model when using the crow search algorithm (CSA). In addition, to overcome the limitations of the standalone models, the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) was employed to enhance the accuracy of DSR forecasting. Therefore, three hybrid models including CEEMDAN-GEP, CEEMDAN-MARS, and CEEMDAN-SaMARS were proposed to forecast DSR in Busan and Incheon stations in South Korea. The performance of proposed models were evaluated and affirmed that the accuracy of the CEEMDAN-SaMARS model (NSE = 0.878–0.883) outperformed CEEMDAN-MARS (NSE = 0.819–0.818), CEEMDAN-GEP (NSE = 0.873–0.789), SaMARS (NSE = 0.846–0.769), MARS (NSE = 0.819–0.758), and GEP (NSE = 0.814–0.755) models at both stations. Therefore, it can be concluded that the optimized CEEMDAN-SaMARS model significantly enhanced the accuracy of DSR forecasting compared to that of standalone models.

Forecast Bankruptcy Using a Blend of Clustering and MARS Model - Case of US Banks

Multivariate adaptive regression splines (MARS) in chromatographic quantitative structure–retention relationship studies

Background: Myocardial perfusion scintigraphy (MPS) is an important tool for evaluating ischemia in diabetic populations. However, applications of advanced predictive models like multivariate adaptive regression splines (MARS) to estimate summed stress scores (SSS) are lacking. Methods: In this study, 1028 diabetic women undergoing Thallium-201 MPS were analyzed. The dataset was split into training (80%) and testing (20%) subsets. MARS and multiple linear regression (MLR) models were constructed to predict SSS, and their performance was evaluated using root mean square error (RMSE), relative absolute error (RAE), root relative squared error (RRSE), Mean Absolute Percentage Error (MAPE), and Symmetric Mean Absolute Percentage Error (SMAPE). Results: On the testing dataset, the MARS model outperformed the MLR model across all metrics, with an RMSE of 3.25 compared to 3.89 for MLR, an RAE of 0.52 vs. 0.64, and an RRSE of 0.53 vs. 0.67. Similar trends were observed in MAPE (18.7% vs. 22.1%) and SMAPE (17.3% vs. 20.5%). Conclusions: The superior predictive accuracy of the MARS model suggests its potential to enhance non-invasive myocardial risk stratification in diabetic women.

Analyzing angle crashes at unsignalized intersections using machine learning techniques

The presented study used crash modification (CM) factors and CM functions to assess the safety effectiveness of widening shoulders. The study first evaluated CM factors for widening shoulders on rural multilane roadways with the empirical Bayes (EB) observational before–after method to check the overall safety effects. Second, the CM factors were calculated for each aggregated break point according to roadway characteristics such as the original shoulder widths of treated sites in the before period and the actual increased widths. Finally, CM functions were developed with multiple linear regression and multivariate adaptive regression splines (MARS) models to determine the variation of CM factors. The results indicated that widening the shoulders resulted in a 12% crash reduction for total crashes (all severities), 18% for injury crashes, and 21% for severe crashes on rural multilane roadways for all types of crashes. For run-off-roadway crashes, the overall crash reductions of the treatment were 25% for total crashes, 28% for injury crashes, and 31% for severe crashes. Moreover, the results showed that the safety effects varied across sites, depending on roadway characteristics. In particular, the original shoulder widths of treated sites in the before period and the actual increased width were significant parameters that affected the variation of CM factors. Moreover, it was found that the MARS models showed more reliable estimates than normal regression if the variation of CM factors with specific parameters had nonlinear relationships and interaction effects. The proposed CM functions provide general insights into roadway design and selection of sites for increasing shoulder width for reducing crashes.