Partial Linear Regression Model Research Articles

Comparison of Some Robust Methods of Difference Based Ridge Estimator in Semiparametric Regression Model

The semiparametric regression models have received a lot of attention from researchers recently because it combines parametric and nonparametric methods, it is one of the advanced topics in data analysis for various studies, which aims to find the best capabilities and a high level of efficiency. One of the most important semiparametric regression models is the partial linear regression model (PLM), which consists of a parametric component and a nonparametric component, for the purpose of estimating the parametric component, the difference method will be used to remove the nonparametric component. When the analysis hypotheses of the parametric component are not fulfilled, it will suffer from several problems, the most important of which is the problem of complete multicollinearity, besides the multicollinearity, there are also outliers in the data. In this research, the problems of multicollinearity and outliers of the semiparametric regression model were addressed, where simulation was used to generate data with different sample sizes and for different correlations and outlier ratios and for different methods such as [Difference Ridge based M robust with Nadaraya – Watson (DRMNW), Difference Ridge based S robust with Nadaraya – Watson (DRSNW), Difference Ridge based M robust with Smoothing spline (DRMSP), Difference Ridge based S robust with Smoothing spline (DRSSP)], the results showed that method Difference Ridge based M robust with Smoothing spline (DRMSP) is the best estimator.

Unraveling patterns, causes, and nature-based remediation strategy for non-grain production on farmland in hilly regions

The surge in non-grain production on farmland (NGPF) poses significant threats to food security and land sustainability, particularly in hilly regions. However, there remains a lack of clarity on how to effectively balance grain and non-grain production in relation to land remediation. Using Wannian County as a case study, we investigate the evolution of this by leveraging high-precision land surveys and satellite imagery. Through the application of bootstrapped partial linear regression models, we identify key influencers behind each type of NGPF. In proposing land remediation solutions, we integrate the results of NGPF and land quality evaluations to identify mismatches between non-grain production and land attributes (i.e., topography, geology, soil, and land use). Our findings reveal a substantial growth in NGPF, expanding from 3838.72 ha to 5659.64 ha (2010–2020), and predominantly occurring on farmland with favorable natural conditions and connected locations such as proximity to roads, town centers, and industrial plants. Surprisingly, the basic farmland protection policy shows limited effectiveness in curbing NGPF, except for garden operations. We identify 1674 NGPF patches suitable for conversion to grain production and provide land remediation suggestions tailored to low-quality farmland with specific natural barriers, thus complementing the demand for regional non-grain production. This study thereby innovatively proposes nature-based land remediation strategies to address the non-grain production dilemma by tailoring NGPF and land quality, offering valuable insights for sustainable farmland management in China and beyond.

Local linear-$k$NN smoothing for semi-functional partial linear regression

The aim of this paper is to study a semi-functional partial linear regression model. The estimators are constructed by $k$-nearest neighbors local linear method. Some asymptotic results are established for an i.i.d sample under certain conditions, including asymptotic normality of the parametric component and the almost certain convergence (with rate) of the non-parametric component. Lastly, using cross-validation, the performances of our estimation method are presented on simulated data and on real data by comparing them with other known approaches for semi-functional partial linear regression models.

Semi-Functional Partial Linear Quantile Regression Model with Randomly Censored Responses

Semi-Functional Partial Linear Quantile Regression Model with Randomly Censored Responses

Nursing workforce plays a significant role in reducing COVID-19 deaths worldwide: A cross-sectional analysis of data from 178 countries.

Worldwide, the role of nursing workforce in reducing COVID-19 case fatality ratio (CFR) is analyzed with scatter plots, Pearson's r and nonparametric, partial correlation and multiple linear regression models. The potential confounders, median age, health expenditure, physician density, and urbanization were incorporated for calculating the independent role of nursing workforce in protecting against COVID-19 CFR. The study findings suggested that (1) the nursing workforce inversely and significantly correlates with COVID-19 CFR; (2) this relationship remained independent of the confounding effects of each individual confounder or their combination; (3) Nursing workforce was the only variable identified as a significant contributor for reducing COVID-19 CFR, when it was incorporated into stepwise regression model with health expenditure, median age, physician density, and urbanization for analyzing their individual predicting effects on COVID-19 CFR. A strong message for the health authorities is that, although in shortage, nursing workforce showed their significant role in reducing COVID-19 deaths worldwide. This study highlights that the role of nursing workforce should be incorporated into population health research.

