Evaluating the relative importance of predictors in Generalized Additive Models using the gam.hp R package

Generalized Additive Models(GAMs)are widely employed in ecological research,serving as a powerful tool for ecologists to explore complex nonlinear relationships between a response variable and predictors.Nevertheless,evaluating the relative importance of predictors with concurvity(analogous to collinearity)on response variables in GAMs remains a challenge.To address this challenge,we developed an R package named gam.hp.gam.hp calculates individual R^(2) values for predictors,based on the concept of'average shared variance',a method previously introduced for multiple regression and canonical analyses.Through these individual R^(2)s,which add up to the overall R^(2),researchers can evaluate the relative importance of each predictor within GAMs.We illustrate the utility of the gam.hp package by evaluating the relative importance of emission sources and meteorological factors in explaining ozone concentration variability in air quality data from London,UK.We believe that the gam.hp package will improve the interpretation of results obtained from GAMs.

A Comparative Study of Two Tree-Based Models for Predicting Flyrock Velocity at Open Pit Bench Mining

Blasting is a cost-effective technique to break hard rock volumes by using explosives in the mining and civil engineering realms. Moreover, although blasting is a designed process and plays an indispensable role in these industries, it can also have multiple adverse environmental impacts. One such effect is flyrock, which poses risks to nearby machinery, and residential structures, and can even lead to injuries or fatalities. To optimize blasting efficiency as well as restrict side effects, prediction of the blast aftereffects is vital. Therefore, the present work focuses on using two machine learning methods to predict the velocity of flyrock in the open pit mine. To address this issue, a comprehensive dataset was gathered from the open pit mine. Then, Decision Tree and Random Forest algorithms were employed to predict flyrock velocity. The Random Forest model demonstrated superior performance compared to the Decision Tree model. Nonetheless, the performance of the Decision Tree model was deemed satisfactory, as evidenced by its coefficient of determination value of 0.83, mean squared error (MSE) of 4.2, and mean absolute percentage error (MAPE) of 5.6%. Considering these metrics, it is reasonable to conclude that tree-based algorithms can be effective in predicting flyrock velocity.

Application of ACP Nonlinear Math in Analyzing Arithmetic and Radiation Transmission Data (Application 1 & 2) [4-21-2024, 820P] (V)

In this study, we explore the application of ACP (asymptotic curve based and proportionality oriented) Alpha Beta (αβ) Nonlinear Math to analyze arithmetic and radiation transmission data. Specifically, we investigate the relationship between two variables. The novel approach involves collecting elementary “y” data and subsequently analyzing the asymptotic cumulative or demulative (opposite of cumulative) Y data. In part I, we examine the connection between the common linear numbers and ideal nonlinear numbers. In part II, we delve into the relationship between X-ray energy and the radiation transmission for various thin film materials. The fundamental physical law asserts that the nonlinear change in continuous variable Y is negatively proportional to the nonlinear change in continuous variable X, expressed mathematically as dα = −Kdβ. Here: dα {Y, Yu, Yb} represents the change in Y, with Yu and Yb denoting the upper and baseline asymptote of Y. dβ {X, Xu, Xb} represents the change in X, with Xu and Xb denoting the upper and baseline asymptote of X. K represents the proportionality constant or rate constant, which varies based on equation arrangement. K is the key inferential factor for describing physical phenomena.

Zeno’s Paradoxes and Lie Tzu’s Dichotomic Wisdom Explained with Alpha Beta (αβ) Asymptotic Nonlinear Math (Including One Example on Second Order Nonlinear Phenomena)

