Ridge Parameter Research Articles

Some Modified Ridge Estimators for Handling the Multicollinearity Problem

Regression analysis is a statistical process that utilizes two or more predictor variables to predict a response variable. When the predictors included in the regression model are strongly correlated with each other, the problem of multicollinearity arises in the model. Due to this problem, the model variance increases significantly, leading to inconsistent ordinary least-squares estimators that may lead to invalid inferences. There are numerous existing strategies used to solve the multicollinearity issue, and one of the most used methods is ridge regression. The aim of this work is to develop novel estimators for the ridge parameter “γ” and compare them with existing estimators via extensive Monte Carlo simulation and real data sets based on the mean squared error criterion. The study findings indicate that the proposed estimators outperform the existing estimators.

Modified robust ridge M-estimators for linear regression models: an application to tobacco data

The ordinary least squared and ridge regression estimators in a linear regression model are sensitive to outliers in the y-variable. In such situations, ridge M-estimators are widely used which are robust to the y-variable outliers and overcome the multicollinearity problem. Similar to ridge regression, to lower the mean square error (MSE) of ridge M-estimators, it is crucial to select the most robust ridge parameter. The performance of existing estimators for the estimation of robust ridge parameters deteriorates when the degree of multicollinearity, error variance, and y-variable outliers increases from moderate to high. In this paper, some new robust ridge M-estimators have been proposed. The efficiency of the new estimators has been compared through a Monte Carlo simulation study. Based on the MSE criterion, the new estimators outperform existing estimators. A numerical example has been provided to illustrate the simulation results.

Condition-index based new ridge regression estimator for linear regression model with multicollinearity

Ridge regression is employed to estimate the regression parameters while circumventing the multicollinearity among independent variables. The ridge parameter plays a vital role as it controls bias-variance tradeoff. Several methods for choosing the ridge parameter are suggested in the literature. In this paper, we suggest a new ridge estimator which is a function of condition index, number of predictors and error variance. This new proposal has the novelty to have a sort of automatic dealing with the multicollinearity level and signal-to-noise ratio. Extensive Monte Carlo simulations are performed to evaluate the performance of the proposed ridge regression estimators in various scenarios. It has been shown that the our proposed estimator outperforms the closely related estimators in terms of minimum mean squared error (MSE). Finally, two real life applications are also provided.

On the performance of some new ridge parameter estimators in the Poisson-inverse Gaussian ridge regression

The Poisson Inverse Gaussian Regression model (PIGRM) is used for modeling the count datasets to deal with the issue of over-dispersion. Generally, the maximum likelihood estimator (MLE) is used to estimate the PIGRM estimates. In the PIGRM, when the explanatory variables are correlated, the MLE does not provide efficient results. To overcome this problem, we propose a ridge estimator for the PIGRM. The matrix mean square error (MSE) and the scalar MSE properties are derived and then compared with the MLE. In the ridge estimator, ridge parameter play a significant role, so, this study also proposes different ridge parameter estimators for the PIGRM. The performance of the proposed estimator is evaluated with the help of a simulation study and a real-life application using MSE as a performance evaluation criterion. The simulation study and the real-life application results show the superiority of the proposed parameter estimators as compared to the MLE.

A new ridge estimator for linear regression model with some challenging behavior of error term

Ridge regression is a variant of linear regression that aims to circumvent the issue of collinearity among predictors. The ridge parameter has an important role in the bias-variance tradeoff. In this article, we introduce a new approach to select the ridge parameter to deal with the multicollinearity problem with different behavior of the error term. The proposed ridge estimator is a function of the number of predictors and the standard error of the regression model. An extensive simulation study is conducted to assess the performance of the estimators for the linear regression model with different error terms, which include normally distributed, non-normal and heteroscedastic or autocorrelated errors. Based upon the criterion of mean square error (MSE), it is found that the new proposed estimator outperforms OLS, commonly used and closely related estimators. Further, the application of the proposed estimator is provided on the COVID-19 data of India.

