Mapping species assemblages of tropical forests at different hierarchical levels based on multivariate regression trees

Background: Vegetation distribution maps are of great significance for nature protection and management. In diverse tropical forests, accurate spatial mapping of vegetation types is challenging;the high species diversity and abundance of rare species challenge classification concepts, while remote sensing signals may not vary systematically with species composition, complicating the technical capability for delineating vegetation types in the landscape.Methods: We used a combination of field-based compositional data and their relations to environmental variables to predict the distribution of forest types in the Wuzhishan National Natural Reserve(WNNR), Hainan Island,China, using multivariate regression trees(MRT). The MRT was based on arboreal vegetation composition in 132plots of 20 m×20 m with a regular spacing of 1 km. Apart from the MRT, non-metric multidimensional scaling(NMDS) was used to evaluate vegetation-environment relationships.Results: The MRT model worked best when using 14 key environmental variables including topography, climate,latitude and soil, although the difference with the simpler model including only topographical variables was small. The full model classified the 132 plots into 3 vegetation types, 6 formation groups, 20 formations and 65associations at different hierarchical syntaxonomic levels. This model was the basis for forest vegetation maps for the WNNR. MRT and NMDS showed that elevation was the main driving force for the distribution of vegetation types and formation groups. Climate, latitude, and soil(especially available P), together with topographic variables, all influenced the distribution of formations and associations.Conclusions: While elevation determines forest-type distributions, lower-level syntaxonomic forest classes respond to the topographic diversity typical for mountains. Apart from providing the first detailed forest vegetation map for any part of WNNR, we show how, in spite of limitations, MRT with existing environmental data can be a useful method for mapping diverse and remote tropical forests.

Multivariate analysis of oral mucosal ulcers during orthodontic treatment

BACKGROUND Orthodontic treatment can easily cause local soft tissue reactions in the oral cavity of patients under mechanical stress,leading to oral mucosal ulcers and affecting their quality of life.At present,only limited literature has explored the factors leading to oral ulcers in orthodontic treatment,and these research results are still controversial.AIM To investigate the current status and related factors of oral mucosal ulcers during orthodontic treatment,aiming to provide a valuable reference for preventing this disease in clinical practice.METHODS A total of 587 patients who underwent orthodontic treatment at the Peking University School of Stomatology and Hospital of Stomatology between 2020 and 2022 were selected and allocated to an observation or control group according to the incidence of oral mucosal ulcers during orthodontic therapy.A questionnaire survey was constructed to collect patient data,including basic information,lifestyle and eating habits,treatment details,mental factors,and trace element levels,and a comparative analysis of this data was performed between the two groups.RESULTS A logistic regression model with oral ulcers as the dependent variable was established.The regression results showed that age(≥60 years:odds ratio[OR]:6.820;95%confidence interval[CI]:2.226–20.893),smoking history(smoking:OR:4.434;95%CI:2.527–7.782),toothbrush hardness(hard:OR:2.804;95%CI:1.746–4.505),dietary temperature(hot diet:OR:1.399;95%CI:1.220–1.722),treatment course(>1 year:OR:3.830;95%CI:2.203–6.659),and tooth brushing frequency(>1 time per day:OR:0.228;95%CI:0.138–0.377)were independent factors for oral mucosal ulcers(P<0.05).Furthermore,Zn level(OR:0.945;95%CI:0.927–0.964)was a protective factor against oral ulcers,while the SAS(OR:1.284;95%CI:1.197–1.378)and SDS(OR:1.322;95%CI:1.231–1.419)scores were risk factors.CONCLUSION Age≥60 years,smoking history,hard toothbrush,hot diet,treatment course for>1 year,tooth brushing frequency of≤1 time per day,and mental anxiety are independent risk factors for oral mucosal ulcers.Therefore,these factors should receive clinical attention and be incorporated into the development and optimization of preventive strategies for reducing oral ulcer incidence.

