Parameters Of Regression Model Research Articles

Cholesterol, Triglyceride, and Glucose Levels Across Birth Cohorts in the US

Population mean levels of total cholesterol and fasting triglycerides have decreased substantially in the US in recent decades, but improvements in cardiometabolic health may have slowed among younger cohorts. Conversely, prevalence of diabetes (types 1 and 2) and obesity has increased, especially among adults younger than 65 years. It is unclear how trends in cholesterol, triglyceride, and glucose levels have changed across different birth cohorts and whether adverse trends in obesity are associated with these patterns. To quantify national trends in total cholesterol, fasting triglyceride, and fasting glucose levels among cohorts born between 1920 and 1999 and examine the potential association of these patterns with body mass index (BMI). This serial cross-sectional study used National Health and Nutrition Examination Survey (NHANES) data from the 1999-2000 to 2017-2020 cycles. Data were analyzed between November 1, 2023, and July 31, 2024. Participants included nonpregnant and noninstitutionalized US adults 18 years or older, born between 1920 and 1999, who had data collected from 1999 to 2020. Eight 10-year birth cohorts (from 1920 to 1999). Total cholesterol, fasting triglyceride, and fasting glucose levels and BMI. Quantile regression models reported average marginal effects to quantify mean change in cardiometabolic outcome measures per decade of birth years. Parametric regression models estimated the association of birth cohort with outcomes, assessing BMI as the mediator. Of 52 006 participants weighted to represent 264 664 915 US adults, weighted median age was 46 (IQR, 33-60) years and 50.6% were women. For the 50th percentile of measures, mean difference per 1-decade younger birth cohort was -7.1 (95% CI, -8.2 to -6.1) mg/dL for total cholesterol level, -13.1 (95% CI, -15.1 to -11.1) mg/dL for fasting triglyceride level, and 2.7 (95% CI, 2.3-3.1) mg/dL for fasting glucose level. BMI appeared to attenuate the associations between birth cohort and lipid levels and enhanced the associations between birth cohort and fasting glucose levels. However, up to 80% of the associations between birth cohorts and cardiometabolic outcomes were not mediated through BMI. In this cross-sectional study of 52 006 participants representing 264 664 915 US adults, population-level improvements in total cholesterol and triglyceride levels decelerated and adverse trends in glucose levels accelerated in more recent birth cohorts, which was partially mediated by concurrent increases in BMI. Public health initiatives that target antecedent health behaviors are needed to improve cardiometabolic health across generations.

A robust and efficient change point detection method for high-dimensional linear models

In the context of linear models, a key problem of interest is to estimate the regression coefficient. Nevertheless, in certain instances, the vector of unknown coefficient parameters in a linear regression model differs from one segment to another. In this paper, when the dimension of covariates is high, a new method is proposed to examine a linear model in which the regression coefficient of two subpopulations may be different. To achieve robustness and efficiency, we introduce modal linear regression as a means of estimating the unknown coefficient parameters. Furthermore, our proposed method is capable of selecting variables and checking change points. Under certain mild assumptions, the limiting behavior of our proposed method can be established. Additionally, an estimation algorithm based on kick-one-off and SCAD approach is developed to implement in practice. For illustration, simulation studies and a real data are considered to assess the performance of our proposed method.

Evaluating the Performances of Robust Logistic Regression Models in the Presence of Outliers

Logistic regression models are widely used in the field of medical and behavioral sciences. These models are used to describe the effect of explanatory variables on a binary response variable. The maximum likelihood estimator (MLE) is commonly used to estimate the parameters of logistic regression models due to its efficiency under a parametric model. However, evidence has shown that the MLE is highly sensitive to outlying observations which might affect the parameter estimates. Robust methods are put forward to rectify this problem. This paper investigated the robustness of GM-Mallows and GM-Schweppes as an alternative to the commonly used ordinary logistic regression model in the presence of outliers. The study used a Monte Carlos Simulation, by generating a logistic regression model with Five independent normally distributed covariates. 5% of outliers was contaminated to the data on sample sizes 50, 200 and 400 respectively. The results showed that the GM-Mallows estimator perform best across all metrics having the lowest AIC, BIC, MSE and MAE except for n=50. This suggests that the robust methods, especially GM-Mallows, provide more reliable estimates in the presence of outliers. The finding suggests that if there is presence of outliers’ GM-Mallows appears to be the top choice, where the GM-Schweppes offers a middle ground, providing some robustness with perhaps less extreme adjustments. The ordinary logistic regression might be preferred if simplicity and interpretability are prioritized, and there's confidence that outliers are not a significant issue in the data.

