Varying Coefficient Models Research Articles

Lessons learned from applying varying coefficient model to controlled simulation datasets

The development of site- and path-specific (i.e., non-ergodic) ground-motion models (GMMs) can drastically improve the accuracy of probabilistic seismic hazard analyses (PSHAs). The varying coefficient model (VCM) is a novel technique for developing non-ergodic GMMs, which puts epistemic uncertainty into spatially varying coefficients. The coefficients at nearby locations are correlated by a prior distribution imposed on a Gaussian Process. The correlation structure is determined by the data, and later used to predict coefficients and their epistemic uncertainties at new locations. It is important to carefully verify the technique before its results can be accepted by the engineering community. This study used a series of simulation-based controlled ground-motion datasets from CyberShake to test a modified VCM technique, which partitions the epistemic uncertainty into spatially varying source, site, and path terms. Because the simulation parameters (inputs) are known, verification of what is recovered by the VCM from CyberShake simulations is straightforward. We found that the site effects in CyberShake datasets can be reliably estimated by the VCM. However, the densely-located self-similar events in CyberShake datasets along pre-defined faults violate the isotropic assumption underlying the VCM, thus preventing the VCM from capturing the genuine source effects. For path effects, cell-specific attenuation approaches fail to recover the anelastic attenuation pattern of the 3D velocity model, which is most likely due to other unmodeled effects and inappropriate assumption of wave-propagation path. Instead, a midpoint approach that only considers the aggregated path effects can better recover the strong anelastic attenuation within basins by fixing the correlation length of path effects. Lessons learned in this study not only provide guidance for future applications of VCM to both simulation and empirical datasets, but will also guide further development of the technique, with emphasis on the recovery of path effects.

How Neighborhood Characteristics Influence Neighborhood Crimes: A Bayesian Hierarchical Spatial Analysis.

Urban crimes are a severe threat to livable and sustainable urban environments. Many studies have investigated the patterns, causes, and strategies for curbing the occurrence of urban crimes. It is found that neighborhood socioeconomic status, physical environment, and ethnic composition all might play a role in the occurrence of urban crimes. Inspired by the recent interest in exploring urban crime patterns with spatial data analysis techniques and the development of Bayesian hierarchical analytical approaches, we attempt to explore the inherently intricate relationships between urban assaultive violent crimes and the neighborhood socioeconomic status, physical environment, and ethnic composition in Paterson, NJ, using census data of the American Community Survey, alcohol and tobacco sales outlet data, and abandoned property listing data from 2013. Analyses are set at the census block group level. Urban crime data are obtained from the Paterson Police Department. Instead of examining relationships at a global level with both non-spatial and spatial analyses, we examine in depth the potential locally varying relationships at the local level through a Bayesian hierarchical spatially varying coefficient model. At both the global and local analysis levels, it is found that median household income is decisively negatively related to urban crime occurrence. Percentage of African Americans and Hispanics, number of tobacco sales outlets, and number of abandoned properties are all positively related with urban crimes. At the local level of analysis, however, the different factors have varying influence on crime occurrence throughout the city of Paterson, with median household income having the broadest influence across the city. The practice of applying a Bayesian hierarchical spatial analysis framework to understand urban crime occurrence and urban neighborhood characteristics enables urban planners, stakeholders, and public safety officials to engage in more active and targeted crime-reduction strategies.

Crop Yield Prediction Using Bayesian Spatially Varying Coefficient Models with Functional Predictors

Reliable prediction for crop yield is crucial for economic planning, food security monitoring, and agricultural risk management. This study aims to develop a crop yield forecasting model at large spatial scales using meteorological variables closely related to crop growth. The influence of climate patterns on agricultural productivity can be spatially inhomogeneous due to local soil and environmental conditions. We propose a Bayesian spatially varying functional model (BSVFM) to predict county-level corn yield for five Midwestern states, based on annual precipitation and daily maximum and minimum temperature trajectories modeled as multivariate functional predictors. The proposed model accommodates spatial correlation and measurement errors of functional predictors, and respects the spatially heterogeneous relationship between the response and associated predictors by allowing the functional coefficients to vary over space. The model also incorporates a Bayesian variable selection device to further expand its capacity to accommodate spatial heterogeneity. The proposed method is demonstrated to outperform other highly competitive methods in corn yield prediction, owing to the flexibility of allowing spatial heterogeneity with spatially varying coefficients in our model. Our study provides further insights into understanding the impact of climate change on crop yield. Supplementary materials for this article are available online.