Study on QSAR of Taxol and its Derivatives Based on Stepwise Multivariate Linear Regression Analysis

Abstract Using the method of stepwise multivariate linear regression (SMLR), the quantitative structure activity relationships (QSAR) of two isomeric series of taxol and its derivatives have been studied. It was found that the molar refractivity of the C3′substituent of the C13 side chain has significant correlation with its activity. We deduce that structural changes in the C3′substituents may be critical to the anticancer function. It would be useful to the design and synthesis of taxol like compounds with improved activities.

Multivariate adaptive regression splines and neural network models for prediction of pile drivability

Piles are long, slender structural elements used to transfer the loads from the superstructure through weak strata onto stiffer soils or rocks. For driven piles, the impact of the piling hammer induces compression and tension stresses in the piles. Hence, an important design consideration is to check that the strength of the pile is sufficient to resist the stresses caused by the impact of the pile hammer. Due to its complexity, pile drivability lacks a precise analytical solution with regard to the phenomena involved.In situations where measured data or numerical hypothetical results are available, neural networks stand out in mapping the nonlinear interactions and relationships between the system’s predictors and dependent responses. In addition, unlike most computational tools, no mathematical relationship assumption between the dependent and independent variables has to be made. Nevertheless, neural networks have been criticized for their long trial-and-error training process since the optimal configuration is not known a priori. This paper investigates the use of a fairly simple nonparametric regression algorithm known as multivariate adaptive regression splines（MARS）, as an alternative to neural networks, to approximate the relationship between the inputs and dependent response, and to mathematically interpret the relationship between the various parameters. In this paper, the Back propagation neural network（BPNN） and MARS models are developed for assessing pile drivability in relation to the prediction of the Maximum compressive stresses（MCS）, Maximum tensile stresses（MTS）, and Blow per foot（BPF）. A database of more than four thousand piles is utilized for model development and comparative performance between BPNN and MARS predictions.

Advanced reliability analysis of slopes in spatially variable soils using multivariate adaptive regression splines

This study aims to extend the multivariate adaptive regression splines(MARS)-Monte Carlo simulation(MCS) method for reliability analysis of slopes in spatially variable soils. This approach is used to explore the influences of the multiscale spatial variability of soil properties on the probability of failure(P_f) of the slopes. In the proposed approach, the relationship between the factor of safety and the soil strength parameters characterized with spatial variability is approximated by the MARS, with the aid of Karhunen-Loeve expansion. MCS is subsequently performed on the established MARS model to evaluate Pf.Finally, a nominally homogeneous cohesive-frictional slope and a heterogeneous cohesive slope, which are both characterized with different spatial variabilities, are utilized to illustrate the proposed approach.Results showed that the proposed approach can estimate the P_f of the slopes efficiently in spatially variable soils with sufficient accuracy. Moreover, the approach is relatively robust to the influence of different statistics of soil properties, thereby making it an effective and practical tool for addressing slope reliability problems concerning time-consuming deterministic stability models with low levels of P_f.Furthermore, disregarding the multiscale spatial variability of soil properties can overestimate or underestimate the P_f. Although the difference is small in general, the multiscale spatial variability of the soil properties must still be considered in the reliability analysis of heterogeneous slopes, especially for those highly related to cost effective and accurate designs.

Mountain permafrost distribution modeling using Multivariate Adaptive Regression Spline (MARS) in the Wenquan area over the Qinghai-Tibet Plateau

In high mountainous areas, the development and distribution of alpine permafrost is greatly affected by macro- and mi- cro-topographic factors. The effects of latitude, altitude, slope, and aspect on the distribution of permafrost were studied to under- stand the dislribution patterns of permafrost in Wenquan on the Qinghai-Tibet Plateau. Cluster and correlation analysis were per- formed based on 30 m Global Digital Elevation Model （GDEM） data and field data obtained using geophysical exploration and borehole drilling methods. A Multivariate Adaptive Regression Spline model （MARS） was developed to simulate permafrost spa- tial distribution over the studied area. A validation was followed by comparing to 201 geophysical exploration sites, as well as by comparing to two other models, i.e., a binary logistic regression model and the Mean Annual Ground Temperature model （IVlAGT）. The MARS model provides a better simulation than the other two models. Besides the control effect of elevation on permafrost distribution, the MARS model also takes into account the impact of direct solar radiation on permafrost distribution.