Association between education level and access to disease-modifying treatment in patients with multiple sclerosis in France.

We hypothesized that differences in access to disease-modifying treatments (DMTs) could explain the association between socioeconomic status and disability progression in multiple sclerosis (MS). This study aimed to analyze the association between education level and DMT use in France. All patients from OFSEP network with MS onset over 1996-2014 and aged ⩾ 25 years at onset were included. Three time-to-event outcomes were investigated using flexible parametric survival regression models: time from MS onset to first DMT (any) and to platform therapy, and time from platform therapy to switch to high-efficacy therapy. Overall, 7563 patients were included (mean follow-up 12.6 ± 5.9 years). The percentages of patients aged less than 40 years at MS onset and who initiated treatment before the age of 40 years were significantly higher in the groups with a higher education level. The time-to-event outcomes showed no major difference in DMT practices according to education level, except for women who had a significantly shorter time to DMT initiation in medium to very high education level groups versus low, at 5 years from MS clinical onset. Our results suggest that the association between education level and MS disability progression does not solely reflect different therapeutic practices, particularly in men.

Using a Stopping Rule to Optimize Cost-Quality Tradeoffs in a Large, Mixed-Mode Survey: A Simulation Study

Rising nonresponse and the increasing costs of conducting surveys are creating pressure on survey organizations to efficiently allocate resources. The challenge is to produce the highest quality data possible within a fixed budget. We use a stopping rule designed to minimize a function of cost and errors. The rule is based on the product of predicted costs and the predicted mean squared error of a survey estimate. We simulate the impact of implementing the stopping rule on the 2019 US Survey of Doctorate Recipients (SDR), which is a longitudinal survey conducted every two years in the US using web, mail, and CATI. We vary the types of models used to generate the input predictions (parametric regression vs. nonparametric tree models) and the timing of the implementation of the rule. We found that the modeling approach made less difference, while the timing of the implementation of the stopping rule made a large difference in outcomes. The rule is multivariate and optimizes outcomes for two variables. It performed better for one variable, leading to reduced costs and only small increases in errors. The other variable had larger error increases.

A new parametric quantile regression model based on an Owen distribution

Quantile regression is a versatile statistical tool for modeling conditional quantiles, offering a comprehensive view of the relationship between explanatory and response variables. This technique is widely used in fields like economics, finance, environmental science, and psychology. This paper introduces a new quantile regression model based on the Owen distribution, which provides flexibility in capturing quantile-specific relationships. The model parameters are estimated using maximum likelihood estimation, with a detailed discussion on the estimation process. Diagnostic measures, including a pseudo- R 2 statistic, quantile residuals, and generalized Cook’s distance, are proposed to assess model adequacy and identify influential data points. Monte Carlo simulations are employed to evaluate the estimators' performance. The model’s effectiveness is illustrated through an application to Chilean household income data, highlighting its advantages over conventional quantile regression models. Implemented in the R programming language, this model is accessible for practical use, offering a valuable addition to the quantile regression field and suggesting promising directions for further research and application across disciplines.

A Comparison between Methods for Estimating the Restricted Gamma Ridge Regression Model Using the Simulation

In this paper, we discuss estimating the parameters of the restricted gamma ridge regression model by combining gamma ridge regression with restricted maximum likelihood. The characteristics of the new estimator and its superiority over the restricted gamma ridge regression estimator and restricted maximum likelihood will be identified, using several formulas for the shrinkage factor k, and it will also be Using the Monte Carlo simulation method to generate data that suffers from the problem of multicollinearity with different sizes (n=25,50,100,250) in light of other influential factors (degree of correlation, number of explanatory variables), and subjecting the parameters to linear restrictions, to get rid of the problem of multicollinearity in light of the subjection of the parameters to the model has linear constraints and the model parameters will be estimated using four estimation methods that rely on the mean square error (MSE) as a standard for comparison between the estimation methods, Through the results of the simulation experiment it was shown that the compound estimator method is the best way to estimate the parameters of the finite gamma regression model . Paper type : Research paper

Estimating time series semiparametric regression model using local polynomial estimator for predicting inflation rate in Indonesia

A model built from a parametric regression model and a nonparametric regression model is called a semiparametric regression (SR) model. The main problem in the SR model is the estimation of the regression function. In this study, we develop the SR model for time series data that is called Time Series Semiparametric Regression (TSSR) model, and discuss estimation of the TSSR model by using local polynomial. Also, we apply it to data of inflation rate (IR) in Indonesia where IR is as response variable, and both IR and money supply in the previous periods are as predictor variables. Next, we compare the results of estimating the IR using the TSSR with the classical method, namely the ARIMA. Also, the TSSR has high accurate criterion for predicting the IR in Indonesia. The results of this study are useful for analyzing Indonesia’s economic growth rate, which is one of the Sustainable Development Goals (SDGs)