Stage-dependent differential influence of metabolic and structural networks on memory across Alzheimer's disease continuum.

Large-scale neuronal network breakdown underlies memory impairment in Alzheimer's disease (AD). However, the differential trajectories of the relationships between network organisation and memory across pathology and cognitive stages in AD remain elusive. We determined whether and how the influences of individual-level structural and metabolic covariance network integrity on memory varied with amyloid pathology across clinical stages without assuming a constant relationship. Seven hundred and eight participants from the Alzheimer's Disease Neuroimaging Initiative were studied. Individual-level structural and metabolic covariance scores in higher-level cognitive and hippocampal networks were derived from magnetic resonance imaging and [18F] fluorodeoxyglucose positron emission tomography using seed-based partial least square analyses. The non-linear associations between network scores and memory across cognitive stages in each pathology group were examined using sparse varying coefficient modelling. We showed that the associations of memory with structural and metabolic networks in the hippocampal and default mode regions exhibited pathology-dependent differential trajectories across cognitive stages using sparse varying coefficient modelling. In amyloid pathology group, there was an early influence of hippocampal structural network deterioration on memory impairment in the preclinical stage, and a biphasic influence of the angular gyrus-seeded default mode metabolic network on memory in both preclinical and dementia stages. In non-amyloid pathology groups, in contrast, the trajectory of the hippocampus-memory association was opposite and weaker overall, while no metabolism covariance networks were related to memory. Key findings were replicated in a larger cohort of 1280 participants. Our findings highlight potential windows of early intervention targeting network breakdown at the preclinical AD stage. Data collection and sharing for this project was funded by the Alzheimer's Disease Neuroimaging Initiative (ADNI) (National Institutes of Health Grant U01 AG024904) and DOD ADNI (Department of Defense award number W81XWH-12-2-0012). We also acknowledge the funding support from the Duke NUS/Khoo Bridge Funding Award (KBrFA/2019-0020) and NMRC Open Fund Large Collaborative Grant (OFLCG09May0035).

Measuring spatial nonstationary effects of POI-based mixed use on urban vibrancy using Bayesian spatially varying coefficients model

Understanding the relationship between mixed land use and urban vibrancy is vital in advanced urban planning applications. This study presents a Bayesian spatially varying coefficient (SVC) model to explore the spatially nonstationary relationship between mixed land use and urban vibrancy after controlling for other factors. We first use the convolutional conditional autoregressive prior to accommodate the ecological bias resulting from unobserved confounders. Then we develop our approach in the case of a single predictor to allow the spatially varying coefficient process. We further introduce a type of the Bayesian SVC model that considers the stratified heterogeneity of the outcome, allowing the coefficients to simultaneously vary at the local and subregion level. We illustrate the proposed model by conducting a case study in Shenzhen using mobile phone data, an officially registered point-of-interest (POI) dataset, and several supplementary datasets. The model evaluation results show that including spatially unstructured and structured component combinations can improve the model's fitness and predictive ability; additionally, considering spatial stratified heterogeneity can further enhance the model's performance. Our findings provide an alternative for measuring the variable local-scale association between mixed-use and urban vibrancy and offer new insights that broaden the fields of environmental science and spatial statistics.

Exploring regional and sociodemographic disparities associated with unenrollment for the disease management program for type 2 Diabetes Mellitus using Bayesian spatial modelling

BackgroundThe disease management program (DMP) for type 2 Diabetes Mellitus (T2DM) is the largest DMP in Germany. Our goal was to analyze regional differences in unenrollment rates, suggest areas for intervention and provide background information, which population groups in which locations are currently not enrolled in the DMP for T2DM.MethodsIn this study, we used data of the 1.7 mil. insurants of the AOK Nordost health insurance. For the visualization of enrollment potential, we used the Besag-York-Mollie model (BYM). The spatial scan statistic (SaTScan) was used to detect areas of unusually high rates of unenrolled diabetics to prioritize areas for intervention. To explore sociodemographic associations, we used Bayesian spatial global regression models. A Spatially varying coefficient model (SVC) revealed in how far the detected associations vary over space.ResultsThe proportion of diabetics currently not enrolled in the DMP T2DM was 36.8% in 2019 and varied within northeastern Germany. Local clusters were detected mainly in Mecklenburg-West-Pomerania and Berlin. The main sociodemographic variables associated with unenrollment were female sex, younger age, being unemployed, foreign citizenship, small household size and the proportion of persons commuting to work outside their residential municipality. The SVC model revealed important spatially varying effects for some but not all associations.ConclusionLower socioeconomic status and foreign citizenship had an ubiquitous effect on not being enrolled. The DMP T2DM therefore does currently not reach those population groups, which have a higher risk for secondary diseases and possible avoidable hospitalizations. Logically, future interventions should focus on these groups. Our methodology clearly suggests areas for intervention and points out, which population group in which locations should be specifically approached.