A Novel Variable Selection Method Based on Ordered Predictors Selection and Successive Projections Algorithm for Predicting Gastrodin Content in Fresh Gastrodia elata Using Fourier Transform Near-Infrared Spectroscopy and Chemometrics.

Gastrodin is one of the most important biologically active components of Gastrodia elata, which has many health benefits as a dietary and health food supplement. However, gastrodin measurement traditionally relies on laboratory and sophisticated instruments. This research was aimed at developing a rapid and non-destructive method based on Fourier transform near infrared (FT-NIR) to predict gastrodin content in fresh Gastrodia elata. Auto-ordered predictors selection (autoOPS) and successive projections algorithm (SPA) were applied to select the most informative variables related to gastrodin content. Based on that, partial least squares regression (PLSR) and multiple linear regression (MLR) models were compared. The autoOPS-SPA-MLR model showed the best prediction performances, with the determination coefficient of prediction (Rp2), ratio performance deviation (RPD) and range error ratio (RER) values of 0.9712, 5.83 and 27.65, respectively. Consequently, these results indicated that FT-NIRS technique combined with chemometrics could be an efficient tool to rapidly quantify gastrodin in Gastrodia elata and thus facilitate quality control of Gastrodia elata.

The Consistency of LSE Estimators in Partial Linear Regression Models under Mixing Random Errors

The Consistency of LSE Estimators in Partial Linear Regression Models under Mixing Random Errors

Urinary epidermal growth factor reflects vascular health in boys with either obesity or type 1 diabetes. A role for renin, or beyond?

An increased blood pressure is a known comorbidity of both type 1 diabetes (T1DM) and obesity in children. Increasing evidence suggests a subtle interplay between epidermal growth factor (EGF) and renin along the juxtaglomerular system, regulating the impact of blood pressure on kidney health and the cardiovascular system. In this study, we investigated the relation between urinary EGF, serum renin and blood pressure in children with obesity or T1DM. 147 non-obese children with T1DM and 126 children with obesity, were included. Blood pressure was measured and mean arterial pressure (MAP) and the pulse pressure (PP) were calculated. Serum renin and urinary EGF levels were determined with a commercial ELISA kit. Partial Spearman rank correlation coefficients and multiple linear regression models were used to study the association between renin, the urinary EGF/urinary creatinine ratio and blood pressure parameters. The urinary EGF/urinary creatinine ratio is correlated with the SBP and the MAP in boys with obesity as well as in boys with T1DM. Multiple regression analysis showed that sex and pulse pressure in male subjects were found to be independently associated with renin. Sex, the presence of diabetes, age, the glomerular filtration rate and both pulse pressure and mean arterial pressure in male subjects were independently associated with urinary EGF/urinary creatinine. In conclusion, in boys with either obesity or diabetes, pulse pressure and mean arterial pressure are negatively associated with the functional integrity of the nephron, which is reflected by a decreased expression of urinary EGF.

A generalized Liu-type estimator for logistic partial linear regression model with multicollinearity

<abstract><p>This paper is concerned with proposing a generalized Liu-type estimator (GLTE) to address the multicollinearity problem of explanatory variable of the linear part in the logistic partially linear regression model. Using the profile likelihood method, we propose the GLTE as a general class of Liu-type estimator, which includes the profile likelihood estimator, the ridge estimator, the Liu estimator and the Liu-type estimator as special cases. The conditional superiority of the proposed GLTE over the other estimators is derived under the asymptotic mean square error matrix (MSEM) criterion. Moreover, the optimal choices of biasing parameters and function of biasing parameter are given. Numerical simulations demonstrate that the proposed GLTE performs better than the existing estimators. An application on a set of real data arising from the study of Indian Liver Patient is shown for illustrating our theoretical results.</p></abstract>

Relationship between sediment load and climate extremes in the major Chinese rivers