Zeno’s paradoxes are a set of philosophical problems that were first introduced by the ancient Greek philosopher Zeno of Elea. Here is the first attempt to use asymptotic approach and nonlinear concepts to address the paradoxes. Among the paradoxes, two of the most famous ones are Zeno’s Room Walk and Zeno’s Achilles. Lie Tsu’s pole halving dichotomy is also discussed in relation to these paradoxes. These paradoxes are first-order nonlinear phenomena, and we expressed them with the concepts of linear and nonlinear variables. In the new nonlinear concepts, variables are classified as either linear or nonlinear. Changes in linear variables are simple changes, while changes in nonlinear variables are nonlinear changes relative to their asymptotes. Continuous asymptotic curves are used to describe and derive the equations for expressing the relationship between two variables. For example, in Zeno’s Room Walk, the equations and curves for a person to walk from the initial wall towards the other wall are different from the equations and curves for a person to walk from the other wall towards the initial wall. One walk has a convex asymptotic curve with a nonlinear equation having two asymptotes, while the other walk has a concave asymptotic curve with a nonlinear equation having a finite starting number and a bottom asymptote. Interestingly, they have the same straight-line expression in a proportionality graph. The Appendix of this discussion includes an example of a second-order nonlinear phenomenon. .

Simulation of Runoff and Sediment Yield for a Kaneri Watershed Using SWAT Model

Watershed as an entry point acts as a beginning to address the issues of sustainable rainwater management for improving livelihoods. Extraction of watershed parameters using Geographical Information System (GIS) and use of simulation models is the current trend for hydrologic evaluation of watersheds. In the present study, the open Source Tool Quantum GIS 2.2.0 was used for preparation of maps to verify the spatial extent of the area. The Soil and Water Assessment Tool (SWAT) having an interface with Arc-View GIS software (ArcGIS 10.1 with Arc SWAT 2012 extension) was selected for the estimation of runoff and sediment yield from Kaneri watershed, located in Western Maharashtra region. The coefficient of determination (R2) for the monthly and yearly runoff was obtained as 0.849 and 0.951 respectively for the calibration period 1979 to 2000 and 0.801 and 0.950 respectively for the validation period 2001-2013. The R2 value in estimating the monthly and yearly sediment yield during calibration period was computed as 0.722 and 0.788 respectively. The R2 for monthly and yearly sediment yield values for validation period was observed to be 0.565 and 0.684 respectively.

Economic Consequences of Gender Equality in Europe

This paper shows influence of gender equality on economy where it analyzed how gender equality in Europe has affected on the development of the frozen food industry and services related to childcare. The development of these industries has given a positive impulse to the development of the whole economy. In this analysis, it is used multiple regressions as one of the most important statistical methods. In the first part of this paper, it shows the connection among the growth of female employment, growth in frozen food expenditure and growth of GDP in United Kingdom. In the second part of paper, it shows the relationship among the growth of labor force participation of women, growth of number of kindergarten and growth of GDP in Hungary. To proof these relationships, it used a multiple regression model. This statistical model was tested by using the T schedule which showed that the model in both the analyses is correct. At the end of the paper, it presents that employment rate and GDP behaves in the same way in European Union. These analyses show that it is necessary to continue to strengthen gender equality if the policy makers want to achieve even greater economic growth. The issue of gender equality is a very important factor in creating employment policy, and statisticians should be more involved in process of employment policy and gender equality

Development of Empirical Models for the Estimation of CBR Value of Soil from Their Index Properties: A Case Study of the Ogbia-Nembe Road in Niger Delta Region of Nigeria

This study developed empirical-mathematical models to predict the California Bearing Ratio (CBR) using soil index properties in Ogbia-Nembe road in the Niger Delta region of Nigeria. The determination of CBR of soil is a laborious operation that requires a longer time and materials leading to increased cost and schedule;this can be reduced by adopting an empirical-mathematical model that can predict the CBR using other simpler soil index properties such as Plastic Limit (PL), the Liquid Limit (LL), the Plasticity Index (PI) and the Moisture Content (MC), which are less laborious and take lesser time to obtain. Thirteen models were developed to understand the relationship between these soil index properties: the independent variable and the California Bearing Ratio (CBR): the dependent variable;Six linear, Six quadratic and One multiple linear regression models were developed for this relationship. Analysis of variance (ANOVA) on the thirteen models showed that the Optimum Moisture Content (OMC) and the Maximum Dry Density (MDD) are better independent variables for the prediction of the CBR value of Ogbia-Nembe soil generating a quadratic model and a multiple linear regression model having a better coefficient of determination R2 = 0.96 and 0.94 respectively, mean square error (MSE) of 0.74 and 1.152 respectively with Root mean square errors of 0.861 and 1.073 accordingly. These models were used to predict the CBR of the soil. The CBR values predicted by the model were further compared with those of the actual experimental test and found to be relatively consistent with minimal variance. This establishes that CBR of any soil can be predicted from the Index Property of the soil and this is more economical and takes lesser time and can be universally adopted for soil investigation.

