Search

Mendelian randomization (MR) utilizes genome-wide association study (GWAS) summary data to infer causal relationships between exposures and outcomes, offering a valuable tool for identifying disease risk factors. Multivariable MR (MVMR) estimates the direct effects of multiple exposures on an outcome. This study tackles the issue of highly correlated exposures commonly observed in metabolomic data, a situation where existing MVMR methods often face reduced statistical power due to multicollinearity. We propose a robust extension of the MVMR framework that leverages constrained maximum likelihood (cML) and employs a Bayesian approach for identifying independent clusters of exposure signals. Applying our method to the UK Biobank metabolomic data for the largest Alzheimer disease (AD) cohort through a two-sample MR approach, we identified two independent signal clusters for AD: glutamine and lipids, with posterior inclusion probabilities (PIPs) of 95.0% and 81.5%, respectively. Our findings corroborate the hypothesized roles of glutamate and lipids in AD, providing quantitative support for their potential involvement. Multivariable Mendelian randomization (MVMR) estimates the direct effects of multiple exposures on an outcome, but it lacks statistical power when exposures are highly correlated. We introduce an extension of MVMR that can identify clusters of correlated exposure signals and use it to assess the effects of metabolites on Alzheimer disease. [ABSTRACT FROM AUTHOR]

The relationship between economic growth and CO2 emissions has been analyzed testing the environmental Kuznets curve hypothesis, but traditional econometric methods may be flawed. An alternative method is proposed using segmented-sample regressions and implemented in 164 countries (98.34% of world population) over different periods from 1822 to 2018. Results suggest that while the association between GDP per capita and CO2 emissions per capita is weakening over time, it remains positive globally, with only some high-income countries showing a reversed association in recent years. While 49 countries have decoupled emissions from economic growth, 115 have not. Most African, American, and Asian countries have not decoupled, whereas most European and Oceanians have. These findings highlight the urgency for effective climate policies because decoupling remains unachieved on a global scale, and we are moving away from, rather than approaching, the Paris Agreement goal of limiting temperature increase to 1.5 °C above preindustrial levels. [ABSTRACT FROM AUTHOR]

The presence of measurement errors in data and multicollinearity among the explanatory variables have negative effects on the estimation of regression coefficients. Within this respect, the motivation of this article is to examine measurement errors and multicollinearity problems simultaneously. In this paper, by utilizing three different forms of corrected score functions three consistent ridge regression estimators are proposed. Theoretical comparisons of these new estimators are examined by implementing the mean squared error criterion. Large sample properties of these estimators are investigated without assuming any distributional assumption. Two numerical examples are presented using real data sets and also a simulation study is performed. The findings indicate that the newly proposed three estimators outperform the existing estimators by the criterion of mean squared error. [ABSTRACT FROM AUTHOR]

Background and Objective: Near‐infrared spectroscopy is an established tool for the estimation of different nutrients in diverse sample matrices. Of these, near‐infrared transmittance (NIT) has very wide usage in whole grain analysis for oil, protein, and other macronutrients. NIT spectra obtained from samples are regressed with actual laboratory values for developing prediction models. However, the spectra obtained are sloppy, slightly noisy, and show baseline drifts. To increase the resolution and signal‐to‐noise ratio, derivatives are common preprocessing tools, typically implemented along with smoothing. Findings: A systematic study on different derivatives (1, 2, and 3) and gaps (2–90) was performed. The germplasm set with high variability for protein content (8.63%–19.56%) was used, and regression models were developed using the modified partial least squares method. Among all, the second‐order derivative gave best‐fit models; hence, the results of the gap with second‐order derivatives are studied in detail. The plot of R2 for external validation set with different gaps at second‐order gave three peaks, namely, at 47, 60, (69, 70, 71) where the highest R2 (0.985) was obtained for the third peak having three consecutive gap segments. Conclusion: Hence, math treatment (2, 70, 2, 1) was finalized considering stability where a high residual prediction deviation of 7.149 and a low bias of (0.021) was obtained. A paired t test and reliability test between predicted and laboratory values confirmed nonsignificant differences between them. Thus, the developed model is robust and precise and can be utilized in high throughput screening of wheat germplasm. Significance and Novelty: Better performance at second derivative and higher gap can be used for developing robust models with low bias by avoiding multi‐collinearity, which is usually a limitation in multi‐variate analysis. [ABSTRACT FROM AUTHOR]

In the analysis of logistic regression models, various biased estimators have been proposed as an alternative to the maximum likelihood estimator (MLE) for estimating model parameters in the presence of multicollinearity. In this study, a new class of biased estimators called Logistic Ridge-type Estimator (LRTE) is proposed by generalizing the existing biased estimators that include two biasing parameters. The performance of the proposed estimator is compared with the other biased estimators in terms of the Matrix Mean Squared Error (MMSE). Two separate Monte Carlo simulation studies are conducted to investigate the performance of the proposed estimator. A numerical example is provided to demonstrate the performance of the proposed biased estimator. The results revealed that LRTE performed better than other existing biased estimators under the conditions investigated in this study. [ABSTRACT FROM AUTHOR]

