Local Parameter Estimates Research Articles

Social determinants of health and newer glucose-lowering drugs adoption among US Medicare beneficiaries with type 2 diabetes.

Two classes of newer glucose-lowering drugs (GLDs), sodium-glucose cotransporter-2 inhibitors and glucagon-like peptide-1 receptor agonists, improve cardiovascular and renal outcomes among patients with type 2 diabetes (T2D). However, racial and ethnic minority groups carry higher cardiovascular risks but have lower access to newer GLDs. Contextual-level social determinants of health (SDOH) may be the underlying factor associated with newer GLD adoption. To identify the association between contextual-level SDOH and real-world adoption of newer GLDs among Medicare beneficiaries and to examine the nonstationarity in the associations. Data were from 15% random samples of January 2017 to December 2018 nationwide Medicare beneficiaries. We identified patients with T2D who did not use newer GLDs in the year before the index date-January 1, 2018-and followed the cohort for 1 year to record their status of initiating a newer GLD. We used a geographically weighted multivariable Poisson regression model to determine to what extent the SDOH-newer GLD initiation association (β coefficient) varied geographically. We identified 795,469 eligible Medicare beneficiaries with T2D during the study period from our dataset. Of the study cohort, mean age was 73.1 (SD = 10.5) years, 424,312 (53.3%) were female, 562,994 (70.8%) were non-Hispanic White, 96,891 (12.2%) were non-Hispanic Black, 84,744 (10.6%) were Hispanic, and 29,645 (3.7%) were Asian/Pacific Islander. Newer GLD initiation was negatively associated with the percentage of the population reporting non-Hispanic Black race, Hispanic ethnicity, and unemployment, as revealed by nonspatial regression analyses. The county-level median household income was also associated with higher newer GLD initiation. The spatial analysis presented distinct distributions of local parameter estimates for each contextual-level SDOH. We identified key contextual-level SDOH associated with real-world adoption of newer GLDs and explored their geographic variation through spatially explicit, data-driven analytical approaches. Identifying areas of strong association between SDOH and newer GLD initiation is crucial for policymakers to allocate resources and develop interventions that address structural inequities.

When everyone’s doing it: The relative effects of geographical context and social determinants of health on teen birth rates

Geographic disparities in teen birth rates in the U.S. persist, despite overall reductions over the last two decades. Research suggests these disparities might be driven by spatial variations in social determinants of health (SDOH). An alternative view is that “place” or “geographical context” affects teen birth rates so that they would remain uneven across the U.S. even if all SDOH were constant. We use multiscale geographically weighted regression (MGWR) to quantify the relative effects of geographical context, independent of SDOH, on county-level teen birth rates across the U.S. Findings indicate that even if all counties had identical compositions with respect to SDOH, strong geographic disparities in teen birth rates would still persist. Additionally, local parameter estimates show the relationships between several components of SDOH and teen birth rates vary over space in both direction and magnitude, confirming that global regression techniques commonly employed to examine these relationships likely obscure meaningful contextual differences in these relationships. Findings from this analysis suggest that reducing geographic disparities in teen birth rates will require not only ameliorating differences in SDOH across counties but also combating community norms that contribute to high rates of teen birth, particularly in the southern U.S. Further, the results suggest that if geographical context is not incorporated into models of SDOH, the effects of such determinants may be interpreted incorrectly.

Spatial Analysis on the Variances of Landslide Factors Using Geographically Weighted Logistic Regression in Penang Island, Malaysia