ASSESSMENT OF LOCAL INFLUENCE IN MULTIVARIATE REGRESSION MODEL

In this article, authors introduce a method to assess local influence of obser- vations on the parameter estimates and prediction in multivariate regression model. The diagnostics under the perturbations of error variance, response variables and explanatory variables are derived, and the results are compared with those of case- deletion. Two examples are analyzed for illustration.

A sludge volume index (SVI) model based on the multivariate local quadratic polynomial regression method

In this study, a multivariate local quadratic polynomial regression(MLQPR) method is proposed to design a model for the sludge volume index(SVI). In MLQPR, a quadratic polynomial regression function is established to describe the relationship between SVI and the relative variables, and the important terms of the quadratic polynomial regression function are determined by the significant test of the corresponding coefficients. Moreover, a local estimation method is introduced to adjust the weights of the quadratic polynomial regression function to improve the model accuracy. Finally, the proposed method is applied to predict the SVI values in a real wastewater treatment process(WWTP). The experimental results demonstrate that the proposed MLQPR method has faster testing speed and more accurate results than some existing methods.

Using multivariate adaptive regression splines to develop relationship between rock quality designation and permeability

The assessment of in situ permeability of rock mass is challenging for large-scale projects such as reservoirs created by dams,where water tightness issues are of prime importance.The in situ permeability is strongly related to the frequency and distribution of discontinuities in the rock mass and quantified by rock quality designation(RQD).This paper analyzes the data of hydraulic conductivity and discontinuities sampled at different depths during the borehole investigations in the limestone and sandstone formations for the construction of hydraulic structures in Oman.Cores recovered from boreholes provide RQD data,and in situ Lugeon tests elucidate the permeability.A modern technique of multivariate adaptive regression splines(MARS)assisted in correlating permeability and RQD along with the depth.In situ permeability shows a declining trend with increasing RQD,and the depth of investigation is within 50 m.This type of relationship can be developed based on detailed initial investigations at the site where the hydraulic conductivity of discontinuous rocks is required to be delineated.The relationship can approximate the permeability by only measuring the RQD in later investigations on the same site,thus saving the time and cost of the site investigations.The applicability of the relationship developed in this study to another location requires a lithological similarity of the rock mass that can be verified through preliminary investigation at the site.

Mapping QTL for Categorical Traits with Multivariate Regression

Simple linear regression analysis has been used to map QTL for quantitative traits. Many traits of biological interest and/or economical importance in various species show binary phenotypic distributions (e.g., presence or absence). It has been shown that such a binary trait also can be analyzed with the simple linear regression, subject to virtually no loss in power compared to the generalized linear model analysis. Binary trait is a special case of a multiple categorical trait (e.g., low, medium or high). We propose a mechanism to decompose a multiple categorical trait into an array of correlated binary variables. The categorical trait turned multiple binary traits are analyzed with a multivariate linear regression method. Turning the problem of categorical trait mapping into that of multivariate mapping allows the exploration of pleiotropic effects of QTL for different categories. Efficiency of the method is verified through a series of simulation experiments.

COX MULTIVARIATE REGRESSION ANALYSIS OF RECURRENCE FACTORS FOR COLONIC CARCINOMA

Objective: To determine the independent prognostic factors in the recurrence of colonic carcinoma after curative resection. Methods: Two hundred and one patients undergoing curative resections for colonic carcinoma were investigated by univariate and Cox multivariate regression analyses. Ten factors contributed to the rate were analyzed. Results: Dukes stages, obstruction, postoperative chemotherapy as well as the growth manner of the tumor were significantly associated with the recurrence rate of colonic carcinoma (P<0.05) by univariate analysis, while Dukes stages, obstruction, and postoperative chemotherapy were significant factors by the multivariate analysis. Conclusion: Dukes stages, obstruction, and postoperative chemotherapy are independent prognostic factors in the recurrence of colonic carcinoma.

