scholarly journals Robust SiZer Approach for Varying Coefficient Models

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Hui-Guo Zhang ◽  
Chang-Lin Mei ◽  
He-Ling Wang
Keyword(s):  
Confidence Interval ◽  
Environmental Data ◽  
Varying Coefficient Models ◽  
Bootstrap Confidence Interval ◽  
Varying Coefficient Model ◽  
Absolute Deviation ◽  
Data Set ◽  
Zero Crossing ◽  
Varying Coefficient ◽  
Fitting Procedure

Varying coefficient models have widely been applied to many practical fields for exploring dynamic patterns of the regression relationships. In this study, we propose a robust scenario of SiZer (significant zero crossing of derivatives) inference approach based on the local least absolute deviation fitting procedure and the bootstrap confidence interval to uncover the statistically significant features of the coefficient functions in a varying coefficient model under different smoothing scales. The simulation study shows that the proposed SiZer approach is quite robust to outliers and performs well in finding the significant features of the coefficient functions. Furthermore, a real environmental data set is analyzed to demonstrate the application of the proposed approach.

Additive varying-coefficient model for nonlinear gene-environment interactions

2018 ◽  
Vol 17 (2) ◽  
Author(s):  
Cen Wu ◽  
Ping-Shou Zhong ◽  
Yuehua Cui
Keyword(s):  
Variable Selection ◽  
Complex Disease ◽  
Convergence Rates ◽  
Regularity Conditions ◽  
Varying Coefficient Model ◽  
Two Stage ◽  
Absolute Deviation ◽  
Gene Set ◽  
Varying Coefficient ◽  
Gene Environment

Abstract Gene-environment (G×E) interaction plays a pivotal role in understanding the genetic basis of complex disease. When environmental factors are measured continuously, one can assess the genetic sensitivity over different environmental conditions on a disease trait. Motivated by the increasing awareness of gene set based association analysis over single variant based approaches, we proposed an additive varying-coefficient model to jointly model variants in a genetic system. The model allows us to examine how variants in a gene set are moderated by an environment factor to affect a disease phenotype. We approached the problem from a variable selection perspective. In particular, we select variants with varying, constant and zero coefficients, which correspond to cases of G×E interaction, no G×E interaction and no genetic effect, respectively. The procedure was implemented through a two-stage iterative estimation algorithm via the smoothly clipped absolute deviation penalty function. Under certain regularity conditions, we established the consistency property in variable selection as well as effect separation of the two stage iterative estimators, and showed the optimal convergence rates of the estimates for varying effects. In addition, we showed that the estimate of non-zero constant coefficients enjoy the oracle property. The utility of our procedure was demonstrated through simulation studies and real data analysis.

scholarly journals Liu Estimator in Semiparametric Partially Linear Varying Coefficient Models

2019 ◽  
Vol 8 (6) ◽  
pp. 69
Author(s):  
Jing Li ◽  
Xueyan Li
Keyword(s):  
Varying Coefficient Models ◽  
Varying Coefficient Model ◽  
Liu Estimator ◽  
Biased Estimation ◽  
Varying Coefficient ◽  
Partially Linear ◽  
Constant Coefficients ◽  
Linear Restrictions

This paper considers biased estimation for partially linear varying coefficient model to overcome the problem of multicollinearity. By the Liu estimation approach, we construct a profile Liu estimator for the constant coefficients. Furthermore, a restricted profile-Liu estimator is proposed for the situation that some additional linear restrictions are available. The properties of the proposed estimators are investigated.

scholarly journals Selection of the Bandwidth Matrix in Spatial Varying Coefficient Models to Detect Anisotropic Regression Relationships

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2343
Author(s):  
Xijian Hu ◽  
Yaori Lu ◽  
Huiguo Zhang ◽  
Haijun Jiang ◽  
Qingdong Shi
Keyword(s):  
Spatial Data ◽  
Geographic Location ◽  
Two Dimensions ◽  
Varying Coefficient Models ◽  
Two Dimensional ◽  
Varying Coefficient Model ◽  
Varying Coefficient ◽  
Fitting Method ◽  
Adaptive Bandwidth ◽  
Selection Of

The commonly used Geographically Weighted Regression (GWR) fitting method for a spatial varying coefficient model is to select a bandwidth h for the geographic location (u, v), and assign the same weight to the two dimensions. However, spatial data usually present anisotropy. The introduction of a two-dimensional bandwidth matrix not only gives weight from two dimensions separately, but also increases the direction of kernel smoothness. The adaptive bandwidth matrix is more flexible. Therefore, in this paper, a two dimensional bandwidth matrix is introduced into the spatial varying coefficient model for parameter estimation. Through simulation experiments, the results obtained under the adaptive bandwidth matrix are compared with those obtained under the global bandwidth matrix, indicating the effectiveness of introducing the adaptive bandwidth matrix.