Global warming has led to increase in climate extremes, which altered both hydrological cycles and soil erosion processes. However, the responses of river sediment load to climate change, especially climate extremes have not been well understood due to a lack of comprehensive assessment. This study investigated the temporal trends and spatial patterns of sediment load at 70 hydrological stations during the period of 1956–2019 in ten major river basins in China. Both the partial linear square regression model and the double mass curve method were used to quantify the contribution of key climatic indices and anthropogenic driving forces. Overall, the annual total sediment load exhibited a significant negative trend (P < 0.01), decreasing from 1842.18 Mt/yr in 1960 s to 322.72 Mt/yr in 2010 s (82.48 %). The significant decline of sediment load was particularly obvious in the Yangtze River basin and the Yellow River basin. The abrupt changes of sediment load mostly occurred in 1985–2000. Human activities were primarily response for sediment load changes in most basins. The sediment load in mainstream was mainly regulated by reservoirs, while the tributaries were largely affected by soil and water conservation measures. Intensive human activities have led to substantial changes in land surface and resulted in weakened correlation between sediment load and climate extremes. Generally, precipitation, erosive rainfall and precipitation amount in flood period were closely related to sediment load. In the Southwest River basin and Northwest River basin, the sediment load had a relatively good relationship with extreme temperature, which was related to alpine snowmelt and permafrost degradation due to climate warming. This study provides good insights for a better understanding of the interaction between river sediment load and climate extremes variables, which will be valuable for decision-making in river basin management.

Rapid detection of phenytoin sodium by partial-least squares and linear regression models combined with surface-enhanced Raman spectroscopy

Surface-enhanced Raman spectroscopy (SERS) for quantitative analysis is challenging owing to the unstable enhanced effect. However, it can be improved by combining it with chemometrics. In this study, we established a quantitative analysis method for phenytoin sodium (PS) based on partial least-squares (PLS) and linear regression (LR) models combined with SERS. Gold nanoparticles (AuNPs) were optimally enhanced substrates for PS. 180 PS samples in the concentration range of 0.98 − 980 μg mL−1 were used to establish a quantitative prediction model by PLS regression, and an accurate and robust prediction was achieved. Furthermore, we found that SERS peak intensity showed a good linear correlation with the concentration of PS in the concentration range of 1 – 80 μg mL −1. After using P-mercaptobenzoic acid as an internal standard, the accuracy and precision of the LR model were significantly improved compared with that of the model without an internal standard. In general, PLS chemometrics and LR model with internal standard which were combined with SERS in this paper provide new possible analytical methods for analytes to develop a rapid and sensitive quantitative analysis method.

LAI-Based Phenological Changes and Climate Sensitivity Analysis in the Three-River Headwaters Region

Global climate changes have a great impact on terrestrial ecosystems. Vegetation is an important component of ecosystems, and the impact of climate changes on ecosystems can be determined by studying vegetation phenology. Vegetation phenology refers to the phenomenon of periodic changes in plants, such as germination, flowering and defoliation, with the seasonal change of climate during the annual growth cycle, and it is considered to be one of the most efficient indicators to monitor climate changes. This study collected the global land surface satellite leaf area index (GLASS LAI) products, meteorological data sets and other auxiliary data in the Three-River headwaters region from 2001 to 2018; rebuilt the vegetation LAI annual growth curve by using the asymmetric Gaussian (A-G) fitting method and extracted the three vegetation phenological data (including Start of Growing Season (SOS), End of Growing Season (EOS) and Length of Growing Season (LOS)) by the maximum slope method. In addition, it also integrated Sen’s trend analysis method and the Mann-Kendall test method to explore the temporal and spatial variation trends of vegetation phenology and explored the relationship between vegetation phenology and meteorological factors through a partial correlation analysis and multiple linear regression models. The results of this study showed that: (1) the SOS of vegetation in the Three-River headwaters region is concentrated between the beginning and the end of May, with an interannual change rate of −0.14 d/a. The EOS of vegetation is concentrated between the beginning and the middle of October, with an interannual change rate of 0.02 d/a. The LOS of vegetation is concentrated between 4 and 5 months, with an interannual change rate of 0.21 d/a. (2) Through the comparison and verification with the vegetation phenological data observed at the stations, it was found that the precision of the vegetation phonology extracted by the A-G method and the maximum slope method based on GLASS LAI data is higher (MAE is 7.6 d, RMSE is 8.4 d) and slightly better than the vegetation phenological data (MAE is 9.9 d, RMSE is 10.9 d) extracted based on the moderate resolution imaging spectroradiometer normalized difference vegetation index (MODIS NDVI) product. (3) The correlation between the SOS of vegetation and the average temperature in March–May is the strongest. The SOS of vegetation is advanced by 1.97 days for every 1 °C increase in the average temperature in March–May; the correlation between the EOS of vegetation and the cumulative sunshine duration in August–October is the strongest. The EOS of vegetation is advanced by 0.07 days for every 10-h increase in the cumulative sunshine duration in August–October.