A Monte Carlo study on the ridge parameter of the seemingly unrelated ridge regression models

The ridge regression approach can also be applied to deal with multicollinearity in the seemingly unrelated regression equations (SURE) models. However, to get the ridge-type estimators of the coefficients in a SURE model, choosing the ridge parameter has always been an important and challenging task. Herein, to cope with this issue, an optimal choice of the ridge parameter is proposed based on the generalized cross-validation (GCV) criterion. Moreover, some existing estimators of this parameter, in the context of the ordinary ridge regression models, are extended to be used in the SURE models. All these estimators, including the proposed and extended ones, and several state-of-the-art alternatives (altogether 36 different estimators) are compared with each other in terms of the GCV criterion. Lastly, an application of the methodology is given on chronic renal failure effect data.

Research of cultivators’ working bodies influence on damage on damage to potato plants, weed control, and formation of ridges

Purpose. Reducing the negative impact of passive cultivator working bodies on potato plants by improving them, optimizing technology elements for inter-row cultivation, and forming ridges. Methods. Analysis of the conducted patent search – in accordance with DSTU 3575-97. Technological schemes of the cultivator were developed based on the analysis of literature data and design schemes of cultivator working bodies. Laboratory and field studies were conducted by generally accepted methods. Results. It was experimentally established that during the cultivation of potato plantations, the best result was obtained by using improved passive working bodies in combination: a V-shaped weep + a rotary harrow + a device for forming ridges for all indicators that were included in the study. Reducing the level of mechanical damage from 9.5 % in the control variant to 6.6 % in the 4th variant, weed infestation of plantings from 2.2 to 1.3 pcs/m2 during flowering of potatoes; parameters of the formed ridges at the time of harvesting were: height 25.0 cm vs. control variant 21.0 cm, width 64.3 cm vs. 59.0 cm. Conclusions. The model of the unit for the formation of ridges (disk hiller) in combination with a V-shaped weep and a rotary harrow ensured the formation of a potato ridge of optimal shape and size. The effect of working bodies on damage to potato plants, weed control in the cultivation area, and the formation of ridges was determined. The highest conditional net profit was 43.9 thousand UAH/ha in the 4th variant, which exceeds the control by 24.8 thousand UAH/ha. Keywords: disk hiller, work tools, weed infestation, parameters of ridges, potatoes.

Calculation of parameters of subsurface ridges in a steady flow of groundwater channels

In solving the problems associated with the design and operation of large canals with many subsurface channels, it is important to determine the parameters of the parameters of the grids moving under the bottom and the flow rates. To date, a large number of field and laboratory research data on the movement of groups in the world have been obtained. Attempts have been made by some authors to summarize this information, but so far they have not been able to obtain perfectly reliable results. Therefore, new suggestions are being made by researchers to improve the formulas previously obtained.

Comparison of link functions for the estimation of logistic ridge regression: an application to urine data

The logistic regression model is applied in situations when the response variable is of binary nature and follows the Bernoulli distribution. The maximum likelihood estimation (MLE) is used to estimate the unknown parameters of the logistic regression. However, in the presence of multicollinearity, MLE is not a reliable estimation method due to its large variance and high standard errors. To overcome this problem, we consider the logistic ridge regression estimator (LRRE) under different link functions. Moreover, we also propose some ridge parameters for the LRRE and compare the performance of these ridge parameters with the available best ones. A Monte Carlo simulation study and a real dataset are considered for the evaluation of LRRE using scalar mean squared error as performance evaluation criteria. The simulation results indicate the superiority of the LRRE with a specified link function over the MLE in the presence of multicollinearity. From the simulation and real data application results, it is observed that the LRRE with ridge parameters k_8 and k_9 under logit and probit link functions is superior to the other ridge parameters with other link functions.

A review of ridge parameter selection: minimization of the mean squared error vs. mitigation of multicollinearity

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.

Ridge estimator in a mixed Poisson regression model

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.

Alternative Ridge Parameters in Linear Model

The ridge regression estimator produces efficient estimates than the Ordinary Least Square Estimator in a linear regression model that has multicollinearity problem. However, the efficiency of the ridge estimator depends on the choice of the ridge parameter, k. This parameter being the biasing parameter that shrinks the coefficient as it tends towards positive infinity needs to be chosen optimally to minimize the mean squared errors of the parameters. In this study, the ridge parameters are classified into different forms, various types and diverse kinds. These classifications resulted into proposing some other techniques of Ridge parameter estimation. Investigation of the existing and proposed ridge parameters were done by conducting Monte-Carlo experiments. Results from simulation study and reallife data application show that some newly proposed ridge parameters are among those that provide efficient estimates.