Linear Programming-Based Sparse Kernel Regression with L1-Norm Minimization for Nonlinear System Modeling

This paper integrates L1-norm structural risk minimization with L1-norm approximation error to develop a new optimization framework for solving the parameters of sparse kernel regression models, addressing the challenges posed by complex model structures, over-fitting, and limited modeling accuracy in traditional nonlinear system modeling. The first L1-norm regulates the complexity of the model structure to maintain its sparsity, while another L1-norm is essential for ensuring modeling accuracy. In the optimization of support vector regression (SVR), the L2-norm structural risk is converted to an L1-norm framework through the condition of non-negative Lagrange multipliers. Furthermore, L1-norm optimization for modeling accuracy is attained by minimizing the maximum approximation error. The integrated L1-norm of structural risk and approximation errors creates a new, simplified optimization problem that is solved using linear programming (LP) instead of the more complex quadratic programming (QP). The proposed sparse kernel regression model has the following notable features: (1) it is solved through relatively simple LP; (2) it effectively balances the trade-off between model complexity and modeling accuracy; and (3) the solution is globally optimal rather than just locally optimal. In our three experiments, the sparsity metrics of SVs% were 2.67%, 1.40%, and 0.8%, with test RMSE values of 0.0667, 0.0701, 0.0614 (sinusoidal signal), and 0.0431 (step signal), respectively. This demonstrates the balance between sparsity and modeling accuracy.

Weighted fast-trimmed likelihood estimator for mixture regression models

The fast-trimmed likelihood estimate is a robust method to estimate the parameters of a mixture regression model. However, this method is vulnerable to the presence of bad leverage points, which are outliers in the direction of independent variables. To address this issue, we propose the weighted fast-trimmed likelihood estimate to mitigate the impact of leverage points. The proposed method applies the weights of the minimum covariance determinant to the rows suspected of containing leverage points. Notably, both real data and simulation studies were considered to determine the efficiency of the proposed method compared to the previous methods. The results reveal that the weighted fast-trimmed estimate method is more robust and reliable than the fast-trimmed likelihood estimate and the expectation–maximization (EM) methods, particularly in cases with small sample sizes.

The Estimating Parameter and Number of Knots for Nonparametric Regression Methods in Modelling Time Series Data

This research aims to explore and compare several nonparametric regression techniques, including smoothing splines, natural cubic splines, B-splines, and penalized spline methods. The focus is on estimating parameters and determining the optimal number of knots to forecast cyclic and nonlinear patterns, applying these methods to simulated and real-world datasets, such as Thailand’s coal import data. Cross-validation techniques are used to control and specify the number of knots, ensuring the curve fits the data points accurately. The study applies nonparametric regression to forecast time series data with cyclic patterns and nonlinear forms in the dependent variable, treating the independent variable as sequential data. Simulated data featuring cyclical patterns resembling economic cycles and nonlinear data with complex equations to capture variable interactions are used for experimentation. These simulations include variations in standard deviations and sample sizes. The evaluation criterion for the simulated data is the minimum average mean square error (MSE), which indicates the most efficient parameter estimation. For the real data, monthly coal import data from Thailand is used to estimate the parameters of the nonparametric regression model, with the MSE as the evaluation metric. The performance of these techniques is also assessed in forecasting future values, where the mean absolute percentage error (MAPE) is calculated. Among the methods, the natural cubic spline consistently yields the lowest average mean square error across all standard deviations and sample sizes in the simulated data. While the natural cubic spline excels in parameter estimation, B-splines show strong performance in forecasting future values.

Combined application of methods of maximum consistency and anti-robust parameter estimation in the construction of regression models

Objective. The purpose of the study is to solve the problem of calculating the parameters of a linear regression model based on the joint application of anti-robust estimation methods and maximum consistency between the real and calculated values of the dependent variable in continuous form. Method. The unknown parameters of the model are calculated by reducing the original problem to a linear programming problem. Its solution should not cause computational difficulties due to the significant number of developed effective software tools. Result. The generated linear programming problem has a dimension acceptable for real situations. Conclusion. The results of solving a numerical example indicate the effectiveness of the method proposed in the work for calculating the parameters of a linear regression model based on the joint application of anti-robust estimation methods and maximum consistency. The final choice of parameter values remains with the model developer.