LIMITING BEHAVIOR OF RECURSIVE M-ESTIMATORS IN MULTIVARIATE LINEAR REGRESSION MODELS AND THEIR ASYMPTOTIC EFFICIENCIES

Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters. In this article, it is shown that for a nondecreasing ul （t）, under some mild conditions the recursive M-estimators of regression coefficients and scatter parameters are strongly consistent and the recursive M-estimator of the regression coefficients is also asymptotically normal distributed. Furthermore, optimal recursive M-estimators, asymptotic efficiencies of recursive M-estimators and asymptotic relative efficiencies between recursive M-estimators of regression coefficients are studied.

Expanding the Scope of Multivariate Regression Approaches in Cross-Omics Research

Recent technological advancements and developments have led to a dramatic increase in the amount of high-dimensional data and thus have increased the demand for proper and efficient multivariate regression methods.Numerous traditional multivariate approaches such as principal component analysis have been used broadly in various research areas,including investment analysis,image identification,and population genetic structure analysis.However,these common approaches have the limitations of ignoring the correlations between responses and a low variable selection efficiency.Therefore,in this article,we introduce the reduced rank regression method and its extensions,sparse reduced rank regression and subspace assisted regression with row sparsity,which hold potential to meet the above demands and thus improve the interpretability of regression models.We conducted a simulation study to evaluate their performance and compared them with several other variable selection methods.For different application scenarios,we also provide selection suggestions based on predictive ability and variable selection accuracy.Finally,to demonstrate the practical value of these methods in the field of microbiome research,we applied our chosen method to real population-level microbiome data,the results of which validated our method.Our method extensions provide valuable guidelines for future omics research,especially with respect to multivariate regression,and could pave the way for novel discoveries in microbiome and related research fields.

Multivariate adaptive regression splines based simulation optimization using move-limit strategy

This paper makes an approach to the approximate optimum in structural design,which combines the global response surface（GRS） based multivariate adaptive regression splines（MARS） with Move-Limit strategy（MLS）.MARS is an adaptive regression process,which fits in with the multidimensional problems.It adopts a modified recursive partitioning strategy to simplify high-dimensional problems into smaller highly accurate models.MLS for moving and resizing the search sub-regions is employed in the space of design variables.The quality of the approximation functions and the convergence history of the optimization process are reflected in MLS.The disadvantages of the conventional response surface method（RSM） have been avoided,specifically,highly nonlinear high-dimensional problems.The GRS/MARS with MLS is applied to a high-dimensional test function and an engineering problem to demonstrate its feasibility and convergence,and compared with quadratic response surface（QRS） models in terms of computational efficiency and accuracy.

Two Stage Estimation and Its Covariance Matrix in Multivariate Seemingly Unrelated Regression System

Multivariate seemingly unrelated regression system is raised first and the two stage estimation and its covariance matrix are given. The results of the literatures[1-5] are extended in this paper.

Some Practical Issues Related to Univariate Regression Analysis Prior to Multivariate Regression Analysis in Randomized Controlled Clinical Trials

Often many variables have to be analyzed for their importance in terms of significant contribution and predictability in medical research. One of the possible analytical tools may be the Multiple Linear Regression Analysis. However, research papers usually report both univariate and multivariate regression analyses of the data. The biostatistician sometimes faces practical difficulties while selecting the independent variables for logical inclusion in the multivariate analysis. The selection criteria for inclusion of a variable in the multivariate regression is that the variable at the univariate level should have a regression coefficient with p 〈 0.20. However, there is a chance that an independent variable with p 〉 0.20 at univariate regression may become significant in the multivariate regression analysis and vice versa, provided the above criteria is not strictly adhered to. We undertook both univariate and multivariate linear regression analyses on data from two multi-centric clinical trials. We recommend that there is no need to restrict the p value of 〈= 0.20. Because of high speed computer and availability of statistical software, the desired results could be achieved by considering all relevant independent variables in multivariate regression analysis.