On the choice of the ridge parameter: a generalized maximum Tsallis entropy approach

In multiple Regression Model the absence of multicollinearity is essential. The presence of multicollinearity is often caused by including too many (highly correlated) regressors and in this case, the estimates tend to be less precise. For this reason, varies methods have been introduced to solve these problems caused by the existence of multicollinearity. In this paper, a new method to estimate the ridge parameter, based on the ridge trace and an analytical method borrowed from Generalized Maximum Tsallis Entropy, is presented and we call that the Ridge GMET2 estimator. The performance of the new estimator is illustrated through a Monte Carlo simulation study. We compared the Ridge GMET2, Ridge GME and OLS estimators. Mean square error of Ridge GMET2 estimates, is less than corresponding for Ridge-GME and OLS estimates. In some case also, the value of the Ridge-GME and Ridge-GMET2 estimators are nearer, since Tsallis entropy does not depend on the logarithm unlike, the Shannon entropy, so that it is a substantial point that we prefer the Ridge-GMET2 estimator.

More on the Ridge Parameter Estimators for the Gamma Ridge Regression Model: Simulation and Applications

The Gamma ridge regression estimator (GRRE) is commonly used to solve the problem of multicollinearity, when the response variable follows the gamma distribution. Estimation of the ridge parameter estimator is an important issue in the GRRE as well as for other models. Numerous ridge parameter estimators are proposed for the linear and other regression models. So, in this study, we generalized these estimators for the Gamma ridge regression model. A Monte Carlo simulation study and two real-life applications are carried out to evaluate the performance of the proposed ridge regression estimators and then compared with the maximum likelihood method and some existing ridge regression estimators. Based on the simulation study and real-life applications results, we suggest some better choices of the ridge regression estimators for practitioners by applying the Gamma regression model with correlated explanatory variables.

Procedural Roof Generation From a Single Satellite Image

AbstractUrban procedural modeling has benefited from recent advances in deep learning and computer graphics. However, few, if any, approaches have automatically produced procedural building roof models from a single overhead satellite image. Large‐scale roof modeling is important for a variety of applications in urban content creation and in urban planning (e.g., solar panel planning, heating/cooling/rainfall modeling). While the allure of modeling only from satellite images is clear, unfortunately structures obtained from the satellite images are often in low‐resolution, noisy and heavily occluded, thus getting a clean and complete view of urban structures is difficult. In this paper, we present a framework that exploits the inherent structure present in man‐made buildings and roofs by explicitly identifying the compact space of potential building shapes and roof structures. Then, we utilize this relatively compact space with a two‐component solution combining procedural modeling and deep learning. Specifically, we use a building decomposition component to separate the building into roof parts and predict regularized building footprints in a procedural format, and use a roof ridge detection component to refine the individual roof parts by estimating the procedural roof ridge parameters. Our qualitative and quantitative assessments over multiple satellite datasets show that our method outperforms various state‐of‐the‐art methods.

On the performance of link functions in the beta ridge regression model: Simulation and application

AbstractThe beta regression model (BRM) is appropriate when the response variable is continuous and is in the form of ratios and proportions. For the estimation of the BRM, the maximum likelihood estimation (MLE) method is used with a specific link function. However, the MLE provides unstable results when the explanatory variables are correlated. In this study, we consider some ridge parameters for the beta ridge regression estimator (BRRE) under different link functions. However, mostly the researchers do not pay much attention to the suitable link function. So, we consider five link functions to see the performance of ridge parameters in the BRRE. For the performance assessment of ridge parameters and different link functions, a Monte Carlo simulation and a real application are considered, where mean squared error is used as the evaluation criterion. Both the simulation and example findings demonstrate that the BRRE with the log–log link function provides efficient results.