Evaluation and modification of potential evapotranspiration methods in Beijing,China

In this study,seven widely used potential evapotranspiration(ETo)methods were evaluated by comparing with the FAO-56 Penman-Monteith method(PM method)to provide useful information for selecting appropriate ETo equations under data-limited condition in Beijing,China.Statistical methods and parameters,namely linear regression,root mean squared error(RMSE)and mean bias error(MBE),were used to evaluate the seven ETo methods.Results showed that ETo estimated using Kimberly-Penman method have fairly close agreement with the PM method(referring to standard ETo),considering the coefficient of determination(R^(2))of 0.96,RMSE of 0.42 mm/day,and a coefficient of efficiency(E)of 0.96.Locally calibrated Penman and Doorenbos-Pruitt methods also have better agreement with the PM method,correspondingly with R^(2)of 0.99 and 0.95,RMSEs of 0.24 mm/day and 0.21 mm/day,and coefficients of efficiency of 1.02 and 0.99,respectively.The ETo is the most sensitive to vapor pressure deficit(VPD)and net radiation in the Beijing area.Hence,the VPD-based and VPD-radiation combined ETo methods were developed and calibrated.Results showed that the two developed methods performed well in ETo estimation.By fully considering the data-limit situation,the calibrated Turc method,VPD-based method and VPD-radiation-combined method may be attractive alternatives to the more complex Penman−Monteith method in Beijing.

Studying beta diversity: ecological variation partitioning by multiple regression and canonical analysis

Aims Beta diversity is the variation in species composition among sites in a geographic region.Beta diversity is a key concept for understanding the functioning of ecosystems,for the conservation of biodiversity and for ecosystem management.The present report describes how to analyse beta diversity from community composition and associated environmental and spatial data tables.Methods Beta diversity can be studied by computing diversity indices for each site and testing hypotheses about the factors that may explain the variation among sites.Alternatively,one can carry out a direct analysis of the community composition data table over the study sites,as a function of sets of environmental and spatial variables.These analyses are carried out by the statistical method of partitioning the variation of the diversity indices or the community composition data table with respect to environmental and spatial variables.Variation partitioning is briefly described herein.Important findings Variation partitioning is a method of choice for the interpretation of beta diversity using tables of environmental and spatial variables.Beta diversity is an interesting‘currency’for ecologists to compare either different sampling areas or different ecological communities cooccurring in an area.Partitioning must be based upon unbiased estimates of the variation of the community composition data table that is explained by the various tables of explanatory variables.The adjusted coefficient of determination provides such an unbiased estimate in both multiple regression and canonical redundancy analysis.After partitioning,one can test the significance of the fractions of interest and plot maps of the fitted values corresponding to these fractions.

glmm.hp: an R package for computing individual effect of predictors in generalized linear mixed models

Generalized linear mixed models(GLMMs)have been widely used in contemporary ecology studies.However,determination of the relative importance of collinear predictors(i.e.fixed effects)to response variables is one of the challenges in GLMMs.Here,we developed a novel R package,glmm.hp,to decompose marginal R2^(2)explained by fixed effects in GLMMs.The algorithm of glmm.hp is based on the recently proposed approach‘average shared variance’i.e.used for multivariate analysis.We explained the principle and demonstrated the use of this package by simulated dataset.The output of glmm.hp shows individual marginal R2^(2)s that can be used to evaluate the relative importance of predictors,which sums up to the overall marginal R2^(2).Overall,we believe the glmm.hp package will be helpful in the interpretation of GLMM outcomes.