Estimation of volume resources for planted forests using an advanced LiDAR and hyperspectral remote sensing

Planted forests play a key role in alleviating the stress of harvesting woods and carbon emission on natural forests. Accurate estimation of forest volume resources in planted forests is crucial for balancing relationships between ecological benefits from timber production and ecological benefits from biomass energy. In this study, we explored the use of spectral indices (SIs) and wavelet features (WFs) derived from hyperspectral imaging (HSI) data, as well as Light Detection And Ranging (LiDAR) metrics, with three multivariate regression methods for estimating volume resources in subtropical forests. The results showed that using combined LiDAR and HSI metrics generally outperformed LiDAR-only models. HSI metrics exhibited stronger relationships with volume in lower volume plots (volume < 320 m3/ha) but had saturation problem in higher volume plots, which could be well alleviated by LiDAR metrics. Specifically, coupling WFs and SIs as HSI metrics can further reinforce the synergetic use of LiDAR and HSI metrics, especially with the approach of backward elimination. In comparing three regression methods, Gaussian Processes Regression models (CV-R2 = 0.87, rRMSE = 16.12% for the best model) mostly outperformed Partial Linear Squares Regression and Random Forest regression models. The common important LiDAR metrics for three regression methods were height-related (H50) and density-related (D3 and D9) metrics, while the common optimal spectral metrics (WF615, 2, WF685, 5 and REIP) were related to the chlorophyll absorption features. These findings demonstrated the significance of the wavelet approach in strengthening the synergetic use of LiDAR and HSI metrics for enhancing forest parameter estimations.

Partial linear additive distortion measurement errors models

We consider partial linear regression models when all the variables are measured with additive distortion measurement errors. To eliminate the effect caused by the distortion, we propose the conditional mean calibration to obtain calibrated variables. A profile least squares estimator for the parameter is obtained, associated with its normal approximation based and empirical likelihood based confidence intervals. For the hypothesis testing on parameters, a restricted estimator under the null hypothesis and a test statistic are proposed. A smoothly clipped absolute deviation penalty is employed to select the relevant variables. The resulting penalized estimators are shown to be asymptotically normal and have the oracle property. Lastly, a score-type test statistic is then proposed for checking the validity of partial linear models. Simulation studies demonstrate the performance of our proposed procedure and a real example is analyzed as illustrate its practical usage.

Statistical inference in the partial functional linear expectile regression model

Statistical inference in the partial functional linear expectile regression model

Subgroup analysis for functional partial linear regression model

AbstractIn a functional partial linear regression (FPLR) model, where the response variable is scalar while the explanatory variables involve both infinite‐dimensional functional predictors and finite‐dimensional scalar covariates, the relationships between the response and the explanatory variables are often assumed to be the same for all subjects. This article relaxes this assumption and considers a subgroup analysis for the FPLR model, which allows the intercepts to vary for different subgroups from a heterogeneous population. By projecting the functional predictors onto the corresponding eigenspace, the subgroup analysis based on the FPLR model can be simplified to a framework that is similar to the classical subgroup analysis problem. To automatically identify subgroups among observations and estimate the regression parameters of interest, we combine the functional principal component analysis with the concave pairwise penalized approach and develop an ADMM algorithm for functional subgroup analysis. We also establish the consistency of the proposed estimators under mild conditions. Simulation experiments demonstrate that the concave penalized subgroup approach could potentially achieve substantial gains over the ordinary FPLR model. The analysis of data from a creative achievement study is used to illustrate the practical performance of the subgroup analysis for the FPLR model.