The majority of research predicted heating demand using linear regression models, but they did not give current building features enough context. Model problems such as Multicollinearity need to be checked and appropriate features must be chosen based on their significance to produce accurate load predictions and inferences. Numerous building energy efficiency features correlate with each other and with heating load in the energy efficiency dataset. The standard Ordinary Least Square regression has a problem when the dataset shows Multicollinearity. Bayesian supervised machine learning is a popular method for parameter estimation and inference when frequentist statistical assumptions fail. The prediction of the heating load as the energy efficiency output with Bayesian inference in multiple regression with a collinearity problem needs careful data analysis. The parameter estimates and hypothesis tests were significantly impacted by the Multicollinearity problem that occurred among the features in the building energy efficiency dataset. This study demonstrated several shrinkage and informative priors on likelihood in the Bayesian framework as alternative solutions or remedies to reduce the collinearity problem in multiple regression analysis. This manuscript tried to model the standard Ordinary Least Square regression and four distinct Bayesian regression models with several prior distributions using the Hamiltonian Monte Carlo algorithm in Bayesian Regression Modeling using Stan and the package used to fit linear models. Several model comparison and assessment methods were used to select the best-fit regression model for the dataset. The Bayesian regression model with weakly informative prior is the best-fitted model compared to the standard Ordinary Least Squares regression and other Bayesian regression models with shrinkage priors for collinear energy efficiency data. The numerical findings of collinearity were checked using variance inflation factor, estimates of regression coefficient and standard errors, and sensitivity of priors and likelihoods. It is suggested that applied research in science, engineering, agriculture, health, and other disciplines needs to check the Multicollinearity effect for regression modeling for better estimation and inference. [ABSTRACT FROM AUTHOR]

In this paper, a new regression estimator is proposed as an alternative to the ridge estimator in the case of multicollinearity in Bell regression model, called an almost unbiased ridge estimator. Also, we provide the theoretical properties of the new almost unbiased ridge estimator, and some theorems showing under which conditions that the almost unbiased ridge estimator is superior to its competitors. We consider a comprehensive simulation study to demonstrate the superiority of the almost unbiased ridge estimator compared to the usual Bell ridge estimator and the maximum likelihood estimator. The usefulness and superiority of the introduced regression estimator is shown via a real-world data example. According to the results of the simulation study and real-world data example, we conclude that the new almost unbiased ridge regression estimator is superior to its competitors in terms of the mean square error criterion. [ABSTRACT FROM AUTHOR]

AbstractNumerous biased estimators are known to circumvent the multicollinearity problem in linear measurement error models. This article proposes a general biased estimator with the ridge regression and the Liu estimators as special cases. The efficiency of the suggested estimator is compared with ridge regression and Liu estimators under the mean squared error matrix criterion. In addition, a Monte Carlo simulation study and a numerical evaluation have been conducted to elucidate the superiority of the new general biased estimator over other estimators. [ABSTRACT FROM AUTHOR]

The uniaxial compressive strength (UCS) is an essential parameter to study rock characteristics, determined by direct and indirect methods. However, the direct methods of determining rock UCS are lengthy and arduous, presenting a requirement of developing a robust indirect method. This investigation introduces an optimal computational model based on the artificial intelligence approach. For that aim, the relevance vector machine (RVM) and long short-term memory (LSTM) approaches have employed 24 computational models in estimating rock UCS and introducing an optimal computational model. The 514, 146, and 74 data points have trained, tested, and validated the 24 models compiled from the literature. The model comparison reveals that implementing a secondary kernel function in a single kernel-based RVM model enhances the performance. Moreover, the particle swarm (PSO) optimized dual kernel-based RVM model attains higher performance than genetic (GA) optimized RVM models. Conversely, the Adam-optimized LSTM model achieved higher performance than other LSTM models. The overall comparison introduces model MD21 (PSO-optimized RVM model implemented by dual kernels, i.e., Laplacian + polynomial) as an optimal performance model in predicting rock UCS with a correlation coefficient of 0.9979 (in the testing phase) and 0.9939 (in the validation phase). In addition, the multicollinearity analysis reveals that the database variables consist of weak multicollinearity. It is noted that the optimized RVM and LSTM models attain overfitting because of weak multicollinearity and optimization algorithms. The analysis of variance (ANOVA), Z, and Anderson–Darling tests accept the research hypothesis for the compiled database. In addition, the trend of simulated results illustrates the robustness and correctness of the employed model MD21. Highlights: Implementation of hybrid relevance vector machine and long short-term memory computational models to assess uniaxial compressive strength of rock. Comparison of genetic and particle swarm optimized relevance vector machine model to find the best optimization algorithm. Comparison of Adam, root-mean-square proportion, and stochastic gradient descent with momentum optimized long short-term memory models. Illustration of the effect of multicollinearity on performance and curve fitting of optimized computational models. Particle swarm optimized dual kernel-based relevance vector machine is an optimal computational model for assessing rock strength. [ABSTRACT FROM AUTHOR]

In modeling count data with overdispersion and extra zeros, zero-inflated negative binomial (ZINB) regression model is useful. In a regression model, the multicollinearity problem arises when there are some high correlations between predictor variables. This problem leads to the maximum likelihood method will not be an efficient estimator. The ridge and Liu-type estimators have been proposed to combat the multicollinearity problem so that the Liu-type estimator is better. In this paper, we proposed the Liu-type shrinkage estimators, namely linear shrinkage, preliminary test, shrinkage preliminary test, Stein-type, and positive Stein-type Liu estimators to estimate the count parameters in the ZINB model, when some of the predictor variables have not a significant effect to predict the response variable so that a sub-model may be sufficient. The asymptotic distributional biases and variances of the proposed estimators are nicely demonstrated. We also compared the performance of the Liu-type shrinkage estimators along with the Liu-type unrestricted estimator by using an extensive Monte Carlo simulation study. The results show that the performances of the proposed estimators are superior to those based on Liu-type unrestricted estimators. We also applied the proposed estimation methods to Expenditure and Default Data. [ABSTRACT FROM AUTHOR]

