Dataset Information

Spatial smoothing in Bayesian models: a comparison of weights matrix specifications and their impact on inference.

ABSTRACT:

Background

When analysing spatial data, it is important to account for spatial autocorrelation. In Bayesian statistics, spatial autocorrelation is commonly modelled by the intrinsic conditional autoregressive prior distribution. At the heart of this model is a spatial weights matrix which controls the behaviour and degree of spatial smoothing. The purpose of this study is to review the main specifications of the spatial weights matrix found in the literature, and together with some new and less common specifications, compare the effect that they have on smoothing and model performance.

Methods

The popular BYM model is described, and a simple solution for addressing the identifiability issue among the spatial random effects is provided. Seventeen different definitions of the spatial weights matrix are defined, which are classified into four classes: adjacency-based weights, and weights based on geographic distance, distance between covariate values, and a hybrid of geographic and covariate distances. These last two definitions embody the main novelty of this research. Three synthetic data sets are generated, each representing a different underlying spatial structure. These data sets together with a real spatial data set from the literature are analysed using the models. The models are evaluated using the deviance information criterion and Moran's I statistic.

Results

The deviance information criterion indicated that the model which uses binary, first-order adjacency weights to perform spatial smoothing is generally an optimal choice for achieving a good model fit. Distance-based weights also generally perform quite well and offer similar parameter interpretations. The less commonly explored options for performing spatial smoothing generally provided a worse model fit than models with more traditional approaches to smoothing, but usually outperformed the benchmark model which did not conduct spatial smoothing.

Conclusions

The specification of the spatial weights matrix can have a colossal impact on model fit and parameter estimation. The results provide some evidence that a smaller number of neighbours used in defining the spatial weights matrix yields a better model fit, and may provide a more accurate representation of the underlying spatial random field. The commonly used binary, first-order adjacency weights still appear to be a good choice for implementing spatial smoothing.

SUBMITTER: Duncan EW

PROVIDER: S-EPMC5732501 | biostudies-literature | 2017 Dec

REPOSITORIES: biostudies-literature

ACCESS DATA

Publications

Spatial smoothing in Bayesian models: a comparison of weights matrix specifications and their impact on inference.

Duncan Earl W EW White Nicole M NM Mengersen Kerrie K

International journal of health geographics 20171216 1

<h4>Background</h4>When analysing spatial data, it is important to account for spatial autocorrelation. In Bayesian statistics, spatial autocorrelation is commonly modelled by the intrinsic conditional autoregressive prior distribution. At the heart of this model is a spatial weights matrix which controls the behaviour and degree of spatial smoothing. The purpose of this study is to review the main specifications of the spatial weights matrix found in the literature, and together with some new a ...[more]

PMID: 29246157

Similar Datasets

Project description:BACKGROUND:Many methods of spatial smoothing have been developed, for both point data as well as areal data. In Bayesian spatial models, this is achieved by purposefully designed prior(s) or smoothing functions which smooth estimates towards a local or global mean. Smoothing is important for several reasons, not least of all because it increases predictive robustness and reduces uncertainty of the estimates. Despite the benefits of smoothing, this attribute is all but ignored when it comes to model selection. Traditional goodness-of-fit measures focus on model fit and model parsimony, but neglect "goodness-of-smoothing", and are therefore not necessarily good indicators of model performance. Comparing spatial models while taking into account the degree of spatial smoothing is not straightforward because smoothing and model fit can be viewed as opposing goals. Over- and under-smoothing of spatial data are genuine concerns, but have received very little attention in the literature. METHODS:This paper demonstrates the problem with spatial model selection based solely on goodness-of-fit by proposing several methods for quantifying the degree of smoothing. Several commonly used spatial models are fit to real data, and subsequently compared using the goodness-of-fit and goodness-of-smoothing statistics. RESULTS:The proposed goodness-of-smoothing statistics show substantial agreement in the task of model selection, and tend to avoid models that over- or under-smooth. Conversely, the traditional goodness-of-fit criteria often don't agree, and can lead to poor model choice. In particular, the well-known deviance information criterion tended to select under-smoothed models. CONCLUSIONS:Some of the goodness-of-smoothing methods may be improved with modifications and better guidelines for their interpretation. However, these proposed goodness-of-smoothing methods offer researchers a solution to spatial model selection which is easy to implement. Moreover, they highlight the danger in relying on goodness-of-fit measures when comparing spatial models.

Dataset Information

Spatial smoothing in Bayesian models: a comparison of weights matrix specifications and their impact on inference.

Background

Methods

Results

Conclusions

Publications

Spatial smoothing in Bayesian models: a comparison of weights matrix specifications and their impact on inference.

Similar Datasets

OmicsDI is part of the ELIXIR infrastructure

Tweets