Robust estimation for partial functional linear regression models based on FPCA and weighted composite quantile regression

Abstract In this paper, we consider a novel estimation for partial functional linear regression models. The functional principal component analysis method is employed to estimate the slope function and the functional predictive variable, respectively. An efficient estimation based on principal component basis function approximation is used for minimizing the proposed weighted composite quantile regression (WCQR) objective function. Since the proposed WCQR involves a vector of weights, we develop a computational strategy for data-driven selection of the optimal weights. Under some mild conditions, the theoretical properties of the proposed WCQR method are obtained. The simulation study and a real data analysis are provided to illustrate the numerical performance of the resulting estimators.

Bayesian Inference of a Non normal Multivariate Partial Linear Regression Model

This research includes the Bayesian estimation of the parameters of the multivariate partial linear regression model when the random error follows the matrix-variate generalized modified Bessel distribution and found the statistical test of the model represented by finding the Bayes factor criterion, the predictive distribution under assumption that the shape parameters are known. The prior distribution about the model parameters is represented by non-informative information, as well as the simulate on the generated data from the model by a suggested way based on different values ​​of the shape parameters, the kernel function used in the generation was a Gaussian kernel function, the bandwidth (Smoothing) parameter was according to the rule of thumb. It found that the posterior marginal probability distribution of the location matrix and the predictive probability distribution is a matrix-t distribution with different parameters, the posterior marginal probability distribution of the scale matrix is proper distribution but it does not belong to the conjugate family, Through the Bayes factor criterion, it was found that the sample that was used in the generation process was drawn from a population that does not belong to the generalized modified Bessel population.

Association of PAF and its Metabolic Enzymes with GGT and the Fatty Liver Index in Healthy Volunteers.

Platelet-activating-factor (PAF) is a lipid inflammatory mediator implicated in liver disease. Its main biosynthetic enzymes are cytidine diphosphate (CDP)-choline: 1-alkyl-2-acetyl-sn-glycerol-cholinephosphotransferase (PAF-CPT) and acetyl-coenzyme A: lyso-PAF-acetyltransferases (Lyso-PAF-AT). At the same time, PAF acetylhydrolase (PAF-AH) and lipoprotein-associated phospholipase A2 (Lp-PLA2 ) degrade PAF. To explore the relation of PAF metabolism with liver diseases and non-alcoholic fatty liver disease, as reflected by the fatty liver index (FLI). In 106 healthy volunteers, PAF concentration, the activity of its metabolic enzymes and gamma-glutamyl transferase (GGT) were measured in whole blood, leukocytes and serum, respectively and the FLI was calculated. Partial correlations and linear regression models were used. In males, serum GGT activity was positively correlated with abdominal fat (as assessed by analysis of a manually defined region of interest in dual-energy X-ray absorptiometry), triacylglycerols, bound-PAF and Lp-PLA2 , while the FLI was positively correlated with Lp-PLA2 activity. In females, serum GGT activity was negatively associated with high-density lipoprotein cholesterol (HDL-C) (age adjusted correlations, all p<0.05). Lp-PLA2 was a significant determinant of serum GGT activity in males after controlling for age, low- density lipoprotein cholesterol (LDL-C) and abdominal fat. The addition of bound-PAF in the model significantly increased the explained variance of serum GGT activity (total variance explanation 30%). Bound-PAF and Lp-PLA2 activity predicted serum GGT activity while Lp-PLA2 was also related to FLI. Our findings shed light on the metabolic pathways linking Lp-PLA2 to other atherosclerosis and/or oxidative markers, such as HDL-C, LDL-C, GGT and FLI and underline the important role of PAF.

Estimation on functional partially linear single index measurement error model

In this article, we investigate the functional partially linear single index model when measurement error exists in covariates. The main purpose of this article is to correct the biased estimators caused by additive error and construct the asymptotic properties of unknown parameters and function in model. Asymptotic distribution of the parametric component and the convergence rates of the nonparametric part are obtained under some regularity conditions. Compared with existing literatures in this field, such as functional partially linear and semi-functional partial linear regression model with measurement error, good performance in Tecator data analysis illustrates the advantages of the model and the significance of the proposed methodology. In this process, functional slice inverse regression is applied to estimate the functional single index parameter to improve computational efficiency. Furthermore, a simulation study is also carried out for demonstration.