The use of Almon technique is encouraged for estimation of the distributed lag model (DLM) to avoid some serious problems associated with the direct application of the ordinary least squares (OLS) method. In Almon technique, the OLS procedure is applied on the transformed regressors which may be correlated themselves. To tackle this issue, the use of ordinary ridge regression estimator (ORRE) combined with the Almon technique has been considered as an alternative approach in the literature. However, the ORRE may be sensitive to outliers in the y-direction and thus, its use combined with the Almon technique may raise doubts on the estimated lag coefficients. The present work addresses this issue and suggests an alternative estimation method for the DLM, which is robust in the presence of multicollinearity and outliers. The performance of the proposed estimator has been evaluated through an extensive Monte Carlo simulation study and empirical findings are presented using the mean squared error criterion. The results reveal an attractive performance of the proposed estimator in the presence of outliers. [ABSTRACT FROM AUTHOR]

Ridge Estimation (RE) is a widespread method to overcome the problem of collinearity defining a class of estimators depending on the non-negative scalar parameter k. A great number of papers focus on the estimation of this biasing parameter. Traditionally, the mean squared error criterion is used to compare the performance of the different proposed estimators. However, the minimization of the mean squared error (MSE) does not always guarantee the mitigation of collinearity, meaning it is possible, for example, to obtain a variance inflation factor (VIF) higher than 10 for the k that minimizes the MSE. In this paper, we propose the VIF criteria to select the biased ridge parameter. A Monte Carlo simulation is presented with results that support this idea. Also, two real life empirical applications are used to illustrate the contribution of this paper. [ABSTRACT FROM AUTHOR]

Regression analysis is used to predict a dependent variable using one or more independent variables. In the linear regression model, when the independent variables are highly correlated, it leads toward the problem of multicollinearity. Subsequently, the ordinary least squares estimates become inconsistent and may lead to wrong inferences. In such a situation, ridge regression is the most commonly adopted technique. In this paper, we propose some new bootstrap aggregation (bagging) based ridge estimators. The performance of the proposed estimators is evaluated by a simulation study in terms of minimum mean squared error. The simulation results indicate that in the presence of multicollinearity with non-normal or heteroscedastic errors, the bagging-based ridge estimators perform better than conventional ridge estimators. The estimation of biasing parameters using bagging approach promotes the performance of the conventional ridge estimators. Finally, the real-life example is used to demonstrate the application of proposed estimators. [ABSTRACT FROM AUTHOR]

Rapid urbanization worldwide has significantly altered urban climates, creating a need to balance urban growth with thermal environmental quality for sustainable development. This study examines the relationship between land surface temperature (LST) and urban characteristics, particularly focusing on how green cover can mitigate urban heat and how air pollution can increase temperatures. Recognizing the predictive value of LST for urban heat island (UHI) intensity, we analyzed three distinct U.S. cities—Chicago, San Francisco, and Phoenix—each characterized by unique climate and urban planning features. This study investigates the relationship between atmospheric pollutants (SO2, NO2, CO, O3) and the Normalized Difference Vegetation Index (NDVI) with land surface temperature (LST) using regression and correlation analyses. The analysis aims to elucidate how changes in atmospheric pollutants and NDVI affect variations in land surface temperature. Regression analysis is employed to estimate the coefficients of independent variables and quantify their impact on LST. Correlation analysis assesses the linear relationships between variables, providing insights into their pairwise associations. The study also examines multicollinearity between independent variables to identify potential confounding factors. The results reveal significant associations between atmospheric pollutants, NDVI, and land surface temperature, contributing to our understanding of the environmental factors influencing LST dynamics and informing climate change mitigation strategies. The observed inconsistencies in correlations across cities highlight the importance of the local context in environmental studies. Understanding these variations can aid in developing tailored urban planning policies that consider unique city characteristics for more effective climate resilience. Furthermore, a positive association was consistently obtained between pollutants and LST, indicating that increased pollution levels contribute to higher surface temperatures across different urban settings. [ABSTRACT FROM AUTHOR]

The upsurge of stemphylium blight disease noticed during recent cropping years is the prime global threat for lentil (Lens culinaris Medik.) production. Identification of factors that influence lentil yield with the help of an advanced regression model will speed up the progress of lentil crop improvement for biotic stress tolerance. In this context, an experiment was undertaken to identify the key control factors of lentil yield under stemphylium blight stress. The field experiment was laid out under alpha lattice design using fifty lentil genotypes with two replications. An advanced dimension reduction cum regression approach Partial Least Square Regression (PLSR) was employed to mitigate the effect of multi-collinearity among 23 yield-influencing traits along with traditional Stepwise Multiple Linear Regression (SMLR). The results of SMLR analysis indicated that pods per plant, number of seeds per pod, hundred seed weight, superoxide dismutase and pod yield per plant had considerable effects on seed yield per plant with the R-squared value of 0.940. The first four PLSR components were considered to be optimum which were cumulatively explained 93.10% of the total variance towards lentil seed yield. The trait pods per plant was recorded with the highest PLSR regression coefficient devoid of multi-collinearity effects among the independent yield attributing variables under stemphylium blight environment and hence concluded to be the most influencing trait towards lentil seed yield followed by seeds per pod, hundred seed weight, pod yield per plant and superoxide dismutase. [ABSTRACT FROM AUTHOR]

