Kernel averaged predictors for spatio-temporal regression models

Heaton, Matthew J.; Gelfand, Alan E.

doi:10.1016/j.spasta.2012.05.001

Cited by 10 publications

(11 citation statements)

References 28 publications

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“…In contrast to their use of splines to non-parametrically estimate the spatially-varying effect, we assume a constrained functional form of spatial-temporal exposure in order to estimate a latent exposure covariate to use in regression. The use of a constrained functional form is similar to the models developed in 41,42 ; however, in our approach the exposure surface (point pattern data) is fully observed and does not require modeling.…”

Section: Discussionmentioning

confidence: 99%

Spatial Temporal Aggregated Predictors to Examine Built Environment Health Effects

Peterson,

Hirsch,

Sanchez

2021

Preprint

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We propose the spatial-temporal aggregated predictor (STAP) modeling framework to address measurement and estimation issues that arise when assessing the relationship between built environment features (BEF) and health outcomes. Many BEFs can be mapped as point locations and thus traditional exposure metrics are based on the number of features within a pre-specified spatial unit. The size of the spatial unit-or spatial scale-that is most appropriate for a particular health outcome is unknown and its choice inextricably impacts the estimated health effect. A related issue is the lack of knowledge of the temporal scale-or the length of exposure time that is necessary for the BEF to render its full effect on the health outcome. The proposed STAP model enables investigators to estimate both the spatial and temporal scales for a given BEF in a data-driven fashion, thereby providing a flexible solution for measuring the relationship between outcomes and spatial proximity to point-referenced exposures.Simulation studies verify the validity of our method for estimating the scales as well as the association between availability of BEFs' and health outcomes. We apply this method to estimate the spatial-temporal association between supermarkets and BMI using data from the Multi-Ethnic Atherosclerosis Study, demonstrating the method's applicability in cohort studies.

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Section: Discussionmentioning

confidence: 99%

Spatial Temporal Aggregated Predictors to Examine Built Environment Health Effects

Peterson,

Hirsch,

Sanchez

2021

Preprint

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“…Taking a Bayesian perspective (as is the approach here) and specifying a prior for the intensity surface (e.g., a Gaussian process prior), the resulting integrals are random integrals with a complex dependency structure (see Heaton and Gelfand 2012). One common solution to this issue is to assume Λ(u, v) is proportional to closed-form density functions (see Kottas and Sansó 2007;Chakraborty and Gelfand 2010) so that the integrals can be easily computed but, with this approach, specifying/estimating a sufficiently flexible density can be cumbersome.…”

Section: Point Pattern Model For Birthsmentioning

confidence: 99%

Modeling Bronchiolitis Incidence Proportions in the Presence of Spatio-Temporal Uncertainty

Heaton

Berrett

Pugh

et al. 2019

Journal of the American Statistical Association

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Bronchiolitis (inflammation of the lower respiratory tract) in infants is primarily due to viral infection and is the single most common cause of infant hospitalization in the United States. To increase epidemiological understanding of bronchiolitis (and, subsequently, develop better prevention strategies), this research analyzes data on infant bronchiolitis cases from the U.S. Military Health System between the years 2003-2013 in Norfolk, Virginia, USA. For privacy reasons, child home addresses, birth dates, and diagnosis dates were randomized (jittered) creating spatio-temporal uncertainty in the geographic location and timing of bronchiolitis incidents. Using spatio-temporal point patterns, we created a modeling strategy that accounts for the jittering to estimate and quantify the uncertainty for the incidence proportion (IP) of bronchiolitis. Additionally, we regress the IP onto key covariates including pollution where we adequately account for uncertainty in the pollution levels (i.e., covariate uncertainty) using a land use regression model. Our analysis results indicate that the IP is positively associated with sulfur dioxide and population density. Further, we demonstrate how scientific conclusions may change if various sources of uncertainty (either spatio-temporal or covariate uncertainty) are not accounted for. Code submitted with this article was checked by an Associate Editor for Reproducibility and is available as an online supplement.

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“…In (1) we saw that trend phrase is a function of predictor variable in the same location of s. But, as it was mentioned in the introduction section, we are going to apply information of neighboring location in the mean function structure. To achieve the aim, we use kernel averaged predictors on the whole area of study according to methods proposed by Heaton and Gelfand [8,9]. To show the method, assume X(s) follows a Gaussian processes (GP) of the form,…”

Section: Spatial Regression Model Base On Kernel Averaged Predictorsmentioning

confidence: 99%

“…So, in this situation, considering mean based only on the predictor variable value in the same location is not enough and it is also necessary to use neighboring information. Heaton and Gelfand [8,9] presented application method of neighboring information in spatial regression model with normal errors. In this article, the method they have proposed for skew Gaussian regression model is generalized.…”

Section: Introductionmentioning

confidence: 99%

Compare and Evaluate the Performance of Gaussian Spatial Regression Models and Skew Gaussian Spatial Regression Based on Kernel Averaged Predictors

Dehsoukhteh¹

2015

AJTAS

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In many problems in the field of spatial statistics, when modeling the trend functions, predictors or covariates are available and the goal is to build a regression model to describe the relationship between the response and predictors. Generally, in spatial regression models, the trend function is often linear and it is assumed that the response mean is a linear function of predictor values in the same location where the response variable is observed. But, in real applications, the neighboring predictors sometimes provide valuable information about the response variable particulary when the distance between the locations is small. Having considered this subject matter, Heaton and Gelfand [6] suggested using kernel averaged predictors for modeling trend functions in which neighboring predictor information are also used. The models proposed by Heaton an Gelfand seemed to be bound by data normality. So, in many more application problems, spatial response variables follow a skew distribution. Therefore, in this article, skew Gaussian spatial regression model is studied and the performance of the model is presented and evaluated in comparison with Gaussian spatial regression models based on kernel averaged predictors using simulation studies and real examples.

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Kernel averaged predictors for spatio-temporal regression models

Cited by 10 publications

References 28 publications

Spatial Temporal Aggregated Predictors to Examine Built Environment Health Effects

Spatial Temporal Aggregated Predictors to Examine Built Environment Health Effects

Modeling Bronchiolitis Incidence Proportions in the Presence of Spatio-Temporal Uncertainty

Compare and Evaluate the Performance of Gaussian Spatial Regression Models and Skew Gaussian Spatial Regression Based on Kernel Averaged Predictors

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