Local Linear Regression Model Research Articles

KNN Local Linear Regression for Demarcating River Cross-Sections with Point Cloud Data from UAV Photogrammetry URiver-X

Aerial surveying with unmanned aerial vehicles (UAVs) has been popularly employed in river management and flood monitoring. One of the major processes in UAV aerial surveying for river applications is to demarcate the cross-section of a river. From the photo images of aerial surveying, a point cloud dataset can be abstracted with the structure from the motion technique. To accurately demarcate the cross-section from the cloud points, an appropriate delineation technique is required to reproduce the characteristics of natural and manmade channels, including abrupt changes, bumps and lined shapes. Therefore, a nonparametric estimation technique, called the K-nearest neighbor local linear regression (KLR) model, was tested in the current study to demarcate the cross-section of a river with a point cloud dataset from aerial surveying. The proposed technique was tested with synthetically simulated trapezoidal, U-shape and V-shape channels. In addition, the proposed KLR model was compared with the traditional polynomial regression model and another nonparametric technique, locally weighted scatterplot smoothing (LOWESS). The experimental study was performed with the river experiment center in Andong, South Korea. Furthermore, the KLR model was applied to two real case studies in the Migok-cheon stream on Hapcheon-gun and Pori-cheon stream on Yecheon-gun and compared to the other models. With the extensive applications to the feasible river channels, the results indicated that the proposed KLR model can be a suitable alternative for demarcating the cross-section of a river with point cloud data from UAV aerial surveying by reproducing the critical characteristics of natural and manmade channels, including abrupt changes and small bumps as well as different shapes. Finally, the limitation of the UAV-driven demarcation approach was also discussed due to the penetrability of RGB sensors to water.

Utilizing local likelihood in regression discontinuity design: Investigating the impact of antiretroviral therapy eligibility on retention in clinical HIV care in South Africa.

The regression discontinuity (RD) design is a widely utilized approach for assessing treatment effects. It involves assigning treatment based on the value of an observed covariate in relation to a fixed threshold. Although the RD design has been widely employed across various problems, its application to specific data types has received limited attention. For instance, there has been little research on utilizing the RD design when the outcome variable exhibits zero-inflation. This study introduces a novel RD estimator using local likelihood, which overcomes the limitations of the local linear regression model, a popular approach for estimating treatment effects in RD design, by considering the data type of the outcome variable. To determine the optimal bandwidth, we propose a modified Ludwig-Miller cross validation method. A set of simulations is carried out, involving binary, count, and zero-inflated outcome variables, to showcase the superior performance of the suggested method over local linear regression models. Subsequently, the proposed local likelihood model is employed on HIV care data, where antiretroviral therapy eligibility is determined by a CD4 count threshold. A comparison is made between the results obtained using the local likelihood model and those obtained using local linear regression.

Effect of health management service for hypertension patients under framework of Basic Public Health Service Project: a regression discontinuity design

Objective: To evaluate the effect of health management service on hypertension patients (HMSFHP) under the framework of the Basic Public Health Service Project by using regression discontinuity design. Methods: The participants were enrolled from an observational cohort survey in 2015 and followed up was conducted in 2019. The participants with SBP 130-150 mmHg and/or DBP 80-100 mmHg in the baseline survey of the cohort in 2015 were included in the present study. Additionally, we obtained the dates of participants receiving HMSFHP and their blood pressure data from follow-up records, physical examination records and telephone interview. The participants were divided into intervention group and control group based on the cutoff points, i.e. SBP ≥140 mmHg and/or DBP ≥90 mmHg. The local linear regression model were used to estimate the effect of HMSFHP on reducing blood pressure of the participants. Results: After adjusting for age, sex and time length of receiving HMSFHP, the results of the model including participants with 80-100 mmHg for DBP in 2015 indicated that, for the participants who received HMSFHP, the DBP decreased by 6.66 mmHg from 2015 to 2019. For the participants with SBP 130-150 mmHg in 2015, the reduction estimate of the model was -6.17 mmHg, the difference was not significant (P=0.178), suggesting that receiving HMSFHP did not cause change in SBP for the participants who received HMSFHP. Conclusion: Receiving HMSFHP had effect to reduce DBP, and HMSFHP had a positive effect on the control of blood pressure in patients with hypertension.

