Varying Coefficient Models Research Articles

Local signal detection on irregular domains with generalized varying coefficient models

In spatial analysis, it is essential to understand and quantify spatial or temporal heterogeneity. This paper focuses on the generalized spatially varying coefficient model (GSVCM), a powerful framework to accommodate spatial heterogeneity by allowing regression coefficients to vary in a given spatial domain. We propose a penalized bivariate spline method for detecting local signals in GSVCM. The key idea is to use bivariate splines defined on triangulation to approximate nonparametric varying coefficient functions and impose a local penalty on L 2 norms of spline coefficients for each triangle to identify null regions of zero effects. Moreover, we develop model confidence regions as the inference tool to quantify the uncertainty of the estimated null regions. Our method partitions the region of interest using triangulation and efficiently approximates irregular domains. In addition, we propose an efficient algorithm to obtain the proposed estimator using the local quadratic approximation. We also establish the consistency of estimated nonparametric coefficient functions and the estimated null regions. The numerical performance of the proposed method is evaluated in both simulation cases and real data analysis.

In-profile monitoring on univariate profile with application to industrial busbar

In the current research on profile monitoring, most studies treat each profile as a whole to design monitoring statistic. These monitoring methods can only detect whether there exist some anomalies in the process after a complete profile sample is collected. This leads to a lag between the occurrence of a shift and the signaling of an alarm, which hinders engineers from promptly intervening in the out-of-control process. To address this limitation, an in-profile monitoring scheme is proposed in this paper, in which the dynamic influence mechanism of covariates on the response variable is considered. In phase-I, a random varying-coefficient model is utilized to model the dynamic time-varying relationship between covariates and the response variable, and the model parameters are estimated. In Phase-II, for the sequential observations generated by the monitored process, a new monitoring scheme based on the generalized likelihood ratio test is designed. This scheme can adapt to within-profile autocorrelation and arbitrary design points. To enhance online computational efficiency, recursive formulas for calculating the charting statistic are developed. Numerical studies demonstrate that the proposed scheme exhibits satisfactory and robust monitoring performance. Finally, an application to industrial busbar running process monitoring is given to demonstrate the implementation of the scheme.

Does the Kyoto Protocol have a structural impact on the environmental Kuznets curve? An application of the varying coefficient model

Does the Kyoto Protocol have a structural impact on the environmental Kuznets curve? An application of the varying coefficient model

Spatial Variability in Relationships between Early Childhood Lead Exposure and Standardized Test Scores in Fourth Grade North Carolina Public School Students (2013-2016).

Exposure to lead during childhood is detrimental to children's health. The extent to which the association between lead exposure and elementary school academic outcomes varies across geography is not known. Estimate associations between blood lead levels (BLLs) and fourth grade standardized test scores in reading and mathematics in North Carolina using models that allow associations between BLL and test scores to vary spatially across communities. We link geocoded, individual-level, standardized test score data for North Carolina public school students in fourth grade (2013-2016) with detailed birth records and blood lead testing data retrieved from the North Carolina childhood blood lead state registry on samples typically collected at 1-6 y of age. BLLs were categorized as: (reference), , and . We then fit spatially varying coefficient models that incorporate information sharing (smoothness), across neighboring communities via a Gaussian Markov random field to provide a global estimate of the association between BLL and test scores, as well as census tract-specific estimates (i.e., spatial coefficients). Models adjusted for maternal- and child-level covariates and were fit separately for reading and math. The average BLL across the 91,706 individuals in the analysis dataset was . Individuals were distributed across 2,002 (out of 2,195) census tracts in North Carolina. In models adjusting for child sex, birth weight percentile for gestational age, and Medicaid participation as well as maternal race/ethnicity, educational attainment, marital status, and tobacco use, BLLs of , and were associated with overall lower reading test scores of [95% confidence interval (CI): , ], (, ), and (, ), respectively. For BLLs of , , and , spatial coefficients-that is, tract-specific adjustments in reading test score relative to the "global" coefficient-ranged from to 2.52, to 3.90, to 7.85, and to 4.33, respectively. Results for mathematics were similar to those for reading. The association between lead exposure and reading and mathematics test scores exhibits considerable heterogeneity across North Carolina communities. These results emphasize the need for prevention and mitigation efforts with respect to lead exposures everywhere, with special attention to locations where the cognitive impact is elevated. https://doi.org/10.1289/EHP13898.