Hybrid broadband ground-motion simulation validation of small magnitude active shallow crustal earthquakes in New Zealand

This article presents a comprehensive validation of the hybrid broadband ground-motion simulation approach (via the commonly used Graves and Pitarka method) in a New Zealand context with small magnitude point source ruptures using an extensive set of 5218 ground motions recorded at 212 sites from 479 active shallow crustal earthquakes across the country. Modifications to the simulation method inferred from a previous New Zealand validation are implemented, and the improvements are explicitly quantified. Empirical ground-motion models are also considered to provide a benchmark for simulation prediction accuracy and precision. Examination of intensity measure residuals identifies that the simulation method modifications lead to reduced model prediction bias and within-event variability and provides evidence toward the use of spatially varying coefficient models for simulation parameters, such as the high-frequency Brune stress parameter. Additional biases identified include, among others, underprediction of significant durations at soft soil sites and overprediction of short-period pseudo-spectral accelerations at stiff alluvial gravel and rock sites due to low-estimated 30 m time-averaged shear-wave velocity values.

Robust and sparse learning of varying coefficient models with high-dimensional features

ABSTRACT Varying coefficient model (VCM) is extensively used in various scientific fields due to its capability of capturing the changing structure of predictors. Classical mean regression analysis is often complicated in the existence of skewed, heterogeneous and heavy-tailed data. For this purpose, this work employs the idea of model averaging and introduces a novel comprehensive approach by incorporating quantile-adaptive weights across different quantile levels to further improve both least square (LS) and quantile regression (QR) methods. The proposed procedure that adaptively takes advantage of the heterogeneous and sparse nature of input data can gain more efficiency and be well adapted to extreme event case and high-dimensional setting. Motivated by its nice properties, we develop several robust methods to reveal the dynamic close-to-truth structure for VCM and consistently uncover the zero and nonzero patterns in high-dimensional scientific discoveries. We provide a new iterative algorithm that is proven to be asymptotic consistent and can attain the optimal nonparametric convergence rate given regular conditions. These introduced procedures are highlighted with extensive simulation examples and several real data analyses to further show their stronger predictive power compared with LS, composite quantile regression (CQR) and QR methods.

Joint variable selection of both fixed and random effects for Gaussian process-based spatially varying coefficient models

Spatially varying coefficient (SVC) models are a type of regression models for spatial data where covariate effects vary over space. If there are several covariates, a natural question is which covariates have a spatially varying effect and which not. We present a new variable selection approach for Gaussian process-based SVC models. It relies on a penalized maximum likelihood estimation and allows joint variable selection both with respect to fixed effects and Gaussian process random effects. We validate our approach in a simulation study as well as a real world data set. In the simulation study, the penalized maximum likelihood estimation correctly identifies zero fixed and random effects, while the penalty-induced bias of non-zero estimates is negligible. In the real data application, our proposed penalized maximum likelihood estimation yields sparser SVC models and achieves a smaller information criterion than classical maximum likelihood estimation. In a cross-validation study applied on the real data, we show that our proposed penalized maximum likelihood estimation consistently yields the sparsest SVC models while achieving similar predictive performance compared to other SVC modeling methodologies.