Nonparametric and Semiparametric Quantile Regression via a New MM Algorithm

Quantile regression is a popular method with a wide range of scientific applications, but the computation for quantile regression is challenging. Hunter and Lange proposed an MM algorithm for solving optimization problems in parametric quantile regression models. For nonparametric and semiparametric quantile regression, their algorithm can be applied to estimate unknown quantile functions in a pointwise manner. However, the resulting estimates may suffer from drawbacks like nonsmooth with discontinuous points and unstable at extreme quantile levels. To remedy the above issues, we propose a new MM algorithm and show that it yields continuous, smoother, and faster estimated quantile functions. We systematically study the new MM algorithm using the local linear quantile regression model. We prove that the proposed algorithm preserves the monotone descent property in an asymptotic sense. We then extend it to some popular nonparametric and semiparametric quantile regression models. For semiparametric models, we propose new efficient backfitting algorithms based on the new MM algorithm. Compared to traditional backfitting algorithms, the new procedures can significantly reduce computational costs for fully iterative backfitting. The performance of the proposed algorithms is demonstrated via extensive simulation studies and a real data example. Supplementary materials for this article are available online.

Early Warning of Abnormal Bridge Frequencies Based on a Local Correlation Model under Multiple Environmental Conditions

The accuracy of frequency prediction is markedly affected by the nonlinearity and model degradation caused by multiple environmental conditions, which may hinder the prediction accuracy and detectability of damage. Therefore, this paper proposes a local correlation model (LCM) between multiorder bridge frequencies and multiple environmental factors for early warning of abnormal frequencies. First, partial least-squares analysis was conducted to extract several environmental principal components sensitive to modal frequencies. The most relevant local data set for each online environmental sample was selected according to similarity measurements based on Euclidean distance metrics. On this basis, more accurate environment–frequency relation models were formed using relatively simple local linear regression models. To filter out the residual environmental variability not suppressed by the LCM and to enlarge slightly abnormal frequency variation, a warning index (i.e., the weighted Mahalanobis distance) was defined using the residual subspatial reconstruction of principal component analysis. Finally, the validity of the proposed method was verified on a cable-stayed bridge. The results show that in contrast to conventional methods, the proposed LCM can accurately describe complicated frequency variations under changing environmental conditions by considering both the nonlinearity of environmental conditions and the time-varying properties of relation models. The detectability of frequency anomalies induced by sudden events can be effectively improved.

Comparison of Different Artificial Intelligence Techniques to Predict Floods in Jhelum River, Pakistan

Floods are among the major natural disasters that cause loss of life and economic damage worldwide. Floods damage homes, crops, roads, and basic infrastructure, forcing people to migrate from high flood-risk areas. However, due to a lack of information about the effective variables in forecasting, the development of an accurate flood forecasting system remains difficult. The flooding process is quite complex as it has a nonlinear relationship with various meteorological and topographic parameters. Therefore, there is always a need to develop regional models that could be used effectively for water resource management in a particular locality. This study aims to establish and evaluate various data-driven flood forecasting models in the Jhelum River, Punjab, Pakistan. The performance of Local Linear Regression (LLR), Dynamic Local Linear Regression (DLLR), Two Layer Back Propagation (TLBP), Conjugate Gradient (CG), and Broyden–Fletcher–Goldfarb–Shanno (BFGS)-based ANN models were evaluated using R2, variance, bias, RMSE and MSE. The R2, bias, and RMSE values of the best-performing LLR model were 0.908, 0.009205, and 1.018017 for training and 0.831, −0.05344, and 0.919695 for testing. Overall, the LLR model performed best for both the training and validation periods and can be used for the prediction of floods in the Jhelum River. Moreover, the model provides a baseline to develop an early warning system for floods in the study area.