Analysis of multi-wave solitary solutions of (2+1)-dimensional coupled system of Boiti–Leon–Pempinelli

This work examines the (2+1)-dimensional Boiti–Leon–Pempinelli model, which finds its use in hydrodynamics. This model explains how water waves vary over time in hydrodynamics. We provide new explicit solutions to the generalized (2+1)-dimensional Boiti–Leon–Pempinelli equation by applying the Sardar sub-equation technique. This method is shown to be a reliable and practical tool for solving nonlinear wave equations. Furthermore, different types of solitary wave solutions are constructed: w-shaped, breather waved, chirped, dark, bright, kink, unique, periodic, and more. The results obtained with the variable coefficient Boiti–Leon–Pempinelli equation are stable and different from previous methods. As compared to their constant-coefficient counterparts, the variable-coefficient models are more general here. In the current work, the problem is solved using the Sardar Sub-problem Technique to produce distinct soliton solutions with parameters. Plotting these graphs of the solutions will help you better comprehend the model. The outcomes demonstrate how well the method works to solve nonlinear partial differential equations, which are common in mathematical physics.With the help of this method, we may examine a variety of solutions from significant physical perspectives.

The “effect modifier” of US interest rate in the economic policy uncertainties and economic conditions of fifty (50) US states: A semi-parametric smooth varying-coefficient approach

In this study, we investigate the relationship between economic policy uncertainty [EPU] and the economic conditions of the 50 US states, as well as the role of interest rates. We use a semi-parametric smooth varying coefficient model (SVCM) to examine how interest rate affects the nexus of EPU-economic conditions. Our findings suggest a negative relationship between EPU and economic conditions and that when the interest rate is around 3 %, the negative impact of EPU on economic conditions decreases in more than 60 % of US states. Furthermore, we find that the rate of change in the interest rate between 2 % and 3 % helps mitigate the negative effects of EPU and improves economic conditions in several states. Our results remain consistent across different interest rate periods, regardless of whether the uncertainty is of internal or external origin.

A Bayesian spatial–temporal varying coefficients model for estimating excess deaths associated with respiratory infections

Abstract Disease surveillance data are used for monitoring and understanding disease burden, which provides valuable information in allocating health programme resources. Statistical methods play an important role in estimating disease burden since disease surveillance systems are prone to undercounting. This paper is motivated by the challenge of estimating mortality associated with respiratory infections (e.g. influenza and COVID-19) that are not ascertained from death certificates. We propose a Bayesian spatial–temporal model incorporating measures of infection activity to estimate excess deaths. Particularly, the inclusion of time-varying coefficients allows us to better characterize associations between infection activity and mortality counts time series. Software to implement this method is available in the R package NBRegAD. Applying our modelling framework to weekly state-wide COVID-19 data in the US from 8 March 2020 to 3 July 2022, we identified temporal and spatial differences in excess deaths between different age groups. We estimated the total number of COVID-19 deaths in the US to be 1,168,481 (95% CI: 1,148,953 1,187,187) compared to the 1,022,147 from using only death certificate information. The analysis also suggests that the most severe undercounting was in the 18–49 years age group with an estimated underascertainment rate of 0.21 (95% CI: 0.16, 0.25).

M-estimation for varying coefficient models with a functional response in a reproducing kernel Hilbert space

M-estimation for varying coefficient models with a functional response in a reproducing kernel Hilbert space

Local Walsh-average regression for spatial autoregression single index varying coefficient models

. In real life, a large number of variables are spatially correlated in adjacent regions in various fields, such as finance, sociology, ecology, and geographic information systems. And the factors affecting these variables often have both linear and non linear relationships with them, how to accurately depict the relationship between them with a spatial regression model is a significant work. In order to further accurately describe the relationship between explanatory variables and response variables, we establish a spatial autoregressive single index varying coefficient model. The least squares method is the main method of model estimation but it is not robust enough when the parameter distribution is not normal. We present a new estimation method based on local Walsh average-regression. Under some general assumptions, we establish the asymptotic properties of the parametric and non parametric estimators. We further verify the accuracy and efficiency of the estimators under the condition of non normal error distribution through numerical experiments. In addition, the robustness of the proposed method is verified when the spatial weight matrix is interfered and when the bandwidth is changed within a certain range. Finally, we demonstrate the accuracy of forecasting by our proposed model compared with traditional spatial autoregressive model through real data analysis.

Speeding up estimation of spatially varying coefficients models

Speeding up estimation of spatially varying coefficients models

Digital economy and the urban–rural income gap: Impact, mechanisms, and spatial heterogeneity

This study examines how digital economy development in China impacts the urban–rural income gap. We construct a digital economy development index using panel data from 30 provinces and cities in China from 2013 to 2021. By combining a spatially varying coefficient model with a chain–mediated effect model, we quantify the impact of digital economy on the urban–rural income gap and examine its spatial heterogeneity. The results show that the digital economy influences the urban–rural income gap through four different pathways, each of which exhibits significant spatial variation. As these paths offset each other, the digital economy development in Beijing, Inner Mongolia, Shanxi, Henan, Hubei, Jiangxi, Jiangsu, Guangdong, and other provinces has widened the urban–rural income gap, resulting in a digital divide effect. However, in most areas of China's northeast, east coast, and western regions, the digital economy development has narrowed the income gap, resulting in a digital dividend effect. This study investigates the relevant debates among scholars and provides valuable insights and foundations for strategic decision making to reduce the urban–rural income gap in various regions.