In this article, we define mixed predictor and stochastic restricted ridge predictor of partially linear mixed measurement error models by taking advantage of Kernel approximation. Under matrix mean square error criterion, we make the comparison of the superiorities the linear combinations of the new defined predictors. Then we investigate the asymptotic normality characteristics and the situation of the unknown covariance matrix of measurement errors. Finally, the study is ended with a Monte Carlo simulation study and COVID-19 data application. [ABSTRACT FROM AUTHOR]

Recently, there has been an increased focus on enhancing the accuracy of machine learning techniques. However, there is the possibility to improve it by selecting the optimal tuning parameters, especially when data heterogeneity and multicollinearity exist. Therefore, this study proposed a statistical model to study the importance of changing the crude oil prices in the European Union, in which it should meet state-of-the-art developments on economic, political, environmental, and social challenges. The proposed model is Elastic-net quantile regression, which provides more accurate estimations to tackle multicollinearity, heavy-tailed distributions, heterogeneity, and selecting the most significant variables. The performance has been verified by several statistical criteria. The main findings of numerical simulation and real data application confirm the superiority of the proposed Elastic-net quantile regression at the optimal tuning parameters, as it provided significant information in detecting changes in oil prices. Accordingly, based on the significant selected variables; the exchange rate has the highest influence on oil price changes at high frequencies, followed by retail trade, interest rates, and the consumer price index. The importance of this research is that policymakers take advantage of the vital importance of developing energy policies and decisions in their planning. [ABSTRACT FROM AUTHOR]

This article investigates the potential of OpenStreetMap (OSM) data in predicting local well-being and resilience in Italy. The linear Least Absolute Shrinkage and Selection Operator (LASSO) is used to handle multicollinearity problems and select the most influential OSM features. The data-driven approach provides evidence that OSM information is highly correlated with several socioeconomic metrics at a provincial scale (NUTS-3 level). Moreover, it claims that some specific points of interest—e.g., bookmakers—can be used for a rapid territorial appraisal of vulnerable territories, i.e., areas that are affected by economic backwardness, poor institutions, low human capital and that, for these adverse conditions, deserve special attention by policymakers concerned with a reduction of regional disparities. While OSM can become a powerful source for policy planning, monitoring and evaluation, future works in the field should explore the scalability of the approach, its use for forecasting purposes, and the adoption of various models and tools such as machine learning techniques to grasp even non-linear relationships between variables. [ABSTRACT FROM AUTHOR]

AbstractThe Ordinary Least Squares estimator estimates the parameter vectors in a linear regression model. However, it gives misleading results when the input variables are highly correlated, emanating the issue of multicollinearity. In light of multicollinearity, we wish to obtain more accurate estimators of the regression coefficients than the least square estimators. The main problem of least square estimation is to tackle multicollinearity so as to get more accurate estimates. In this paper, we introduce a New Modified Generalized Two Parameter Estimator by merging the Generalized Two Parameter Estimator and the Modified Two Parameter Estimator and compare it with other known estimators like Ordinary Least Squares Estimator, Ridge Regression Estimator, Liu estimator, Modified Ridge Estimator, Modified Liu Estimator and Modified Two Parameter Estimator. Mean Squared Error Matrix criterion was used to compare the new estimator over existing estimators. The estimation of the biased parameters is discussed. Necessary and sufficient conditions are derived to compare the proposed estimator with the existing estimators. The excellence of the new estimator over existing estimators is illustrated with the help of real data set and a Monte Carlo simulation study. The results indicate that the newly developed estimator is more efficient as it has lower mean square error. [ABSTRACT FROM AUTHOR]

A Partially linear mixed effects model relating a response Y to predictors $ (X,Z,T) $ (X,Z,T) with the mean function $ X^{T}\beta +Zb+g(T) $ XTβ+Zb+g(T) is considered in this paper. When the parametric parts' variable X are measured with additive error and there is ill-conditioned data suffering from multicollinearity, a new kernel two-parameter prediction method using the kernel ridge and Liu regression approach is suggested. The kernel two parameter estimator of β and the predictor of b are derived by modifying the likelihood and Henderson methods. Matrix mean square error comparisons are calculated. We also demonstrate that under suitable conditions, the resulting estimator of β is asymptotically normal. The situation with an unknown measurement error covariance matrix is handled. A Monte Carlo simulation study, together with an earthquake data example, is compiled to evaluate the effectiveness of the proposed approach at the end of the paper. [ABSTRACT FROM AUTHOR]

Logistic regression has been a widely used prediction technique to analyze categorical variables. However, if the assumptions are violated the results may be biased. The study in this paper applied an analytical technique namely generalized ordered logit model. A case study of using urban light rail under pandemic conditions was applied for the analysis. The results suggested that logistic regression should not be applied before exploring the multicollinearity and applying the test of parallel lines. If the assumptions are violated, generalized ordered logit model should be considered. Regarding the predictive variables, sociodemographic, socioeconomic and travel pattern, related variables were found to have a statistically significant impact on the perception of safety and infrastructure of urban light rail. The outcomes of the study would provide a deeper understanding of developing regression models for categorical variables for future studies. [ABSTRACT FROM AUTHOR]