Landslides are one of the common natural disasters involving mostly movement of soil surfaces associated with gravitational attraction. Their adverse losses and significant damage, which always result in at least 17% of casualties and billions of dollars of financial losses worldwide, have made landslides the third most notorious phenomenon devastating many parts of the world. Malaysia has had multiple landslide occurrences, particularly in highly urbanized areas, such as Penang Island, owing to the declining vegetation cover in hilly terrains. Thus, this study aims to delineate the spatial relationship variances between landslide occurrences and the influencing factors in the area of interest. Ten influencing factors considered, including distance to roads, distance to rivers, distance to faults, slope angle, slope aspect, curvature, rainfall annual average, lithology, soil series, and land use. In this study, we use a software (GWR 4.0) as a medium for the analysis processing, coupled with GIS. A local statistical technique, Geographically Weighted Logistic Regression (GWLR), is primacy in capturing the geographical variation of the model coefficients that considers non-stationary variables and models their relationships, as well as processes regression coefficients over space. Goodness-of-fit criteria were used to evaluate the GWLR model, namely AICc that decrease from 872.202167 to 800.856998. Bayesian Information Criterion (BIC) shows a decrease in value from 925.784185 to 945.196942. Likewise, deviance decreased from 849.931675 to 739.175630, while pdev increased from 0.379457 to 0.460321. These goodness-of-fit criteria values express GWLR as the best model for local measure. The variances in both local parameter estimates and the t-values (negative and positive values) show the level of significance for each landslide factor in influencing landslide occurrences across the study area. The results of the local parameter estimates and the t-values also show that the slope angle and the slope aspect spatially affect landslide occurrences across the study area. Therefore, a proper perspective and a thorough understanding of the certain slope condition must be established for future mitigation actions to support the agenda of SDG 15, which promotes resilience and disaster risk reduction.

Determination of the best knot and bandwidth in geographically weighted truncated spline nonparametric regression using generalized cross validation

This study proposes the development of nonparametric regression for data containing spatial heterogeneity with local parameter estimates for each observation location. GWTSNR combines Truncated Spline Nonparametric Regression (TSNR) and Geographically Weighted Regression (GWR). So it is necessary to determine the optimum knot point from TSNR and determine the best geographic weighting (bandwidth) from GWR by deciding the best knot point and bandwidth using Generalized Cross Validation (GCV). The case study analyzed the Morbidity Rate in North Sumatra in 2020. This study will estimate the model using knot points 1, 2, and 3 and geographic weighting of the Kernel Function, Gaussian, Bisquare, Tricube, and Exponential. Based on data analysis, we obtained that the best model for Morbidity Rate data in North Sumatra 2020 based on the minimum GCV value is the model using knots 1 and the Kernel Function of Bisquare. Based on the GWTSNR model, the significant predictors in each district/city were grouped into eight groups. Furthermore, the GWTSNR is better at modeling morbidity rates in North Sumatra 2020 by obtaining adjusted R-square = 96.235 than the TSNR by obtaining adjusted R-squared = 70.159. Some of the highlights of the proposed approach are:•The method combines nonparametric and spatial regression in determining morbidity rate modeling.•There were three-knot points tested in the truncated spline nonparametric regression and four geographic weightings in the spatial regression and then to determine the best knot and bandwidth using Generalized Cross Validation.•This paper will determine regional groupings in North Sumatra 2020 based on significant predictors in modeling morbidity rates.

Spatial variability in factors influencing maternal health service use in Jimma Zone, Ethiopia: a geographically-weighted regression analysis

BackgroundPersisting within-country disparities in maternal health service access are significant barriers to attaining the Sustainable Development Goals aimed at reducing inequalities and ensuring good health for all. Sub-national decision-makers mandated to deliver health services play a central role in advancing equity but require appropriate evidence to craft effective responses. We use spatial analyses to identify locally-relevant barriers to access using sub-national data from rural areas in Jimma Zone, Ethiopia.MethodsCross-sectional data from 3727 households, in three districts, collected at baseline in a cluster randomized controlled trial were analysed using geographically-weighted regressions. These models help to quantify associations within women’s proximal contexts by generating local parameter estimates. Data subsets, representing an empirically-identified scale for neighbourhood, were used. Local associations between outcomes (antenatal, delivery, and postnatal care use) and potential explanatory factors at individual-level (ex: health information source), interpersonal-level (ex: companion support availability) and health service-levels (ex: nearby health facility type) were modelled. Statistically significant local odds ratios were mapped to demonstrate how relevance and magnitude of associations between various explanatory factors and service outcomes change depending on locality.ResultsSignificant spatial variability in relationships between all services and their explanatory factors (p < 0.001) was detected, apart from the association between delivery care and women’s decision-making involvement (p = 0.124). Local models helped to pinpoint factors, such as danger sign awareness, that were relevant for some localities but not others. Among factors with more widespread influence, such as that of prior service use, variation in estimate magnitudes between localities was uncovered. Prominence of factors also differed between services; companion support, for example, had wider influence for delivery than postnatal care. No significant local associations with postnatal care use were detected for some factors, including wealth and decision involvement, at the selected neighbourhood scale.ConclusionsSpatial variability in service use associations means that the relative importance of explanatory factors changes with locality. These differences have important implications for the design of equity-oriented and responsive health systems. Reductions in within-country disparities are also unlikely if uniform solutions are applied to heterogeneous contexts. Multi-scale models, accommodating factor-specific neighbourhood scaling, may help to improve estimated local associations.