Stage-dependent differential impact of network communication on cognitive function across the continuum of cognitive decline in Parkinson's disease

ObjectiveOur objective was to explore the patterns of resting-state network (RSN) connectivity alterations and investigate how the influences of individual-level network connections on cognition varied across clinical stages without assuming a constant relationship. Methods108 PD patients with continuum of cognitive decline (PD-NC = 46, PD-MCI = 43, PDD = 19) and 34 healthy controls (HCs) underwent resting-state functional MRI and neuropsychological tests. Independent component analysis (ICA) and graph theory analyses (GTA) were employed to explore RSN connection changes. Additionally, stage-dependent differential impact of network communication on cognitive performance were examined using sparse varying coefficient modeling. ResultsCompared to HCs, the dorsal attention network (DAN) and dorsal sensorimotor network (dSMN) were central networks with decreased connections in PD-NC and PD-MCI stage, while the lateral visual network (LVN) emerged as a central network in patients with dementia. Additionally, connectivity of the cerebellum network (CBN) increased in the PD-NC and PD-MCI stages. GTA demonstrated decreased nodal metrics for DAN and dSMN, coupled with an increase for CBN. Moreover, the degree centrality (DC) values of DAN and dSMN exhibited a stage-dependent differential impact on cognitive performance across the continuum of cognitive decline. ConclusionOur findings suggest that across the progression of cognitive impairment, the LVN gradually transitions into a core node with reduced connectivity, while the enhancement of connections in CBN diminishes. Furthermore, the non-linear relationship between the DC values of RSNs and cognitive decline indicates the potential for tailored interventions targeting specific stages.

Distributed Heterogeneity Learning for Generalized Partially Linear Models with Spatially Varying Coefficients

Spatial heterogeneity is of great importance in social, economic, and environmental science studies. The spatially varying coefficient model is a popular and effective spatial regression technique to address spatial heterogeneity. However, accounting for heterogeneity comes at the cost of reducing model parsimony. To balance flexibility and parsimony, this article develops a class of generalized partially linear spatially varying coefficient models which allow the inclusion of both constant and spatially varying effects of covariates. Another significant challenge in many applications comes from the enormous size of the spatial datasets collected from modern technologies. To tackle this challenge, we design a novel distributed heterogeneity learning (DHL) method based on bivariate spline smoothing over a triangulation of the domain. The proposed DHL algorithm has a simple, scalable, and communication-efficient implementation scheme that can almost achieve linear speedup. In addition, this article provides rigorous theoretical support for the DHL framework. We prove that the DHL constant coefficient estimators are asymptotic normal and the DHL spline estimators reach the same convergence rate as the global spline estimators obtained using the entire dataset. The proposed DHL method is evaluated through extensive simulation studies and analyses of U.S. loan application data. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

On solvability and optimal controls for impulsive stochastic integrodifferential varying-coefficient model

This article concentrates in analyzing optimal controls for stochastic integrodifferential equation (SIDE) in Hilbert space. Necessary parameters are imposed to demonstrate the system that follows a unique variation of parameter formula using Leray Schauder Alternative. Subsequently, the existence of optimal control is investigated for the considered Lagrange control problem. The theoretical example with the mechanical example of ethanol fuelled engine are discussed to validate the results obtained.

Generalized Geographically Weighted Regression Model within a Modularized Bayesian Framework.

Geographically weighted regression (GWR) models handle geographical dependence through a spatially varying coefficient model and have been widely used in applied science, but its general Bayesian extension is unclear because it involves a weighted log-likelihood which does not imply a probability distribution on data. We present a Bayesian GWR model and show that its essence is dealing with partial misspecification of the model. Current modularized Bayesian inference models accommodate partial misspecification from a single component of the model. We extend these models to handle partial misspecification in more than one component of the model, as required for our Bayesian GWR model. Information from the various spatial locations is manipulated via a geographically weighted kernel and the optimal manipulation is chosen according to a Kullback-Leibler (KL) divergence. We justify the model via an information risk minimization approach and show the consistency of the proposed estimator in terms of a geographically weighted KL divergence.