As one of the important lakes in the "One Lake and Two Seas" of the Inner Mongolia Autonomous Region, the monitoring of water quality in Lake Daihai has attracted increasing attention, and the concentration of chlorophyll-a directly affects the water quality, making the monitoring of chlorophyll-a concentration in Lake Daihai particularly crucial. Traditional methods of monitoring chlorophyll-a concentration are not only inefficient but also require significant human and material resources. Remote sensing technology has the advantages of wide coverage and short update cycles. For lakes such as Daihai with a high salinity content, salinity is considered a key factor when inverting the concentration of chlorophyll-a. In this study, machine learning models, including model stacking from ensemble learning, a ridge regression model, and a random forest model, were constructed. After comparing the training accuracy of the three models on Zhuhai-1 satellite data, the random forest model, which had the highest accuracy, was selected as the final training model. By comparing the accuracy changes before and after adding salinity factors to the random forest model, a high-precision model for inverting chlorophyll-a concentration in hypersaline lakes was obtained. The research results show that, without considering the salinity factor, the root mean square error (RMSE) of the model was 0.056, and the coefficient of determination (R2) was 0.64, indicating moderate model performance. After adding the salinity factor, the model accuracy significantly improved: the RMSE decreased to 0.047, and the R2 increased to 0.92. This study provides a solid basis for the application of remote sensing technology in hypersaline aquatic environments, confirming the importance of considering salinity when estimating chlorophyll-a concentration in hypersaline waters. This research helps us gain a deeper understanding of the water quality and ecosystem evolution in Daihai Lake. [ABSTRACT FROM AUTHOR]

This article assesses the predictive accuracy of factor models utilizing Partial·Least·Squares (PLS) and Principal·Component·Analysis (PCA) in comparison to autometrics and penalization techniques. The simulation exercise examines three types of scenarios by introducing the issues of multicollinearity, heteroscedasticity, and autocorrelation. The number of predictors and sample size are adjusted to observe the effects. The accuracy of the models is evaluated by calculating the Root·Mean·Square·Error (RMSE) and the Mean·Absolute·Error (MAE). In the presence of severe multicollinearity, the factor approach utilizing (PLS demonstrates exceptional performance in comparison. Autometrics achieves the lowest RMSE and MAE values across all levels of heteroscedasticity. Autometrics provides better forecasts with low and moderate autocorrelation. However, Elastic·Smoothly·Clipped·Absolute·Deviation (E-SCAD) forecasts well with severe autocorrelation. In addition to the simulation, we employ a popular Pakistani macroeconomic dataset for empirical research. The dataset contains 79 monthly variables from January 2013 to December 2020. The competing approaches perform differently compared to the simulation datasets, although "The PLS factor approach outperforms its competing approaches in forecasting, with lower RMSE and MAE". It is more probable that the actual dataset exhibits a high degree of multicollinearity. [ABSTRACT FROM AUTHOR]

The present work focuses on the performance of two types of shrinkage priors—the horseshoe prior and the recently developed regularized horseshoe prior—in the context of inducing sparsity in path analysis and growth curve models. Prior research has shown that these horseshoe priors induce sparsity by at least as much as the "gold standard" spike-and-slab prior. The horseshoe priors are compared to the ridge prior and lasso prior, as well as default non-informative priors, in terms of the percent shrinkage in the model parameters and out-of-sample predictive performance. Empirical studies using data from two large-scale educational assessments reveal the clear advantages of the horseshoe priors in terms of both shrinkage and predictive performance. Simulation studies reveal clear advantages in terms of shrinkage, but less obvious advantages in terms of predictive performance, except in the small sample size condition where both horseshoe priors provide noticeably improved predictive performance. [ABSTRACT FROM AUTHOR]

In multilevel models, disaggregating predictors into level-specific parts (typically accomplished via centering) benefits parameter estimates and their interpretations. However, the importance of level-specificity has been sparsely addressed in multilevel literature concerning collinearity. In this study, we develop novel insights into the interactivity of centering and collinearity in multilevel models. After integrating the broad literatures on centering and collinearity, we review level-specific and conflated correlations in multilevel data. Next, by deriving formal relationships between predictor collinearity and multilevel model estimates, we demonstrate how the consequences of collinearity change across different centering specifications and identify data characteristics that may exacerbate or mitigate those consequences. We show that when all or some level-1 predictors are uncentered, slope estimates can be greatly biased by collinearity. Disaggregation of all predictors eliminates the possibility that fixed effect estimates will be biased due to collinearity alone; however, under some data conditions, collinearity is associated with biased standard errors and random effect (co)variance estimates. Finally, we illustrate the importance of disaggregation for diagnosing collinearity in multilevel data and provide recommendations for the use of level-specific collinearity diagnostics. Overall, the necessity of disaggregation for identifying and managing collinearity's consequences in multilevel models is clarified in novel ways. [ABSTRACT FROM AUTHOR]

The generalized linear model approach of the mixed Poisson regression models (MPRM) is suitable for over-dispersed count data. The maximum likelihood estimator (MLE) is adopted to estimate their regression coefficients. However, the variance of the MLE becomes high when the covariates are collinear. The Poisson-Modification of Quasi Lindley (PMQL) regression model is a recently introduced model as an alternative MPRM. The variance of the proposed MLE for the PMQL regression model is high in the presence of multicollinearity. This paper adopts the ridge regression method for the PMQL regression model to combat such an issue, and we use several notable methods to estimate its ridge parameter. A Monte Carlo simulation study was designed to evaluate the performance of the MLE and the different PMQL ridge regression estimators by using their scalar mean square (SMSE) values. Further, we analyzed a simulated data and a real-life applications to show the consistency of the simulation results. The simulation and applications results indicate that the PMQL ridge regression estimators dominate the MLE when multicollinearity exists. [ABSTRACT FROM AUTHOR]