Geographically Weighted Regression with Kernel Weighted Function on Poverty Cases in West Java Province

Spatial regression analysis is a form of regression model that considers spatial effects. Geographically weighted regression (GWR) is the spatial regression methods that can be used to deal with the problem of spatial diversity. This method generates local model parameter estimates for each observation location. The application of spatial statistics can be done in all areas such as the problem of poverty. Poverty can be influenced by factors of proximity between regions, so that in determining the poverty factor, the proximity factor of the region cannot be ignored. West Java Province is a province with the largest population, so this study aims to model the poverty data in West Java Province by incorporating spatial effects. The weighting function used for the GWR model is the function of the fixed and adaptive kernels. The analysis results show that the fixed exponential kernel function has the smallest cross validation (CV) value, so the weighting matrix used in the model is determined by the exponential kernel function. The largest value and the smallest AIC value are owned by the GWR model with an exponential kernel function. Based on the results obtained by the the ANOVA table to test GWR's global goodness, the GWR model is more effective than global regression. Therefore, the GWR model is the best model when it used in West Java’s poverty cases. The effect of each explanatory variable on the percentage of poverty varies in each district/city in West Java Province.

On the measurement of bias in geographically weighted regression models

Under the realization that Geographically Weighted Regression (GWR) is a data-borrowing technique, this paper derives expressions for the amount of bias introduced to local parameter estimates by borrowing data from locations where the processes might be different from those at the regression location. This is done for both GWR and Multiscale GWR (MGWR). We demonstrate the accuracy of our expressions for bias through a comparison with empirically derived estimates based on a simulated dataset with known local parameter values. By being able to compute the bias in both models we are able to demonstrate the superiority of MGWR. We then demonstrate the utility of a corrected Akaike Information Criterion statistic in finding optimal bandwidths in both GWR and MGWR as a trade-off between minimizing both bias and uncertainty. We further show how bias in one set of local parameter estimates can affect the bias in another set of local estimates. The bias derived from borrowing data from other locations appears to be very small.

Exploring Spatially Non-Stationary and Scale-Dependent Responses of Ecosystem Services to Urbanization in Wuhan, China

Ecosystem services (ESs) are facing challenges from urbanization processes globally. Exploring how ESs respond to urbanization provides valuable information for ecological protection and urban landscape planning. Previous studies mainly focused on the global and single-scaled responses of ESs but ignored the spatially heterogenous and scale-dependent characteristics of these responses. This study chose Wuhan City in China as the study area to explore the spatially varying and scale-dependent responses of ESs, i.e., grain productivity, carbon sequestration, biodiversity potential and erosion prevention, to urbanization using geographically weighted regression (GWR). The results showed that the responses of ESs were spatially nonstationary evidenced by a set of local parameter estimates in GWR models, and scale-dependent indicated by two kinds of scale effects: effect of different bandwidths and effect of grid scales. The stationary index of GWR declined rapidly as the bandwidth increased until reaching to a distance threshold. Moreover, GWR outperformed ordinary least square at both grid scales (i.e., 5 km and 10 km scales) and behaved better at finer scale. The spatially non-stationary and scale-dependent responses of ESs to urbanization are expected to provide beneficial guidance for ecologically friendly urban planning.

Inference in Multiscale Geographically Weighted Regression

A recent paper expands the well‐known geographically weighted regression (GWR) framework significantly by allowing the bandwidth or smoothing factor in GWR to be derived separately for each covariate in the model—a framework referred to as multiscale GWR (MGWR). However, one limitation of the MGWR framework is that, until now, no inference about the local parameter estimates was possible. Formally, the so‐called “hat matrix,” which projects the observed response vector into the predicted response vector, was available in GWR but not in MGWR. This paper addresses this limitation by reframing GWR as a Generalized Additive Model, extending this framework to MGWR and then deriving standard errors for the local parameters in MGWR. In addition, we also demonstrate how the effective number of parameters can be obtained for the overall fit of an MGWR model and for each of the covariates within the model. This statistic is essential for comparing model fit between MGWR, GWR, and traditional global models, as well as for adjusting multiple hypothesis tests. We demonstrate these advances to the MGWR framework with both a simulated data set and a real‐world data set and provide a link to new software for MGWR (MGWR1.0) which includes the novel inferential framework for MGWR described here.