AN ADAPTIVE LOCAL LINEAR REGRESSION METHOD FOR MOBILE SIGNAL STRENGTH WITH APPLICATION TO RESPONSE SURFACE METHODOLOGY

The received signal strength is vital in telecommunication network or technology as it is affected by varying environmental factors such as temperature (T0C), relative humidity (H%), air quality index (m) and distance from base station (m). In this paper, we seek to find a regression model via a circumscribed central composite design that can adequately represent the functional relationship between the received signal strength and the respective factors applied to response surface methodology with the goal to obtain settings of these factors that would simultaneously optimize the received signal strength (Long Term Evolution (LTE), Third Generation network (3G) and second Generation network (2G)) technologies. The frequently utilized regression model is the parametric regression model (second-order model), though superior but lack credibility in terms of model misspecification and as a result, the optimum setting of the factors are miscalculated. In addressing the pitfall of the parametric regression model (PRM), we introduce a flexible adaptive local linear regression model that can capture local trend in the data, which ordinarily a misspecified PRM could not address. In the application, two regression models were used and the results show that the adaptive local linear regression model outperformed the parametric counterpart in terms of goodness-of-fit statistics, residual plot and optimization of the received signal strength.

Building Local Models for Flexible Degradation Modeling and Prognostics

To avoid unexpected failures of engineering systems, sensors have been widely used to monitor the degradation process of the systems. A number of studies have been conducted to analyze the collected sensor signals and predict the failure time. However, the existing studies are usually restricted and cannot be adapted to different practical situations. In this paper, we propose a systematic method for degradation modeling and prognosis that can be widely applied in different scenarios. In particular, the proposed method is capable to handle one or multiple sensors, powerful to capture the nonlinear relations between sensor signals and the degradation process with few assumptions, generic to consider multiple failure modes, flexible to deal with unequally spaced sensor measurements or asynchronous signals, and easily understandable with little preprocessing required. The main idea is to predict the failure time of an in-service unit based on a subset of the nearest historical units, where features are extracted from each sensor to describe the progression of sensor signals and local linear regression models are constructed to establish the relation between failure time and the extracted features. The prediction variance is then used as the goodness-of-fit measure, based on which decision-level fusion and feature-level fusion are proposed to combine multiple sensors. A case study with two datasets on the degradation modeling of aircraft engines is conducted which shows satisfactory performance of the proposed method. Note to Practitioners—This paper aims at modeling the collected sensor signals to understand the degradation process of the monitored engineering systems and predict the failure time. The main idea is to measure the similarity of units and predict the failure time of an in-service unit based on a subset of the nearest historical units. The developed method is widely applicable in different practical situations such as multiple sensors, multiple failure modes, asynchronous signals, and missing data. Furthermore, the method requires little preprocessing. There are several steps involved for implementing the proposed method: 1) collecting the sensor signals for historical units and the in-service unit; 2) extracting features from each sensor signal; 3) constructing a local linear model to predict the failure time based on the extracted features, and obtaining the prediction variance on the in-service unit; and 4) combining the information of different sensors using the decision-level fusion or feature-level fusion, if each unit is monitored by multiple sensors.

LAND-USE and land-cover change processes in Pampa biome and relation with environmental and socioeconomic data