A biased estimator, compared to least squares estimators, is one of the most used statistical procedures to overcome the problem of multicollinearity. Liu-type estimators, which are biased estimators, are preferred in a wide range of fields. In this article, we propose an almost unbiased Liu-type (AUNL) estimator and discuss its performance under the mean square error matrix criterion among existing estimators. The proposed AUNL estimator is a general estimator and is based on the function of a single biasing parameter. It includes an ordinary least squares estimator, an almost unbiased ridge estimator, an almost unbiased Liu estimator, and an almost unbiased two-parameter estimator. Finally, real data examples and a Monte Carlo simulation are provided to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

The evolution of smart cities, driven by advancements in information transmission and the fusion of sensor technologies with IoT, faces challenges from substantial data traffic affecting Quality of Service factors like throughput and causing data loss and delivery delays. In order to improve traffic-aware data transmission in IoT-based smart city applications, a novel deep learning technique called the Multicollinearity Deming Regression-based Deep Perceptive NeurAl Learning Classifier (MERPAL) method is introduced. The proposed Deep Multilayer Perceptive Classifier consists of multiple layers such as input, output, and a number of hidden layers for assessing the given input. The number of nodes taken as input is passed to the primary hidden layer, where the energy and bandwidth availability of the nodes are assessed. The second hidden layer then uses the Multicollinearity Deming Regression to evaluate the estimated energy level and bandwidth of the nodes. After that, the analyzed results are given to the soft step activation function in the third hidden layer. The activation function identifies the best nodes based on energy level and bandwidth availability for efficient data delivery and helps minimize the network traffic. The simulation results indicate that MERPAL demonstrates superior performance compared to existing methods, exhibiting a 7% enhancement in data packet delivery ratio, a 15% increase in throughput, along with a reduction of 20% in packet loss and 14% in delay. [ABSTRACT FROM AUTHOR]

There is a real need for comparability and consistency of findings obtained from different multivariate methods, based on different assumptions and sensitivity to data errors. This study aims to investigate essential aspects of data screening prior to analysis, particularly the detection of outliers, communalities, multicollinearity, and Kaiser-Meyer-Olkin (KMO) and Bartlett’s tests, and to examine the influence of changing test parameters such as the number of convergence, number of bootstrap runs, FPEAK value, and minimum value of coefficient of determination (R2 ) on model results. Positive matrix factorization (PMF) and Unmix were applied to monitoring data collected from a receptor site. Findings of communalities estimate and multicollinearity indicated possible data errors in Ca, Cu, Na, and Mn, which affected the stability of source profiles. PMF detected biomass burning, coal combustion, traffic, industrial emissions, Mn-enriched sources, and secondary aerosols, while the Unmix model identified similar sources with comparable profiles, apart from profiles of vehicle exhaust and industrial emissions showing slight differences. Unmix was highly influenced by outliers, multicollinearity, and, to a lesser extent, change in sample size compared to PMF. We recommend interpreting the results of Bootstrapping, rather than basic runs for both PMF and Unmix. We also recommend data screening prior to further modeling. We suggest checking multicollinearity using more than one statistical measure, particularly VIF (Variance Inflation Factor) values together with tolerance values. [ABSTRACT FROM AUTHOR]

Landslides pose a significant risk to human life and property, making landslide susceptibility mapping (LSM) a crucial component of landslide risk assessment. However, spatial correlations among mapping units are often neglected in statistical or machine learning models proposed for LSM. This study proposes KNN-GCN, a deep learning model for slope-unit-based LSM based on a graph convolutional network (GCN) and the K-nearest neighbor (KNN) algorithm. The model was experimentally applied to the Lueyang region and validated through the following steps. Firstly, we collected data for 15 landslide causal factors and from landslide inventories and established a slope unit map (SUM) through slope unit division. Next, we performed a multicollinearity analysis of landslide causal factors and divided the training and test sets at a 7:3 ratio. We then constructed a GCN model based on a slope unit graph (SUG) generated from the SUM using the KNN algorithm. The proposed KNN-GCN model was tuned using a grid search with fivefold cross-validation on the training set, and then trained and validated on training and test sets separately. Finally, the performance of the KNN-GCN model was compared with that of six other models which were categorized into two groups: CG#1 was the traditional KNN, support vector regression (SVC), and automated machine learning (AutoML), and CG#2 included KNN-G, SVC-G and AutoML-G with additional spatial information. Our results demonstrate that the proposed model achieves superior performance (area under the curve [AUC] = 0.8351) and generates the most comprehensible susceptibility map with distinct boundaries between different susceptibility levels. Notably, while the proposed KNN-GCN model displays exceptional performance in slope-unit-based LSM, its implementation requires high-level computing resources, and it is not recommended for small datasets. [ABSTRACT FROM AUTHOR]