GEOGRAPHICALLY WEIGHTED LOGISTIC REGRESSION DENGAN FUNGSI KERNEL FIXED GAUSSIAN PADA KEMISKINAN JAWA TENGAH

Poverty alleviation is a problem faced by many countries in the world, included Indonesia. Poverty in Indonesia still relatively high. Poverty is one indicator of welfare. In general, the decline in poverty means that people's welfare increasing. Poverty is a multi-dimensional problem, which involves various microeconomic and macroeconomic factors, including the influence of the surrounding region. Modeling with geographically weighted regression (GWR) accommodates heterogeneous effects of independent variables on the dependent variable and produces a local parameter estimates. Central Java has the second highest poverty rate among provinces in Java. This study will model poverty in Central Java with a model that accommodates the influence of the surrounding region, named Geographically Weighted Logistic Regression (GWLR). Poverty modeling in Central Java with GWLR, in general, literacy rates (AMH), per capita GRDP, and Labor Force Participation Rate (TPAK) significantly affected poverty in Central Java with values that varied between districts / cities.

Simulation models predict that school-age children are responsible for most human-to-mosquito Plasmodium falciparum transmission in southern Malawi

BackgroundMalaria persists in some high-transmission areas despite extensive control efforts. Progress toward elimination may require effective targeting of specific human populations that act as key transmission reservoirs.MethodsParameterized using molecular-based Plasmodium falciparum infection data from cross-sectional community studies in southern Malawi, a simulation model was developed to predict the proportions of human-to-mosquito transmission arising from (a) children under 5 years old (U5s), (b) school-age children (SAC, 5–15 years), (c) young adults (16–30 years), and (d) adults > 30 years. The model incorporates mosquito biting heterogeneity and differential infectivity (i.e. probability that a blood-fed mosquito develops oocysts) by age and gametocyte density.ResultsThe model predicted that SAC were responsible for more than 60% of new mosquito infections in both dry and rainy seasons, even though they comprise only 30% of this southern Malawi population. Young adults were the second largest contributors, while U5s and adults over 30 were each responsible for < 10% of transmission. While the specific predicted values are sensitive to the relative infectiousness of SAC, this group remained the most important contributor to mosquito infections under all realistic estimates.ConclusionsThese results suggest that U5 children play a small role compared to SAC in maintaining P. falciparum transmission in southern Malawi. Models that assume biting homogeneity overestimate the importance of U5s. To reduce transmission, interventions will need to reach more SAC and young adults. This publicly available model can be used by others to estimate age-specific transmission contributions in epidemiologically similar sites with local parameter estimates of P. falciparum prevalence and bed net use.

Situation analysis of healthcare service delivery using geographically weighted regression: (A case study of Sironko District, Eastern Uganda)

Geography plays an important role in planning and allocation of healthcare resources for an effective and efficient health system. Lack of statistical information analyzed using geostatistical tools then becomes a major bottleneck to proper planning and policy formulation in healthcare delivery. This study sought to compare existing health staffing, funding and medical supplies data given minimal national healthcare package, spatially explore the relationship between health service utilization and gaps in resource allocation, and to develop propositions to support the health policy. Facility survey and secondary data collection from the District Health Office and the Ministry of Health were utilized. Geographically Weighted Regression was used to spatially explore the relationships between Out-patient department attendance and gaps in health funding, staffing and stock-out days for essential drugs in health facilities. Global Moran’s I test was performed on the standard residuals to statistically test for their randomness. The analysis yielded local parameter estimates which were mapped to reveal the spatial variation of the relationships. There was strong influence of facility allocation gap in the North West diminishing towards South East, Strong negative influence of the staffing gap in the South West diminishing eastwards, and High influence of Stock-Out days in the South compared to the South West. Basing on the observations, the study proposed increased health vote while revising allocation based more on need other than solely on budgetary allocation of funds, increased staffing and providence of incentives for disadvantaged areas, and monitoring of drug supply and dispensing at health centres.