Evaluation of the Performance of Kernel Non-parametric Regression and Ordinary Least Squares Regression

Researchers need to understand the differences between parametric and nonparametric regression models and how they work with available information about the relationship between response and explanatory variables and the distribution of random errors. This paper proposes a new nonparametric regression function for the kernel and employs it with the Nadaraya-Watson kernel estimator method and the Gaussian kernel function. The proposed kernel function (AMS) is then compared to the Gaussian kernel and the traditional parametric method, the ordinary least squares method (OLS). The objective of this study is to examine the effectiveness of nonparametric regression and identify the best-performing model when employing the Nadaraya-Watson kernel estimator method with the proposed kernel function (AMS), the Gaussian kernel, and the ordinary least squares (OLS) method. Additionally, it determines which method yields the most accurate results when analyzing nonparametric regression models and provides valuable insights for practitioners looking to apply these techniques in real-world scenarios. However, criteria such as generalized cross-validation (GCV), mean square error (MSE), and coefficient determination are used to select the most efficient estimated model. Simulated data was used to evaluate the performance and efficiency of estimators using different sample sizes. The results favorable the simulation illustrate that the Nadaraya-Watson kernel estimator using the proposed kernel function (AMS) exhibited favorable and superior performance compared to other methods. The coefficients of determination indicate that the highest values attained were 98%, 99%, and 99%. The proposed function (AMS) yielded the lowest MSE and GCV values across all samples. Therefore, this suggests that the model can generate precise predictions and enhance the performance of the focused data.

Rank-transformed subsampling: inference for multiple data splitting and exchangeable p-values

Abstract Many testing problems are readily amenable to randomized tests, such as those employing data splitting. However, despite their usefulness in principle, randomized tests have obvious drawbacks. Firstly, two analyses of the same dataset may lead to different results. Secondly, the test typically loses power because it does not fully utilize the entire sample. As a remedy to these drawbacks, we study how to combine the test statistics or p-values resulting from multiple random realizations, such as through random data splits. We develop rank-transformed subsampling as a general method for delivering large-sample inference about the combined statistic or p-value under mild assumptions. We apply our methodology to a wide range of problems, including testing unimodality in high-dimensional data, testing goodness-of-fit of parametric quantile regression models, testing no direct effect in a sequentially randomized trial and calibrating cross-fit double machine learning confidence intervals. In contrast to existing p-value aggregation schemes that can be highly conservative, our method enjoys Type I error control that asymptotically approaches the nominal level. Moreover, compared to using the ordinary subsampling, we show that our rank transform can remove the first-order bias in approximating the null under alternatives and greatly improve power.

A Hard Re-descending Hybrid Robust Regression Estimation Technique Using Direct Weights

A hybrid approach of M and R estimators using an iterative procedure is proposed to detect outliers and estimation of regression parameters for linear models. We consider the deviation of each residual from its median to measure the likelihood of the corresponding data point to be an outlier. Also, the proposed work develops a reliable algorithm to estimate parameters of regression model that is unaffected by outliers. The significance of the proposed work is a novel hybrid approach of weighing the observations based on the order of residuals. Our proposal is illustrated using Monte Carlo simulation and analysed for few benchmark data sets.

Addressing Autocorrelation, Multicollinearity, and Heavy-Tail Errors in the Linear Regression Model

The most popular estimator for estimating parameters of linear regression models is the Ordinary Least Squares (OLS) Estimator. The OLS is considered the best linear unbiased estimator when certain assumptions are not violated. However, when autocorrelation, multicollinearity, and heavy-tail error are jointly present in the dataset, the OLS estimator is inefficient and imprecise. In this paper, we developed an estimator of linear regression model parameters that jointly handle multicollinearity, autocorrelation, and heavy tail errors. The new estimator, LADHLKL, was derived by combining the Hildreth-Lu (HL), the Kibria Lukman (KL), and the Least Absolute Deviation (LAD) estimators. The LADHLKL poses both the characteristics of the LAD, HL, and KL estimators which makes it resistant to both problems. We examined the properties of the proposed estimator and compared its performance with other existing estimators in terms of mean square error. An application to real-life data and simulation study revealed that the proposed estimator dominates other estimators in all the considered conditions in terms of mean square error.