Pampa biome in the last years has gone through a process of change in land use, chiefly due to the conversion of grassland vegetation for agriculture of grains and silviculture. The main objective of this work is to analyze processes of Land-Use and Land-Cover (LUCC) in the Brazilian Pampa Biome, mapped from Multitemporal data of MODIS sensor, including the main processes of landscape transformation. The period studied was 2000 and 2014, and MODIS-EVI images and night DMSP-OLS images were used for generation of land use and cover maps, through decision tree classification. IBGE census sectors’ limits were used. To investigate the processes of landscape transformation of Pampa Biome, environmental variables were used including geomorphometric data, landscape metrics and climate data and socioeconomic variables. Local (GWR) and global linear regression models were used in addition to procedures for spatial clustering (SKATER algorithm). Reduction of around 25% of grassland class in 15-year interval was verified, from 10,252,740 ha to 7,676,208 ha. On the other hand, agriculture areas like Soybean class obtained 145.56% increase in their total area, from 855,087 ha in 2000, to 2,099,837 ha in 2014. Silviculture class also presented increase of over 167% of its total area. The main factors in the global regression model that negatively contributed to grassland degradation process are: population density, height against the closest drainage (HAND Model) and degradation patches in the grassland. Factors that positively contributed are: population residing in domiciles, average of number of residents in domiciles, Soybean expansion patches and distance from Soybean expansion process. It was concluded that orbital data along with geoprocessing techniques provided tools for monitoring changes in land use and cover.

Local linear regression analysis for interval-valued data

Interval-valued data, a type of symbolic data, is given as an interval in which the observation object is not a single value. It can also occur frequently in the process of aggregating large databases into a form that is easy to manage. Various regression methods for interval-valued data have been proposed relatively recently. In this paper, we introduce a nonparametric regression model using the kernel function and a nonlinear regression model for the interval-valued data. We also propose applying the local linear regression model, one of the nonparametric methods, to the interval-valued data. Simulations based on several distributions of the center point and the range are conducted using each of the methods presented in this paper. Various conditions confirm that the performance of the proposed local linear estimator is better than the others.

Understanding the Impact of Observation Data Uncertainty on Probabilistic Streamflow Forecasts Using a Dynamic Hierarchical Model

AbstractEarlier researches have proposed algorithms to quantify the measurement uncertainty in rating curves and found that the magnitude of the uncertainty can be significant enough to impact hydrologic modeling. Therefore, they suggested frameworks to include measurement uncertainty in the rating curve to make it robust. Despite their efforts, a robust rating curve is often ignored in traditional practices, considering the investment of time and money as well as the resulting benefit from it. In the current research, we are interested in understanding the role of the measurement error variance in real‐time streamflow forecasting. Our objectives are (i) to employ a state‐of‐the‐art statistical forecasting model that can handle measurement uncertainty in daily streamflow and (ii) to understand the trade‐off in forecasting performance when substantial knowledge regarding the measurement uncertainty is provided to the modeler. We apply the Bayesian dynamic hierarchical model (BDHM) on four gauging sites in the United States. Results show that the BDHM performs better than the daily climatology and local linear regression model. Also, the forecast variance changes proportionally with the change in the error variance as an input in the observation equation. Following this, we design a simulation‐based study, which assigns the measurement error in the reported streamflow to obtain multiple realizations of the true streamflow. The inclusion of substantial knowledge about the true error improves the BDHM's performance by lowering the CRPS (continuous rank probability score) values. However, the inclusion increases the forecast variance to bring the true streamflow within the sampling variability of the forecasted streamflow. Overall, an improved trade‐off between the success rate of forecasts and the forecast variance can be achieved by including the measurement error in the BDHM for rivers that witness less dispersed streamflow data.

Association Between Fetal Exposure to Famine and Anthropometric Measures in Adulthood: A Regression Discontinuity Approach.

The aim of this study was to investigate the differences in six anthropometric measurements of people born during and immediately after the 1959 to 1961 Great Chinese Famine using aregression discontinuity approach. Data were drawn from the baseline of theChina Kadoorie Biobank study, and a subset of data from 76,912 participants was analyzed. We performed regression discontinuity among participants who were born during the famine (October 1959 to October 1962) and immediately after the famine period (November 1962 to October 1964) by using local linear and parametric regressions. All analyses were conducted by sex and study area. Significantly, there were increases of 0.30 kg/m2 (P = 0.007) in BMI, 0.81 kg (P = 0.028) in weight, 8.57 mm (P = 0.004) in waist circumference, and 5.07 mm (P = 0.004) in hip circumference for rural women who were exposed to famine during their fetal period compared with those who were not exposed to famine in utero. However, such statistically significant increases in anthropometric values were not observed in local linear regression and most parametric models among rural men or in theurban population. Rural Chinese women who were exposed to famine duringthe fetal period were observed to have higher levels of BMI, weight, waist circumference, and hip circumference in adulthood.