The Poisson-Inverse Gaussian regression model (PIGRM) is commonly used to analyze count datasets with over-dispersion. While the maximum likelihood estimator (MLE) is a standard choice for estimating PIGRM parameters, its performance may be suboptimal in the presence of correlated explanatory variables. To overcome this limitation, we introduce a novel Liu-type estimator for PIGRM. Our analysis includes an examination of the matrix mean square error (MMSE) and scalar mean square error (SMSE) properties of the proposed estimator, comparing them with those of the MLE, ridge, and Liu estimators. We also present several parameters of the Liu-type estimator for PIGRM. We evaluated the performance of the proposed estimator through a simulation study and application to real-life data, using SMSE as the primary evaluation criterion. Our results demonstrate that the proposed estimators outperform the MLE, ridge, and Liu estimators in both simulated and real-world scenarios. [ABSTRACT FROM AUTHOR]

Abstract The relationship between economic growth and CO2 emissions has been analyzed testing the environmental Kuznets curve hypothesis, but traditional econometric methods may be flawed. An alternative method is proposed using segmented-sample regressions and implemented in 164 countries (98.34% of world population) over different periods from 1822 to 2018. Results suggest that while the association between GDP per capita and CO2 emissions per capita is weakening over time, it remains positive globally, with only some high-income countries showing a reversed association in recent years. While 49 countries have decoupled emissions from economic growth, 115 have not. Most African, American, and Asian countries have not decoupled, whereas most European and Oceanians have. These findings highlight the urgency for effective climate policies because decoupling remains unachieved on a global scale, and we are moving away from, rather than approaching, the Paris Agreement goal of limiting temperature increase to 1.5 °C above preindustrial levels.

Regression analysis is one of the statistical methods used to determine the causal relationship between one or more explanatory variables to the affected variable. The problem that often occurs in regression analysis is that there are multicollonity and outliers. To deal with such problems can be solved using ridge regression analysis and robust regression. Ridge regression can solve the problem of multicollinearas by assigning a constant k to the matrix Z′Z. But in this method the resulting bias value is still high, so to overcome this problem, the jackknife ridge regression method is used. Meanwhile, to overcome outliers in the data using robust regression methods which have several estimation methods, two of which are the Generalized-M (GM) estimator and the Least Trimmed Square (LTS) estimator. The aim of the study is to solve the problem of multicollinearity and outliers simultaneously using robust jackknife ridge regression method with GM estimators and LTS estimators. The results showed that the robust ridge jackknife regression method with LTS estimator can control multicollinearity and outliers simultaneously better based on MSE, AIC and BIC values compared to the robust ridge jackknife regression method with GM estimators. This is indicated by the value MSE = -6.60371, AIC = 75.823 and BIC = 81.642 on LTS estimators that are of lower value than GM estimators.

In case of multicollinearity, PRESS statistics has been proposed to be used in the selection of the ridge biasing parameter of the ridge estimator which is introduced as an alternative to BLUE. This newly proposed PRESS statistic for the ridge estimator, CPRESS k , depends on the conditional ridge residual and can be computed once at a time by fitting the linear mixed model with all the observations. We also define R RidPred 2 statistic to evaluate the predictive ability of the ridge fit. Since the PRESS statistic for the BLUE is a special CPRESS k statistic, we indirectly also give closed form solution of the PRESS statistic for the BLUE. Then, we compared the predictive performance of the linear mixed model via the statistics CPRESS k , G C V k and C p by considering a real data analysis and a simulation study where the optimal ridge biaisng parameter is obtained by minimizing each statistic. The study shows that the ridge predictors improve the predictive performance of a linear mixed model over BLUE in the presence of multicollinearity and each statistic gives a different optimum ridge biasing value and they show the best predictive performance at their optimum ridge biasing values. In addition, the simulation study has shown that the intensity of variance and multicollinearity is effective in determining the optimum ridge biasing value and this optimum ridge biasing value is effective on the superiority of the predictive performance of ridge estimator over BLUE. [ABSTRACT FROM AUTHOR]

In ridge regression, we are often concerned with acquiring ridge estimators that lead to the smallest mean square error (MSE). In this article, we have considered the problem of ridge estimation in the presence of multicollinearity and heteroscedasticity. We have introduced a scaling factor which leads to significantly improved performance of the ridge estimators as compared to their classical counterparts. For illustration purposes, we have applied our proposed methodology to some of the popular existing ridge estimators but it can be extended to other estimators as well. We have also compared our proposed estimator with popular existing estimators dealing estimation problem in the same scenario. Extensive simulations reveal the suitability of the proposed strategy, particularly in the presence of severe multicollinearity and heteroscedasticity. A real-life application highlights that the proposed strategy has the potential to be a useful tool for data analysis in the case of collinear predictors and heteroscedastic errors. [ABSTRACT FROM AUTHOR]

The multicollinearity of measurement data leads to the low accuracy of the data-driven methods for estimating voltage-power sensitivity in distribution networks. In this paper, a data-driven method embedded with topological information is proposed to address the problem. First, the voltage-power sensitivity matrix is decomposed into principal and secondary components, where the principal component is closely related to the distribution network topology and the secondary component is the error between the principal component and the actual value. Then, the principal and secondary components are estimated sequentially in two stages, and their data-driven estimation models based on quadratic programming are established, respectively. The key of the model in the first stage is the constraint based on the distribution network topology information, and the key of the model in the second stage is the constraint that the ratio of the secondary component to the principal component is tiny. Finally, the accuracy and efficiency of the proposed method is validated in the IEEE 33-bus system with a set of measurement data, and comparisons are made with ordinary least square regression, ridge regression, and LASSO regression. The simulation results show that the accuracy of the proposed method is significantly improved by orders of magnitude.