Making maps of cosmological parameters

We provide a fast algorithm to diagnose any directional dependence in the cosmological parameters by calculating maps of local cosmological parameter estimates and their joint errors. The technique implements a fast quadratic estimator technique based on Wiener filtering and convolution of the sky with a patch shape. It uses only three map-resolution spherical harmonic transforms per parameter and applies to any data set with full sky or a partial sky coverage. We apply this method to Planck SMICA-2015 and obtain fluctuation map for six cosmological parameters. Our estimate shows that the Planck data is consistent with a single global value of the cosmological parameters and is not influenced by any severe local contaminations. This method is applicable also to other angular or 3D data sets of future missions to scrutinize any local variation in the cosmological parameters.

A fully non-stationary linear coregionalization model for multivariate random fields

This paper introduces an extension of the traditional stationary linear coregionalization model to handle the lack of stationarity. Under the proposed model, coregionalization matrices are spatially dependent, and basic univariate spatial dependence structures are non-stationary. A parameter estimation procedure of the proposed non-stationary linear coregionalization model is developed under the local stationarity framework. The proposed estimation procedure is based on the method of moments and involves a matrix-valued local stationary variogram kernel estimator, a weighted local least squares method in combination with a kernel smoothing technique. Local parameter estimates are knitted together for prediction and simulation purposes. The proposed non-stationary multivariate spatial modeling approach is illustrated using two real bivariate data examples. Prediction performance comparison is carried out with the classical stationary multivariate spatial modeling approach. According to several criteria, the prediction performance of the proposed non-stationary multivariate spatial modeling approach appears to be significantly better.

Distributed adaptive asymptotically consensus tracking control of uncertain Euler-Lagrange systems under directed graph condition

In this paper, a backstepping based distributed adaptive control scheme is proposed for multiple uncertain Euler-Lagrange systems under directed graph condition. The common desired trajectory is allowed totally unknown by part of the subsystems and the linearly parameterized trajectory model assumed in currently available results is no longer needed. To compensate the effects due to unknown trajectory information, a smooth function of consensus errors and certain positive integrable functions are introduced in designing virtual control inputs. Besides, to overcome the difficulty of completely counteracting the coupling terms of distributed consensus errors and parameter estimation errors in the presence of asymmetric Laplacian matrix, extra information transmission of local parameter estimates are introduced among linked subsystem and adaptive gain technique is adopted to generate distributed torque inputs. It is shown that with the proposed distributed adaptive control scheme, global uniform boundedness of all the closed-loop signals and asymptotically output consensus tracking can be achieved.

A Comparison of Spatially Varying Regression Coefficient Estimates Using Geographically Weighted and Spatial‐Filter‐Based Techniques

Geographically weighted regression (GWR) is a technique that explores spatial nonstationarity in data‐generating processes by allowing regression coefficients to vary spatially. It is a widely applied technique across domains because it is intuitive and conforms to the well‐understood framework of regression. An alternative method to GWR that has been suggested is spatial filtering, which it has been argued provides a superior alternative to GWR by producing spatially varying regression coefficients that are not correlated with each other and which display less spatial autocorrelation. It is, therefore, worthwhile to examine these claims by comparing the output from both methods. We do this by using simulated data that represent two sets of spatially varying processes and examining how well both techniques replicate the known local parameter values. The article finds no support that spatial filtering produces local parameter estimates with superior properties. The results indicate that the original spatial filtering specification is prone to overfitting and is generally inferior to GWR, while an alternative specification that minimizes the mean square error (MSE) of coefficient estimates produces results that are similar to GWR. However, since we generally do not know the true coefficients, the MSE minimizing specification is impractical for applied research.