A Partially Nonergodic Ground-Motion Model for Cascadia Interface Earthquakes

ABSTRACT The Abrahamson and Gulerce (2020) ground-motion model (GMM), called AG20, is modified to include the nonergodic effects from the suite of 3D numerical simulations of long-period ground motions from M 9 megathrust earthquakes on the Cascadia subduction zone developed by the M 9 project (Frankel et al., 2018). Three modifications are made to the AG20 model. First, the scaling of the basin effects as a function of the depth to a shear-wave velocity of 2.5 km/s (Z2.5) is modified to be consistent with the Z2.5 scaling from the 3D simulations. Second, the spatial distribution of the nonergodic site terms is estimated using the varying coefficient model for the region covered by the 3D velocity model. The change in the median ground motion due to the nonergodic site terms ranges from factors of 0.25 to 5 at a period of 3 s. Third, a reduction in the aleatory variability for single-station sigma is estimated. On average, including the nonergodic site terms reduces the sigma by 15%–25% compared with an ergodic sigma for Cascadia. In addition, a spatially varying single-station sigma model is developed, showing the highest variability for sites near the basin edges. Application of nonergodic GMMs requires an estimate of the epistemic uncertainty in the nonergodic terms. Without simulation results for different 3D velocity models, we assumed that the epistemic uncertainty due to uncertainty in the 3D velocity model is half of the between-site standard deviation from the simulations. As an example, the seismic hazard for interface events using the nonergodic GMM is compared with the hazard using the original AG20 GMM.

Penalized estimation of a class of single-index varying-coefficient models for integrative genomic analysis.

Recent technological advances have made it possible to collect high-dimensional genomic data along with clinical data on a large number of subjects. In the studies of chronic diseases such as cancer, it is of great interest to integrate clinical and genomic data to build a comprehensive understanding of the disease mechanisms. Despite extensive studies on integrative analysis, it remains an ongoing challenge to model the interaction effects between clinical and genomic variables, due to high dimensionality of the data and heterogeneity across data types. In this paper, we propose an integrative approach that models interaction effects using a single-index varying-coefficient model, where the effects of genomic features can be modified by clinical variables. We propose a penalized approach for separate selection of main and interaction effects. Notably, the proposed methods can be applied to right-censored survival outcomes based on a Cox proportional hazards model. We demonstrate the advantages of the proposed methods through extensive simulation studies and provide applications to a motivating cancer genomicstudy.

China's place attractivity, population mobility and its mechanisms: Perspectives from a full spectrum of spatial analyses

AbstractUnderstanding the potential mechanisms of population mobility is important in population studies. The current study calculates a place attractivity score and collects 12 socioeconomic and natural condition factors at the prefecture‐level in China. A full spectrum of spatial autoregression and eigenfunction‐based spatial filtering models are employed to investigate the relationship between place attractivity and the factors at the global level, which assumes the relationship stays the same everywhere. A random‐effects eigenfunction‐based spatial filtering spatially varying coefficient model is used to check the relationships at local level, which admits that relationships might be different in different locations. Results suggest that the eigenvector spatial filtering analysis models perform better than other models. China's population mobility is primarily driven by economic push‐pull factors. Accessibility, job opportunity, temperature and terrain also play roles in determining a prefecture's attractivity. Local analysis suggests that the relationships are likely only true in large migration destinations.

Extraction of Continuous and Discrete Spatial Heterogeneities: Fusion Model of Spatially Varying Coefficient Model and Sparse Modelling

Geospatial phenomena often have spatial heterogeneity, which is caused by differences in the data generation process from place to place. There are two types of spatial heterogeneity: continuous and discrete, and there has been much discussion about how to analyze one type of spatial heterogeneity. Although geospatial phenomena can have both types of spatial heterogeneities, previous studies have not sufficiently discussed how to consider these two different types of spatial heterogeneity simultaneously and how to detect them separately, which may lead to biased estimates and the wrong interpretation of geospatial phenomena. This study proposes a new approach for the analysis of spatial data with both heterogeneities by combining the eigenvector spatial filtering-based spatially varying coefficient (ESF-SVC) model, which assumes the continuous spatial heterogeneity and generalized lasso (GL) estimation, which assumes discrete spatial heterogeneity and proposes the ESF-GL-SVC model. The performance of ESF-GL-SVC was evaluated through experiments based on a Monte Carlo simulation and confirms that the ESF-GL-SVC showed better performance in estimating coefficients with both types of spatial heterogeneity than the previous two models. The application of the apartment rent data showed that the ESF-GL-SVC outputs the result with the smallest BIC value, and the estimated coefficients depict continuous and discrete spatial heterogeneity in the dataset. Reasonable coefficients were estimated using the ESF-GL-SVC, although some coefficients by ESF-SVC were not.