Binary logistic regression (BLR) is a statistical method that utilizes one or more independent variables to make predictions about the outcome of a categorical dependent variable. The examples in this article demonstrate the utilization of biological data in statistical software such as SPSS and Excel to illustrate BLR. The primary objective of this essay is to provide readers with a comprehensive understanding of binomial logistic regression. This presentation examines the appropriate circumstances for utilizing this specific regression technique and provides guidance on assessing the adequacy of the regression model.

AbstractRidge regression is a commonly used prediction method in cases of multicollinearity among regressors in multiple linear regression model. In this study, the performances of 366 different estimators proposed in the literature for ridge parameter estimation were evaluated. The criteria of estimators’ ratio of generating outliers and the proportion of normality besides the Mean Square Error (MSE) criterion were used for diagnosing ridge parameter estimators. Besides, the effect of outliers and deviations from normality generated by the ridge parameter estimators on the MSE was revealed by Spearman’s Rho correlation analysis. To do so, a Monte Carlo simulation was designed for 2420 different cases, considering the simulation parameters comprehensively in terms of the number of regressors, sample size, collinearity level and error variances. The results revealed that some ridge parameter estimators recommended according to MSE criterion, do not perform well in terms of outlier generation and normality criteria. Significant inter-linear correlations were also found among the ridge parameter estimators’ MSE performance criterion, ratios of outlier generation criterion and normality criterion. Thus, it is suggested that an effective ridge parameter estimator should perform well in terms of outlier generation and normality criteria, as well as having small MSE value. [ABSTRACT FROM AUTHOR]

AbstractRegression analysis is widely used to predict the response variable utilizing one or more predictor variables. In many fields of study, the predictors are highly correlated causing multicollinearity problem that severely affects the efficiency of ordinary least square (OLS) estimators by significantly inflating their variances. To solve the multicollinearity problem, various one and two parameter ridge estimators are available in literature. In this article, a class of modified two parameter Lipovetsky–Conklin ridge estimators is proposed based on eigen values of X′X matrix that provide an automatic dealing option for treating different levels of multicollinearity. An extensive simulations study followed by real life example is used to evaluate the performance of proposed estimators based on MSE criterion. In most of the simulation conditions, our proposed estimators outperformed the existing estimators. [ABSTRACT FROM AUTHOR]

Aeromagnetic surveys are widely used in geological exploration, mineral resource assessment, environmental monitoring, military reconnaissance, and other areas. It is necessary to perform magnetic compensation for interference in these fields. In recent years, large unmanned aerial vehicles (UAVs) have been more suitable for magnetic detection missions because of the greater loads they can carry. This article proposes some methods for the magnetic compensation of large multiload UAVs. Because of the interference of the large platform and instrument noise, the standard deviations (stds) of the compensation data used in this paper are larger. At the beginning of this article, using the traditional T-L model, we avoid the shortcomings of the anti-magnetic interference ability of triaxial magnetic gate magnetometers. The direction cosine information is obtained by using an inertial navigation system, the global positioning system, and a triaxial magnetic gate magnetometer. Then, we increase the amplitude of the maneuvers in the compensation process; this reduces the multicollinearity problems in the compensation matrix to a certain extent, but it also results in greater magnetic field interference. Lastly, we employ the method of Lasso regularization Newton iteration (LRNM). Compared to the traditional methods of least squares (LS) and singular value decomposition (SVD), LRNM provides improvements of 34% and 27%, respectively. In summary, this series of schemes can be used to perform effective compensation for large multi-load UAVs and improve the actual use of large UAVs, making them more accurate in the measurement of aeromagnetic survey data. [ABSTRACT FROM AUTHOR]

The capacity of particulate matter (PM) to generate reactive oxygen species (ROS) in vivo leading to oxidative stress is thought to be a main pathway in the health effects of PM inhalation. Exogenous ROS from PM can be assessed by acellular oxidative potential (OP) measurements as a proxy of the induction of oxidative stress in the lungs. Here, we investigate the importance of OP apportionment methods for OP distribution by PM 10 sources in different types of environments. PM 10 sources derived from receptor models (e.g., EPA positive matrix factorization (EPA PMF)) are coupled with regression models expressing the associations between PM 10 sources and PM 10 OP measured by ascorbic acid (OP AA) and dithiothreitol assay (OP DTT). These relationships are compared for eight regression techniques: ordinary least squares, weighted least squares, positive least squares, Ridge, Lasso, generalized linear model, random forest, and multilayer perceptron. The models are evaluated on 1 year of PM 10 samples and chemical analyses at each of six sites of different typologies in France to assess the possible impact of PM source variability on PM 10 OP apportionment. PM 10 source-specific OP DTT and OP AA and out-of-sample apportionment accuracy vary substantially by model, highlighting the importance of model selection according to the datasets. Recommendations for the selection of the most accurate model are provided, encompassing considerations such as multicollinearity and homoscedasticity. [ABSTRACT FROM AUTHOR]

AbstractIn this article, we begin by providing a theoretical comparison between Farebrother’s estimator and the ridge estimator, in terms of the MSE matrix criterion, under three distinct restrictions when r is random. Additionally, we propose an estimate of parameter k for Farebrother’s estimator. Subsequently, we present a Monte Carlo simulation experiment to compare Farebrother’s estimator with OLS, RLS, and ridge estimators. [ABSTRACT FROM AUTHOR]