Spatiotemporal Dynamics and Spatial Determinants of Urban Growth in Suzhou, China

This paper analyzes the spatiotemporal dynamics of urban growth and models its spatial determinants in China through a case study of Suzhou, a rapidly industrializing and globalizing city. We conducted spatial analysis on land use data derived from multi-temporal remote sensing images of Suzhou from 1986 to 2008. Three urban growth types, namely infilling, edge-expansion, and leapfrog, were identified. We used landscape metrics to quantify the temporal trend of urban growth in Suzhou. During these 22 years, Suzhou’s urbanization changed from bottom-up rural urbanization to city-based top-down urban expansion. The underlying mechanism changed from TVE (town village enterprise) driven rural industrialization to FDI (foreign direct investment) driven development zone fever. Furthermore, we employed both global and local logistic regressions to model the probability of urban land conversion against a set of spatial variables. The global logistic regression model found the significance of proximity, neighborhood conditions, and socioeconomic factors. The logistic geographically weighted regression (GWR) model improved the global regression model with better model goodness-of-fit and higher prediction accuracy. More importantly, the local parameter estimates of variables enabled us to exam spatial variations of the influences of variables on urban growth in Suzhou.

A direct maximum likelihood optimization approach to identification of LPV time-delay systems

This paper is concerned with parameter estimation for a single-input single-output (SISO) linear parameter varying (LPV) system in an input–output setting with output-error (OE) time-delay model structure. Since the practical industrial processes are inherently nonlinear and are often operated over several working points with transition dynamic periods between different working points, the multiple-model LPV model is considered in this paper. A global maximization method is firstly used to estimate an autoregressive with exogenous input (ARX) time-delay model for each local process in a noniterative way. Then the Maximum Likelihood (ML) estimator is developed to identify a global LPV OE model based on the local process data and the transition data with the parameters initialized based on the local parameter estimates for the ARX time-delay models. One numerical example and two practical simulation examples are presented to demonstrate the effectiveness of the proposed method.

Spatially varying coefficient models in real estate: Eigenvector spatial filtering and alternative approaches

Real estate policies in urban areas require the recognition of spatial heterogeneity in housing prices to account for local settings. In response to the growing number of spatially varying coefficient models in housing applications, this study evaluated four models in terms of their spatial patterns of local parameter estimates, multicollinearity between local coefficients, and their predictive accuracy, utilizing housing data for the metropolitan area of Vienna (Austria). The comparison covered the spatial expansion method (SEM), moving window regression (MWR), geographically weighted regression (GWR), and genetic algorithm-based eigenvector spatial filtering (ESF), an approach that had not previously been employed in real estate research. The results highlight the following strengths and limitations of each method: 1) In contrast to SEM, MWR, and GWR, ESF depicts more localized patterns of the parameter estimates and does not smooth local particularities. 2) ESF is less affected by multicollinearity between the local parameter estimates than MWR, GWR, and SEM. 3) Even though the in-sample explanatory power and prediction accuracy of ESF is superior compared to the competitors, repeated sampling indicates a limited out-of-sample fit and prediction accuracy, suggesting over-fitting tendencies. 4) The application of ESF is less intuitive than MWR and GWR, which are available off-the-shelf.

Distributed Constrained Recursive Nonlinear Least-Squares Estimation: Algorithms and Asymptotics

This paper focuses on the problem of recursive nonlinear least squares parameter estimation in multi-agent networks, in which the individual agents observe sequentially over time an independent and identically distributed (i.i.d.) time-series consisting of a nonlinear function of the true but unknown parameter corrupted by noise. A distributed recursive estimator of the \emph{consensus} + \emph{innovations} type, namely $\mathcal{CIWNLS}$, is proposed, in which the agents update their parameter estimates at each observation sampling epoch in a collaborative way by simultaneously processing the latest locally sensed information~(\emph{innovations}) and the parameter estimates from other agents~(\emph{consensus}) in the local neighborhood conforming to a pre-specified inter-agent communication topology. Under rather weak conditions on the connectivity of the inter-agent communication and a \emph{global observability} criterion, it is shown that at every network agent, the proposed algorithm leads to consistent parameter estimates. Furthermore, under standard smoothness assumptions on the local observation functions, the distributed estimator is shown to yield order-optimal convergence rates, i.e., as far as the order of pathwise convergence is concerned, the local parameter estimates at each agent are as good as the optimal centralized nonlinear least squares estimator which would require access to all the observations across all the agents at all times. In order to benchmark the performance of the proposed distributed $\mathcal{CIWNLS}$ estimator with that of the centralized nonlinear least squares estimator, the asymptotic normality of the estimate sequence is established and the asymptotic covariance of the distributed estimator is evaluated. Finally, simulation results are presented which illustrate and verify the analytical findings.