On the performance of some biased estimators in the gamma regression model: simulation and applications

The gamma regression model is widely applied when the response variable is continuous and positively skewed. In the multicollinearity problem, the usual maximum likelihood estimator is inadequate due to its inflated variance. To reduce this effect, well-known ridge and Liu estimators are generally used. In this study, we propose some shrinkage parameters for the new estimator and compared with some best ridge parameters indicated by Amin et al. [Performance of some ridge estimators for the gamma regression model. Stat Pap. 2020;61:997–1026] and two proposed ridge parameters for the GRM specified by Lukman et al. [A new ridge-type estimator for the gamma regression model. Scientifica. 2021;2021:5545356]. A Monte Carlo simulation study and an empirical application are conducted to assess the effectiveness of the proposed and other estimators. Based on the findings of simulation results and applications, we found that one of our proposed estimators performed the best for small dispersion levels.

Daytime and nighttime warming has no opposite effects on vegetation phenology and productivity in the northern hemisphere

Over the past 50 years, global land surface air temperature has been rising at a much higher rate at night than during the day. Understanding plant responses to the asymmetric daytime and nighttime warming in the context of climate change has been a hot topic in global change biology and global ecology. It has been debatable whether the asymmetric warming has opposite effects on vegetation activity (e.g., phenology, productivity). Here we settle the debate by scrutinizing the underpinnings of different statistical methods and revealing how the misuse or improper use of these methods could mischaracterize the effects of asymmetric warming with in situ and satellite observations. The use of the ordinary least square (OLS) methods including both daytime (Tmax) and nighttime (Tmin) temperature in the multiple regression models could overlook the multicollinearity problem and yield the misinterpretations that Tmax and Tmin had opposite effects on spring phenology, autumn phenology, gross primary production (GPP), and normalized difference vegetation index (NDVI). However, when the OLS methods were applied with Tmax and Tmin included in separate models or alternatively the ridge regression (RR) method with properly selected ridge parameter was used, the effects of Tmax and Tmin on vegetation activity were generally in the same direction. The use of the RR method with improperly selected ridge parameter could also mischaracterize the effects of asymmetric warming. Our findings show that daytime and nighttime warming has no opposite effects on vegetation phenology and productivity in the northern hemisphere, and properly dealing with the multicollinearity problem is critical for understanding the effects of asymmetric warming on vegetation activity.

Cooperative Suppression of Negative Effects Associated With Multicollinearity and Abnormal Data for Aeromagnetic Compensation

Compensating the magnetic interference related to the airplane maneuvers is essential to high-precision aeromagnetic measurement. In estimating the compensation coefficients, aeromagnetic compensation based on the Tolles-Lawson model needs to address the reduction in accuracy and robustness arising from several negative effects. Because existing methods only suppress single effects independently, the scope of their application is very limited. To address this problem, a cooperative suppression method of the negative effects associated with multicollinearity and abnormal data is proposed in this study. For this method, abnormal data produced by the dead-zone effect of a classical optically-pumped magnetic sensor are assigned lower weights, thereby reducing their negative influence in the estimation of the compensation coefficient. Moreover, a ridge parameter is added to further reduce the multicollinearity of the compensation coefficient. Theoretical evaluation shows that, in the presence of 20% abnormal data and 0.5 correlation, this method reduces the mean square error for the coefficient to 0.76 compared with 4.39 for the least-squares method, 3.43 for the ridge method, 2.13 for the robust method. For practicality verification, we built an experimental platform and mounted it on an aeromagnetic survey airplane, and then performed a compensation flight test. The results demonstrate an improved ratio for our method of 12.79, which is significantly higher than 0.56 for the least-squares method, 2.73 for the ridge method, 4.29 for the robust method, and 7.95 for the state-of-the-art commercial compensator.

Modification of technology and aerodynamics of moving hot bulk materials

Variants of pneumatic transport with temperature data of the material are given. Methods for protecting the container from thermal heating are listed. An unloading device for cargo containers for pipeline transport of hot bulk materials has been developed. The proposed system of two integral equations will make it possible to calculate with sufficient accuracy the required compressed air pressure, geometric parameters of aerodynamic ridges for a given length of the unloading section of rotating containers and their translational speed. The presence of aerodynamic ridges will reduce the loss of energy from friction when moving containers in a spiral.