A method for real power transfer allocation using multivariable regression analysis

A multivariable regression(MVR) approach is proposed to identify the real power transfer between generators and loads.Based on solved load flow results,it first uses modified nodal equation method(MNE) to determine real power contribution from each generator to loads.Then,the results of MNE method and load flow information are utilized to determine suitable regression coefficients using MVR model to estimate the power transfer.The 25-bus equivalent system of south Malaysia is utilized as a test system to illustrate the effectiveness of the MVR output compared to that of the MNE method.The error of the estimate of MVR method ranges from 0.001 4 to 0.007 9.Furthermore,when compared to MNE method,MVR method computes generator contribution to loads within 26.40 ms whereas the MNE method takes 360 ms for the calculation of same real power transfer allocation.Therefore,MVR method is more suitable for real time power transfer allocation.

Multivariate Aggregated NOMA for Resource Aware Wireless Network Communication Security

NonorthogonalMultiple Access(NOMA)is incorporated into the wireless network systems to achieve better connectivity,spectral and energy effectiveness,higher data transfer rate,and also obtain the high quality of services(QoS).In order to improve throughput and minimum latency,aMultivariate Renkonen Regressive Weighted Preference Bootstrap Aggregation based Nonorthogonal Multiple Access(MRRWPBA-NOMA)technique is introduced for network communication.In the downlink transmission,each mobile device’s resources and their characteristics like energy,bandwidth,and trust are measured.Followed by,the Weighted Preference Bootstrap Aggregation is applied to recognize the resource-efficient mobile devices for aware data transmission by constructing the different weak hypotheses i.e.,Multivariate Renkonen Regression functions.Based on the classification,resource and trust-aware devices are selected for transmission.Simulation of the proposed MRRWPBA-NOMA technique and existing methods are carried out with different metrics such as data delivery ratio,throughput,latency,packet loss rate,and energy efficiency,signaling overhead.The simulation results assessment indicates that the proposed MRRWPBA-NOMA outperforms well than the conventional methods.

Medium-Term Electric Load Forecasting Using Multivariable Linear and Non-Linear Regression

Medium-term forecasting is an important category of electric load forecasting that covers a time span of up to one year ahead. It suits outage and maintenance planning, as well as load switching operation. We propose a new methodol-ogy that uses hourly daily loads to predict the next year hourly loads, and hence predict the peak loads expected to be reached in the next coming year. The technique is based on implementing multivariable regression on previous year's hourly loads. Three regression models are investigated in this research: the linear, the polynomial, and the exponential power. The proposed models are applied to real loads of the Jordanian power system. Results obtained using the pro-posed methods showed that their performance is close and they outperform results obtained using the widely used ex-ponential regression technique. Moreover, peak load prediction has about 90% accuracy using the proposed method-ology. The methods are generic and simple and can be implemented to hourly loads of any power system. No extra in-formation other than the hourly loads is required.

Using Multivariable Linear Regression Technique for Modeling Productivity Construction in Iraq

Productivity is a very important element in the process of construction project management especially with regard to the estimation of the duration of the construction activities, this study aims at developing construction productivity estimating model for marble finishing works of floors using Multivariable Linear Regression technique (MLR). The model was developed based on 100 set of data collected in Iraq for different types of projects such as residential, commercial and educational projects. Which these are used in developing the model and evaluating its performance. Ten influencing factors are utilized for productivity forecasting by MLR model, and they include age, experience, number of the assist labor, height of the floor, size of the marbles tiles, security conditions, health status for the work team, weather conditions, site condition, and availability of construction materials. One model was built for the prediction of the productivity of marble finishing works for floors. It was found that MLR have the ability to predict the productivity for finishing works with excellent degree of accuracy of the coefficient of correlation (R) 90.6%, and average accuracy percentage of 96.3%. This indicates that the relationship between the independent and independent variables of the developed models is good and the predicted values from a forecast model fit with the real-life data.