Robust Variable Selection for Single-Index Varying-Coefficient Model with Missing Data in Covariates

As applied sciences grow by leaps and bounds, semiparametric regression analyses have broad applications in various fields, such as engineering, finance, medicine, and public health. Single-index varying-coefficient model is a common class of semiparametric models due to its flexibility and ease of interpretation. The standard single-index varying-coefficient regression models consist mainly of parametric regression and semiparametric regression, which assume that all covariates can be observed. The assumptions are relaxed by taking the models with missing covariates into consideration. To eliminate the possibility of bias due to missing data, we propose a probability weighted objective function. In this paper, we investigate the robust variable selection for a single-index varying-coefficient model with missing covariates. Using parametric and nonparametric estimates of the likelihood of observations with fully observed covariates, we examine the estimators for estimating the likelihood of observations. For variable selection, we use a weighted objective function penalized by a non-convex SCAD. Theoretical challenges include the treatment of missing data and a single-index varying-coefficient model that uses both the non-smooth loss function and the non-convex penalty function. We provide Monte Carlo simulations to evaluate the performance of our approach.

Spatially Varying Coefficient Regression with GAM Gaussian Process splines: GAM(e)-on

Abstract. This paper describes initial work exploring GAM Gaussian Process (GP) splines parameterised by observation location, as a geographical varying coefficient model. Similar to GWR, this approach accommodates process spatial heterogeneity and generates spatially distributed, local coefficient estimates. These can be mapped to indicate the nature of the heterogeneity. The paper investigates the effect of the smoothing parameters used in the splines and how they alter the nature of the modelled heterogeneity. It optimises these in the GAM GP and the tuned model has subtle but important differences with the initial model. This has impacts on the nature of the process understanding (inference) that can be extracted from the model. This in turn suggest the need examine the underlying semantics of the resultant models in relation to the scale of process suggested by the smoothing parameters. A number of areas of further work are identified.

Spatially clustered varying coefficient model

In various applications with large spatial regions, the relationship between the response variable and the covariates is expected to exhibit complex spatial patterns. We propose a spatially clustered varying coefficient model, where the regression coefficients are allowed to vary smoothly within each cluster but change abruptly across the boundaries of adjacent clusters, and we develop a unified approach for simultaneous coefficient estimation and cluster identification. The varying coefficients are approximated by penalized splines, and the clusters are identified through a fused concave penalty on differences in neighboring locations, where the spatial neighbors are specified by the minimum spanning tree (MST). The optimization is solved efficiently based on the alternating direction method of multipliers, using the sparsity structure from MST. Furthermore, we establish the oracle property of the proposed method considering the structure of MST. Numerical studies show that the proposed method can efficiently incorporate spatial neighborhood information and automatically detect possible spatially clustered patterns in the regression coefficients. An empirical study in oceanography illustrates that the proposed method is promising to provide informative results.

Multivariate partial linear varying coefficients model for gene-environment interactions with multiple longitudinal traits.

Correlated phenotypes often share common genetic determinants. Thus, a multi‐trait analysis can potentially increase association power and help in understanding pleiotropic effect. When multiple traits are jointly measured over time, the correlation information between multivariate longitudinal responses can help to gain power in association analysis, and the longitudinal traits can provide insights on the dynamic gene effect over time. In this work, we propose a multivariate partially linear varying coefficients model to identify genetic variants with their effects potentially modified by environmental factors. We derive a testing framework to jointly test the association of genetic factors and illustrated with a bivariate phenotypic trait, while taking the time varying genetic effects into account. We extend the quadratic inference functions to deal with the longitudinal correlations and used penalized splines for the approximation of nonparametric coefficient functions. Theoretical results such as consistency and asymptotic normality of the estimates are established. The performance of the testing procedure is evaluated through Monte Carlo simulation studies. The utility of the method is demonstrated with a real data set from the Twin Study of Hormones and Behavior across the menstrual cycle project, in which single nucleotide polymorphisms associated with emotional eating behavior are identified.