Identifying potential provenances for climate-change adaptation using spatially variable coefficient models

BackgroundSelection of climate-change adapted ecotypes of commercially valuable species to date relies on DNA-assisted screening followed by growth trials. For trees, such trials can take decades, hence any approach that supports focussing on a likely set of candidates may save time and money. We use a non-stationary statistical analysis with spatially varying coefficients to identify ecotypes that indicate first regions of similarly adapted varieties of Douglas-fir (Pseudotsuga menziesii (Mirbel) Franco) in North America. For over 70,000 plot-level presence-absences, spatial differences in the survival response to climatic conditions are identified.ResultsThe spatially-variable coefficient model fits the data substantially better than a stationary, i.e. constant-effect analysis (as measured by AIC to account for differences in model complexity). Also, clustering the model terms identifies several potential ecotypes that could not be derived from clustering climatic conditions itself. Comparing these six identified ecotypes to known genetically diverging regions shows some congruence, as well as some mismatches. However, comparing ecotypes among each other, we find clear differences in their climate niches.ConclusionWhile our approach is data-demanding and computationally expensive, with the increasing availability of data on species distributions this may be a useful first screening step during the search for climate-change adapted varieties. With our unsupervised learning approach being explorative, finely resolved genotypic data would be helpful to improve its quantitative validation.

GeoShapley: A Game Theory Approach to Measuring Spatial Effects in Machine Learning Models

This article introduces GeoShapley, a game theory approach to measuring spatial effects in machine learning models. GeoShapley extends the Nobel Prize–winning Shapley value framework in game theory by conceptualizing location as a player in a model prediction game, which enables the quantification of the importance of location and the synergies between location and other features in a model. GeoShapley is a model-agnostic approach and can be applied to statistical or black-box machine learning models in various structures. The interpretation of GeoShapley is directly linked with spatially varying coefficient models for explaining spatial effects and additive models for explaining non-spatial effects. Using simulated data, GeoShapley values are validated against known data-generating processes and are used for cross-comparison of seven statistical and machine learning models. An empirical example of house price modeling is used to illustrate GeoShapley’s utility and interpretation with real-world data. The method is available as an open source Python package named geoshapley.

A varying-coefficient model for the analysis of methylation sequencing data

DNA methylation is an important epigenetic modification involved in gene regulation. Advances in the next generation sequencing technology have enabled the retrieval of DNA methylation information at single-base-resolution. However, due to the sequencing process and the limited amount of isolated DNA, DNA-methylation-data are often noisy and sparse, which complicates the identification of differentially methylated regions (DMRs), especially when few replicates are available. We present a varying-coefficient model for detecting DMRs by using single-base-resolved methylation information. The model simultaneously smooths the methylation profiles and allows detection of DMRs, while accounting for additional covariates. The proposed model takes into account possible overdispersion by using a beta-binomial distribution. The overdispersion itself can be modeled as a function of the genomic region and explanatory variables. We illustrate the properties of the proposed model by applying it to two real-life case studies.

Enhancing long-term survival prediction with two short-term events: Landmarking with a flexible varying coefficient model.

Patients with cardiovascular diseases who experience disease-related short-term events, such as hospitalizations, often exhibit diverse long-term survival outcomes compared to others. In this study, we aim to improve the prediction of long-term survival probability by incorporating two short-term events using a flexible varying coefficient landmark model. Our objective is to predict the long-term survival among patients who survived up to a pre-specified landmark time since the initial admission. Inverse probability weighting estimation equations are formed based on the information of the short-term outcomes before the landmark time. The kernel smoothing method with the use of cross-validation for bandwidth selection is employed to estimate the time-varying coefficients. The predictive performance of the proposed model is evaluated and compared using predictive measures: area under the receiver operating characteristic curve and Brier score. Simulation studies confirm that parameters under the landmark models can be estimated accurately and the predictive performance of the proposed method consistently outperforms existing methods that either do not incorporate or only partially incorporate information from two short-term events. We demonstrate the practical application of our model using a community-based cohort from the Atherosclerosis Risk in Communities (ARIC) study.

A sparse empirical Bayes approach to high‐dimensional Gaussian process‐based varying coefficient models

AbstractDespite the increasing importance of high‐dimensional varying coefficient models, the study of their Bayesian versions is still in its infancy. This paper contributes to the literature by developing a sparse empirical Bayes formulation that addresses the problem of high‐dimensional model selection in the framework of Bayesian varying coefficient modelling under Gaussian process (GP) priors. To break the computational bottleneck of GP‐based varying coefficient modelling, we introduce the low‐cost computation strategy that incorporates linear algebra techniques and the Laplace approximation into the evaluation of the high‐dimensional posterior model distribution. A simulation study is conducted to demonstrate the superiority of the proposed Bayesian method compared to an existing high‐dimensional varying coefficient modelling approach. In addition, its applicability to real data analysis is illustrated using yeast cell cycle data.