Monotonicity, linearity and symmetry in the price volatility–volume relationship

Purpose This paper aims to investigate the contemporaneous link between price volatility and trading volume in the futures markets of energy. Design/methodology/approach Non-parametric (local linear) regression models and formal statistical tests are used to assess monotonicity, linearity and symmetry. The data are daily price and volumes from five futures markets (West Texas Intermediate, Brent, gasoline, heating oil and natural gas) in the USA. Findings Trading volume and price volatility have, in all markets, a strong nonlinear relation to each other. There are violations of monotonicity locally but not globally. The qualitative nature of the price shocks may have implications for the trading activity locally. Originality/value To the authors’ best knowledge, this is the first manuscript that investigates simultaneously and formally all the three important issues (i.e. monotonicity, linearity and asymmetry) for the price volatility–volume relationship using a highly flexible nonparametric approach.

Local Regression Ranking for Saliency Detection.

Saliency detection is an important and challenging research topic due to the variety and complex of the background and saliency regions. In this paper, we present a novel unsupervised saliency detection approach by exploiting a learning-based ranking framework. First, the local linear regression model is adopted to simulate the local manifold structure of every image element, which is approximately linear. Using the background queries from the boundary prior, we construct a unified objective function to globally minimize all the errors of the local models for the whole image element points. The Laplacian matrix is learned via optimizing the unified objective function. Low-level image features as well as high-level semantic information extracted from deep neural networks are used for the Laplacian matrix learning. Based on the learnt Laplacian matrix, the saliency of the image element is measured as the relevance ranking to the background queries. The foreground queries are obtained from the background-based saliency and the relevance ranking to the foreground queries is calculated in the same way as the background-based saliency. Second, we calculate an enhanced similarity matrix by fusing two different-level deep feature metrics through cross diffusion. A propagation algorithm uses this enhanced similarity matrix to better exploit the intrinsic relevance of similar regions and improve the saliency ranking results effectively. Results on four benchmark datasets with pixel-wise accurate labelling demonstrate that the proposed unsupervised method shows better performance compared with the newest state-of-the-art methods and is competitive with deep learning-based methods.

Explicit and interpretable nonlinear soft sensor models for influent surveillance at a full-scale wastewater treatment plant

In wastewater treatment plants, the most adopted sensors are those with the properties of low cost and fast response. Soft sensors are alternative solutions to the hardware sensor for online monitoring of hard-to-measure variables, such as chemical oxygen demand (COD) and total phosphorus (TP). The purpose of this study is to obtain a modelling approach which is able to identify the nonlinearity of influent and explain the correlation of inputs-outputs. Thus, the variation of influent characteristics was investigated at the first stage, which provided the basis to build global and local multiple linear regression models. Secondly, a nonlinear modelling tool multivariate adaptive regression splines (MARS) was applied for influent COD and TP prediction. Satisfactory prediction accuracy was obtained in terms of root mean square error (RMSE) and R2. Unlike other machine learning techniques which are "black box" models, MARS provided interpretable models which explained the nonlinearity and correlation of inputs-outputs. The MARS models can be used not only for prediction, but also to provide insight of influent variation.

An Improved Robust Regression Model for Response Surface Methodology

In production, manufacturing and several other allied industries, appropriate tool is applied in the analysis of data in order to enhance the opportunity for product and process optimization. A statistical tool that has successfully been used to achieve this goal is Response Surface Methodology (RSM). A recent trend in the modeling phase of RSM involves the use of semi-parametric regression models which are hybrids of the Ordinary Least Squares (OLS) and the Local Linear Regression (LLR) models. In this paper, we propose a modification in the current structure of the semi-parametric Model Robust Regression 2 (MRR2) with a view to improving its sensitivity to local trends and patterns in data. The proposed model is applied to two multiple response optimization problems from the literature. The results of goodness-of-fits and optimal solutions confirm that the proposed model performs better than the MRR2.