Local influence for elliptical partially varying-coefficient model

2017 ◽  
Vol 18 (2) ◽  
pp. 149-174
Author(s):  
Germán Ibacache-Pulgar ◽  
Sebastián Reyes
Keyword(s):  
Penalized Likelihood ◽  
Smoothing Splines ◽  
Local Influence ◽  
Likelihood Method ◽  
Varying Coefficient Models ◽  
Varying Coefficient Model ◽  
Real Dataset ◽  
Varying Coefficient ◽  
Maximum Penalized Likelihood ◽  
Heavy Tailed

In this article, we extend varying-coefficient models with normal errors to elliptical errors in order to permit distributions with heavier and lighter tails than the normal ones. This class of models includes all symmetric continuous distributions, such as Student-t, Pearson VII, power exponential and logistic, among others. Estimation is performed by maximum penalized likelihood method and by using smoothing splines. In order to study the sensitivity of the penalized estimates under some usual perturbation schemes in the model or data, the local influence curvatures are derived and some diagnostic graphics are proposed. A real dataset previously analysed by using varying-coefficient models with normal errors is reanalysed under varying-coefficient models with heavy-tailed errors.

scholarly journals Comparison of Bayesian Varying Coefficient Models for the Development of Nonergodic Ground-Motion Models

2021 ◽  
Author(s):  
Nicolas Kuehn
Keyword(s):  
Ground Motion ◽  
Gaussian Processes ◽  
Large Data ◽  
Local Source ◽  
Varying Coefficient Models ◽  
Data Set ◽  
Varying Coefficient ◽  
Motion Models ◽  
Ground Motion Model ◽  
Ground Motion Models

A nonrgodic ground-motion model explicitly takes systematic local source, path and site effects on the predicted ground-motion into account. With an increasing number of ground-motion records, it s possible to estimate these effects. Landwehr et al. (2016) proposed a varying coefficient model as a tool to estimate nonergodic ground-motion models, based on Gaussian processes. Gaussian processes are computationally expen- sive, so for large data sets, some approximations have to be made. Here, we compare different Bayesian implementations of varying coefficient models, using the probabilistic programming language Stan (Carpenter et al., 2017), and the integrated nested Laplace approximation (INLA) (Rue et al., 2009). The models are used to fit nonergodic models on the California subset of the NGA-West2 data set (Ancheta et al., 2014). We find that both implementations lead to very similar results, both in the estimated parameters and the predicted ground motions.

Simple Index to Assess the Calibration Quality of Safety Performance Functions Based on Multiple Goodness-of-Fit Metrics

2021 ◽  
pp. 036119812110088
Author(s):  
Raul E. Avelar ◽  
Karen Dixon ◽  
Boniphace Kutela ◽  
Sam Klump ◽  
Beth Wemple ◽  
...  
Keyword(s):  
Goodness Of Fit ◽  
Synthetic Data ◽  
Calibration Procedure ◽  
Safety Performance ◽  
Absolute Deviation ◽  
Data Set ◽  
Safety Database ◽  
Simple Index ◽  
Safety Performance Functions

The calibration of safety performance functions (SPFs) is a mechanism included in the Highway Safety Manual (HSM) to adjust SPFs in the HSM for use in intended jurisdictions. Critically, the quality of the calibration procedure must be assessed before using the calibrated SPFs. Multiple resources to aid practitioners in calibrating SPFs have been developed in the years following the publication of the HSM 1st edition. Similarly, the literature suggests multiple ways to assess the goodness-of-fit (GOF) of a calibrated SPF to a data set from a given jurisdiction. This paper uses the calibration results of multiple intersection SPFs to a large Mississippi safety database to examine the relations between multiple GOF metrics. The goal is to develop a sensible single index that leverages the joint information from multiple GOF metrics to assess overall quality of calibration. A factor analysis applied to the calibration results revealed three underlying factors explaining 76% of the variability in the data. From these results, the authors developed an index and performed a sensitivity analysis. The key metrics were found to be, in descending order: the deviation of the cumulative residual (CURE) plot from the 95% confidence area, the mean absolute deviation, the modified R-squared, and the value of the calibration factor. This paper also presents comparisons between the index and alternative scoring strategies, as well as an effort to verify the results using synthetic data. The developed index is recommended to comprehensively assess the quality of the calibrated intersection SPFs.

scholarly journals Handling Complex Missing Data Using Random Forest Approach for an Air Quality Monitoring Dataset: A Case Study of Kuwait Environmental Data (2012 to 2018)

2021 ◽  
Vol 18 (3) ◽  
pp. 1333
Author(s):  
Ahmad R. Alsaber ◽  
Jiazhu Pan ◽  
Adeeba Al-Hurban 
Keyword(s):  
Air Quality ◽  
Missing Data ◽  
Random Forest ◽  
Missing Values ◽  
Imputation Method ◽  
Environmental Data ◽  
Environmental Research ◽  
Quality Data ◽  
Data Set ◽  
Air Quality Data

In environmental research, missing data are often a challenge for statistical modeling. This paper addressed some advanced techniques to deal with missing values in a data set measuring air quality using a multiple imputation (MI) approach. MCAR, MAR, and NMAR missing data techniques are applied to the data set. Five missing data levels are considered: 5%, 10%, 20%, 30%, and 40%. The imputation method used in this paper is an iterative imputation method, missForest, which is related to the random forest approach. Air quality data sets were gathered from five monitoring stations in Kuwait, aggregated to a daily basis. Logarithm transformation was carried out for all pollutant data, in order to normalize their distributions and to minimize skewness. We found high levels of missing values for NO2 (18.4%), CO (18.5%), PM10 (57.4%), SO2 (19.0%), and O3 (18.2%) data. Climatological data (i.e., air temperature, relative humidity, wind direction, and wind speed) were used as control variables for better estimation. The results show that the MAR technique had the lowest RMSE and MAE. We conclude that MI using the missForest approach has a high level of accuracy in estimating missing values. MissForest had the lowest imputation error (RMSE and MAE) among the other imputation methods and, thus, can be considered to be appropriate for analyzing air quality data.

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