A non-ergodic ground-motion model of Fourier amplitude spectra for France

We used an ergodic ground-motion model (GMM) of California of Bayless and Abrahamson (Bull Seismol Soc Am 109(5):2088–2105, 2019) as a backbone model and incorporated the varying-coefficient model (VCM), with a modification for anisotropic path effects, to develop a new non-ergodic GMM for France based on the French RESIF data set (1996–2016). Most of the earthquakes in this database have small-to-moderate magnitudes (M2.0 – M5.2). We developed the GMM for the smoothed effective amplitude spectrum (EAS) rather than for elastic spectral acceleration because it allows the use of small-magnitude data to constrain linear effects of the path and site without the complication of the scaling being affected by differences in the response spectral shape. For the VCM, the coefficients of GMM can vary by geographical location and they are estimated using Gaussian-process regression. There is a separate set of coefficients for each source and site coordinate, including both the mean coefficients and the epistemic uncertainty in the coefficients. We further modify the anelastic attenuation term of a GMM by the cell-specific approach of Dawood and Rodriguez-Marek (Bull Seismol Soc Am. 103 (2B): 1360–1372, 2013) and Kuehn et al. (Bull Seismol Soc Am 109 (2): 575–585, 2019) to allow for azimuth-dependent attenuation for each source which reduces the standard deviation of the residuals at long distances. As an example, we compute the 5 Hz seismic hazard for two sites using the non-ergodic EAS GMM. At the 1E-4 annual frequency of exceedance hazard level, there can be a large difference between the ergodic hazard and the non-ergodic hazard if the distance between the chosen site and the available data is smaller than the correlation length of the non-ergodic terms). The combination of the non-ergodic median ground motion and the reduced aleatory variability can have large implications for seismic-hazard estimation for long return periods. For some sites, the estimated hazard will increase and for other sites, the estimated hazard will decrease compared to the traditional ergodic GMM approach. Due to the skewed distribution of the epistemic uncertainty of the hazard, more of the sites will see a decrease in the mean hazard at the 1E−4 hazard level than will see an increase as a result of using the non-ergodic GMM.

Detection of spatial heterogeneity based on spatial autoregressive varying coefficient models

Spatial autocorrelation and spatial heterogeneity are fundamental properties of geo-referenced data. Spatial autoregressive varying coefficient models have been proposed to simultaneously deal with spatial autocorrelation in the response variable and spatial heterogeneity in the regression relationship. Nevertheless, the identification of spatial heterogeneity in the spatial lag term and in the regression relationship remains to be studied, which is essential to model selection and deep understanding of the intrinsical characteristics of the regression relationship. In this article, based on the two-stage least squares estimation of the spatial autoregressive varying coefficient model and the related null models, two residual sums of squares based statistics are constructed and the bootstrap tests are proposed to detect spatial heterogeneity in the spatial lag term and in the regression relationship, respectively. Then, simulation studies are conducted to assess the performance of the tests. The results show that both tests are of valid size, satisfactory power, and robustness to the model error distribution. Furthermore, a real-life example based on the Boston housing price data is given to demonstrate the application of the proposed tests.

Estimating 1 km gridded daily air temperature using a spatially varying coefficient model with sign preservation

Near-surface air temperature (Ta) is one of the key variables in a variety of studies such as hydrological modeling, assessment of heat waves, and energy modeling. Among existing methods, statistical algorithms are suitable for integrating auxiliary spatial data with station-based Ta data to produce gridded Ta over large areas. However, existing statistical algorithms (e.g., Geographically Weighted Regression (GWR)) cannot always correctly capture and preserve relationships between Ta and explanatory variables, which may increase uncertainties of relevant applications based on the estimated Ta with abnormal spatial patterns. This issue is mainly caused by the lack of enough observations due to the limited spatial coverage of weather stations, leading to abnormal relationships between Ta and explanatory variables. In order to address this issue, in this study, we introduced a new method named the Spatially Varying Coefficient Models with Sign Preservation (SVCM-SP) to estimate gridded Ta using gridded land surface temperature (LST) and elevation as explanatory variables with presetting positive and negative signs for coefficients, respectively. Using this method, first, we calculated the preset parameters of the bivariate spline surface. Second, we used the input data at weather stations and constrained least squares regression to obtain the coefficient surface for both the explanatory variables (i.e., elevation and LST) and the intercept. Third, we calculated the gridded Ta using the 1 km gridded LST and elevation data, and the estimated spatially varying coefficient surfaces. We evaluated the model performance for estimating 1 km gridded daily maximum and minimum Ta (i.e., Tmax and Tmin) data in mainland China from 2003 to 2016 using 10-fold cross-validation and compared its performance with the GWR model. The average root mean square error (RMSE) and mean absolute error (MAE) based on the SVCM-SP are 1.75 °C and 1.22 °C for Tmax, and 1.82 °C and 1.30 °C for Tmin, respectively. The SVCM-SP method showed better performance than the GWR in terms of accuracy, computing efficiency, and has more interpretable coefficients for explanatory variables to get more realistic spatial pattern of gridded Ta. More important, the sign preservation of the SVCM-SP method can mitigate the issue of abnormal relationships between Ta and explanatory variables in the traditional methods such as GWR, and therefore will contribute to future studies in developing better gridded air temperature or relevant data products.