Revisiting Pan Evaporation Trends in Australia a Decade on

AbstractDecreases in pan evaporation (Epan) have been reported around the world despite increasing air temperatures; this was attributed to reductions in wind speed and solar radiation. Using 42 years (1975–2016) of Australian Epan data, we reexamined Epan trends, adding over a decade of observations to previous analyses. Flexible local linear regression models showed that many previously reported decreasing Epan trends have plateaued or reversed. Attribution analysis confirmed that 1975–1994 Epan decreases in southern/western Australia were chiefly driven by decreasing wind speeds. Increasing vapor pressure deficit subsequently became dominant, resulting in 1994–2016 Epan increases. Climate trend analyses should consider applying flexible statistical models to qualitatively understand temporal dynamics, complementing linear models that are able to provide quantitative assessments, especially when multiple drivers are involved.

Context adaptive panchromatic band simulation and detail injection for image pansharpening

General component substitution (CS) pansharpening methods establish a global model over the whole image plane and may lead to unexpected spectral distortion. This paper proposes a context adaptive CS pansharpening method, which features a totally local-based processing procedure. The method consists of two processing blocks. The first block is to simulate a low-resolution panchromatic band by a local linear regression model between panchromatic and multispectral bands. The second block extracts spatial details and adds details back to multispectral bands in locally varying ratios. By recasting the local linear regression model into the guided filtering framework and analyzing the implicit statistical assumptions underlying CS methods, the strengths of the local-based pansharpening algorithm are addressed. Experiments test 7 pairs of images acquired from different sensors, such as GF-2, Quickbird, and Worldview-2. Both quantitative and qualitative evaluations reveal that the presented method can better preserve the spectral information than some state-of-the-art methods.

The Step Construction of Geographically Weighted Panel Regression in Air Polluter Standard Index (APSI) Data

Geographically Weighted Panel Regression or GWPR is a local linear regression model that combines GWR model and panel data regression model with considering spatial effect, especially spatial heterogeneity problem. This article is focused on the soft computation of GWPR model using Fixed Effect Model (FEM). Parameter estimation in GWPR is obtain by Weighted Least Squares (WLS) methods and the resulting model for each location will be different from one to another. This study will compare the fixed-effect GWPR model with several weighting functions. The best model is determined based on the biggest coefficient of determination (R2) value. In this study, the model is applied in the Air Polluter Standard Index (APSI) in Surabaya City, East Java. The results of this study indicate that Fixed Effect GWPR model with a fixed exponential kernel weighting function is the best model to describe the APSI because it has the smallest AIC.

Application of PCA and Clustering Methods in Input Selection of Hybrid Runoff Models

This study has proposed and investigated a novel input variable selection method for nonlinear modelling based on principle component analysis (PCA) and cluster analysis. The proposed approach was applied to daily rainfall-runoff modelling of the Brue catchment of the United Kingdom using wavelet based hybrid forms of two nonlinear models, Artificial Neural Networks (ANNs) and Local Linear Regression (LLR), to identify meaningful wavelet decomposed sub-series. The homogenous group formation capability of cluster analysis and redundancy assessment capability of PCA were applied effectively in this study to solve input selection uncertainties associated with wavelet based hybrid models. Though this concept has been represented in the selection of effective wavelet decomposed subseries in runoff modelling, the application has gotten wider implications in time series modelling with highly redundant and large input space. The study revealed the weakness of conventional forms of cross-correlation analysis and also suggested that input selection could be improved by making sufficient natural clusters (equal to the desired number of input data series) of input space and restricting the search within each cluster according to silhouette or correlation value. The study also highlighted the higher modelling capability of ANN over traditional LLR models in rainfall-runoff modelling of the Brue catchment.