Monte Carlo inference for semiparametric Bayesian regression

Data transformations are essential for broad applicability of parametric regression models. However, for Bayesian analysis, joint inference of the transformation and model parameters typically involves restrictive parametric transformations or nonparametric representations that are computationally inefficient and cumbersome for implementation and theoretical analysis, which limits their usability in practice. This paper introduces a simple, general, and efficient strategy for joint posterior inference of an unknown transformation and all regression model parameters. The proposed approach directly targets the posterior distribution of the transformation by linking it with the marginal distributions of the independent and dependent variables, and then deploys a Bayesian nonparametric model via the Bayesian bootstrap. Crucially, this approach delivers (1) joint posterior consistency under general conditions, including multiple model misspecifications, and (2) efficient Monte Carlo (not Markov chain Monte Carlo) inference for the transformation and all parameters for important special cases. These tools apply across a variety of data domains, including real-valued, positive, and compactly-supported data. Simulation studies and an empirical application demonstrate the effectiveness and efficiency of this strategy for semiparametric Bayesian analysis with linear models, quantile regression, and Gaussian processes. The R package SeBR is available on CRAN.

Regional citrate anticoagulation versus LMWH anticoagulation for CRRT in liver failure patients without increased bleeding risk.

The optimal anticoagulation regimen for continuous renal replacement therapy (CRRT) in liver failure (LF) patients without increased bleeding risk remains controversial. Therefore, we conducted a monocentric retrospective study to evaluate the efficacy and safety of the regional citrate anticoagulation (RCA) versus low molecular weight heparin (LMWH) anticoagulation for CRRT in LF without increased bleeding risk. According to the anticoagulation strategy for CRRT, patients were divided into the RCA and LMWH-anticoagulation groups. The evaluated endpoints were patient survival, filter lifespan, bleeding, citrate accumulation, and totCa/ionCa ratio. Totally 167 and 164 filters were used in the RCA and LMWH group, respectively. The median filter lifespan was significantly longer in the RCA group (34 h (IQR = 24-54) versus 24 h (IQR = 18-45.5) [95%CI, 24.5-33]; p < 0.001). The 4-week mortality rate was significantly higher in the LMWH-anticoagulation group (71 (57.72%) vs 53 (40.46%); p = 0.006). After adjusted the important parameters in the multivariate COX regression model, the mortality risk was significantly reduced in the RCA group (HR = 0.668 [95%CI, 0.468-0.955]; p = 0.027). In the LMWH group, 30 bleeding episodes (24,19%) were observed, whereas only 7 (5.34%) occurred in the RCA group (p < 0.001). Two patients (1.5%) in the RCA group occurred citrate accumulation. In LF patients without increased bleeding risk who underwent CRRT, RCA significantly extended the filter lifespan and improved patient survival rate. There was no significant difference in the rate of adverse events between the two groups.

Unified specification tests in partially linear quantile regression models

We propose specification tests for parametric quantile regression models versus semiparametric alternatives over a continuum of quantile levels. The test statistics are constructed as continuous functionals of a quantile-marked residual process. We show that using an orthogonal projection on the tangent space of nuisance parameters at each quantile index delivers unified asymptotic properties for tests based on different estimators. Consistency of the tests and asymptotic power under a sequence of local alternatives converging to the null at a parametric rate are also discussed. We propose a simple multiplier bootstrap procedure to carry out the tests, whose nominal levels are well approximated in our simulation study for modest sample sizes.

PointPCA: point cloud objective quality assessment using PCA-based descriptors

Point clouds denote a prominent solution for the representation of 3D photo-realistic content in immersive applications. Similarly to other imaging modalities, quality predictions for point cloud contents are vital for a wide range of applications, enabling trade-off optimizations between data quality and data size in every processing step from acquisition to rendering. In this work, we focus on use cases that consider human end-users consuming point cloud contents and, hence, we concentrate on visual quality metrics. In particular, we propose a set of perceptually relevant descriptors based on principal component analysis (PCA) decomposition, which is applied to both geometry and texture data for full-reference point cloud quality assessment. Statistical features are derived from these descriptors to characterize local shape and appearance properties for both a reference and a distorted point cloud. The extracted statistical features are subsequently compared to provide corresponding predictions of visual quality for the distorted point cloud. As part of our method, a learning-based approach is proposed to fuse these individual predictors to a unified perceptual score. We validate the accuracy of the individual predictors, as well as the unified quality scores obtained after regression against subjectively annotated datasets, showing that our metric outperforms state-of-the-art solutions. Insights regarding design decisions are provided through exploratory studies, evaluating the performance of our metric under different parameter configurations, attribute domains, color spaces, and regression models. A software implementation of the proposed metric is made available at the following link: https://github.com/cwi-dis/pointpca.