Spatial Factor Model Research Articles

A Multivariate Dynamic Spatial Factor Model for Speciated Pollutants and Adverse Birth Outcomes.

Evidence suggests that exposure to elevated concentrations of air pollution during pregnancy is associated with increased risks of birth defects and other adverse birth outcomes. While current regulations put limits on total PM concentrations, there are many speciated pollutants within this size class that likely have distinct effects on perinatal health. However, due to correlations between these speciated pollutants, it can be difficult to decipher their effects in a model for birth outcomes. To combat this difficulty, we develop a multivariate spatio-temporal Bayesian model for speciated particulate matter using dynamic spatial factors. These spatial factors can then be interpolated to the pregnant women’s homes to be used to model birth defects. The birth defect model allows the impact of pollutants to vary across different weeks of the pregnancy in order to identify susceptible periods. The proposed methodology is illustrated using pollutant monitoring data from the Environmental Protection Agency and birth records from the National Birth Defect Prevention Study.

A Multivariate Dynamic Spatial Factor Model for Speciated Pollutants and Adverse Birth Outcomes

A Multivariate Dynamic Spatial Factor Model for Speciated Pollutants and Adverse Birth Outcomes

Spatial Dependence in Asset Pricing Models

When analyzing asset prices in isolation, the classical asset pricing models only account for the time-series variation of the asset with the factors. However, valuable information would be lost if some cross-sectional dependence exists across the assets. We extend the factor model in Fama and French (2012) to account for spatial dependence across returns and estimate a spatial factor model. We model the spatial linkages using a measure of physical distance between the properties of listed real estate companies. We find that the spatial factor model is not rejected and the spatial parameter is significant. The spatial factor model performs better than the factor model, substantially improving the model fit. Proximity across the property holdings of real estate companies can predict higher return correlation across the firms, controlling for size, book-to-market, and momentum characteristics.

Do marginalized neighbourhoods have less healthy retail food environments? An analysis using Bayesian spatial latent factor and hurdle models.

BackgroundFindings of whether marginalized neighbourhoods have less healthy retail food environments (RFE) are mixed across countries, in part because inconsistent approaches have been used to characterize RFE ‘healthfulness’ and marginalization, and researchers have used non-spatial statistical methods to respond to this ultimately spatial issue.MethodsThis study uses in-store features to categorize healthy and less healthy food outlets. Bayesian spatial hierarchical models are applied to explore the association between marginalization dimensions and RFE healthfulness (i.e., relative healthy food access that modelled via a probability distribution) at various geographical scales. Marginalization dimensions are derived from a spatial latent factor model. Zero-inflation occurring at the walkable-distance scale is accounted for with a spatial hurdle model.ResultsNeighbourhoods with higher residential instability, material deprivation, and population density are more likely to have access to healthy food outlets within a walkable distance from a binary ‘have’ or ‘not have’ access perspective. At the walkable distance scale however, materially deprived neighbourhoods are found to have less healthy RFE (lower relative healthy food access).ConclusionFood intervention programs should be developed for striking the balance between healthy and less healthy food access in the study region as well as improving opportunities for residents to buy and consume foods consistent with dietary recommendations.

A common spatial factor analysis model for measured neighborhood-level characteristics: The Multi-Ethnic Study of Atherosclerosis

The purpose of this study was to reduce the dimensionality of a set of neighborhood-level variables collected on participants in the Multi-Ethnic Study of Atherosclerosis (MESA) while appropriately accounting for the spatial structure of the data. A common spatial factor analysis model in the Bayesian setting was utilized in order to properly characterize dependencies in the data. Results suggest that use of the spatial factor model can result in more precise estimation of factor scores, improved insight into the spatial patterns in the data, and the ability to more accurately assess associations between the neighborhood environment and health outcomes.

Hierarchical Factor Models for Large Spatially Misaligned Data: A Low‐Rank Predictive Process Approach

This article deals with jointly modeling a large number of geographically referenced outcomes observed over a very large number of locations. We seek to capture associations among the variables as well as the strength of spatial association for each variable. In addition, we reckon with the common setting where not all the variables have been observed over all locations, which leads to spatial misalignment. Dimension reduction is needed in two aspects: (i) the length of the vector of outcomes, and (ii) the very large number of spatial locations. Latent variable (factor) models are usually used to address the former, although low-rank spatial processes offer a rich and flexible modeling option for dealing with a large number of locations. We merge these two ideas to propose a class of hierarchical low-rank spatial factor models. Our framework pursues stochastic selection of the latent factors without resorting to complex computational strategies (such as reversible jump algorithms) by utilizing certain identifiability characterizations for the spatial factor model. A Markov chain Monte Carlo algorithm is developed for estimation that also deals with the spatial misalignment problem. We recover the full posterior distribution of the missing values (along with model parameters) in a Bayesian predictive framework. Various additional modeling and implementation issues are discussed as well. We illustrate our methodology with simulation experiments and an environmental data set involving air pollutants in California.

Joint analysis of multivariate spatial count and zero‐heavy count outcomes using common spatial factor models

This paper discusses joint outcome modeling of multivariate spatial data, where outcomes include count as well as zero‐inflated count data. The framework utilized for the joint spatial count outcome analysis reflects that which is now commonly used for the joint analysis of longitudinal and survival data, termed shared frailty models, in which the outcomes are linked through a shared latent spatial random risk term. We discuss these types of joint mapping models and consider the benefits achieved through such joint modeling in the disease mapping context. We also consider the power of tests for common spatial structure in the context of two spatial maps and develop recommendations on the sort of power achievable in some contexts, as well as overall recommendations on the utility of joint mapping. We illustrate the approaches in an analysis of lung cancer mortality as well as an ecological study of Comandra blister rust infection of lodgepole pine trees. Copyright © 2012 John Wiley & Sons, Ltd.

Fast Bayesian Analysis of Spatial Dynamic Factor Models for Multitemporal Remotely Sensed Imagery

SummaryRemote sensing is one example where data sets that vary across space and time have become so large that ‘standard’ approaches employed by statistical modellers for applied analysis are no longer feasible. We present a Bayesian methodology, which makes use of recently developed algorithms in applied mathematics, for the analysis of large space–time data sets. In particular, a Markov chain Monte Carlo algorithm is proposed for the efficient estimation of spatial dynamic factor models. The spatial dynamic factor model is specified whereby spatial dependence is modelled though the columns of the factor loadings matrix by using a Gaussian Markov random field. Krylov subspace methods are used to take advantage of the sparse matrix structures that are inherent in the model. The methodology is used to analyse remotely sensed data from the Moderate Imaging Spectroradiometer satellite. In particular, the methodology proposed is used in conjunction with high resolution imagery for the classification, in terms of land type, of two regions in central Queensland, Australia.

Generalized spatial dynamic factor models

This paper introduces a new class of spatio-temporal models for measurements belonging to the exponential family of distributions. In this new class, the spatial and temporal components are conditionally independently modeled via a latent factor analysis structure for the (canonical) transformation of the measurements mean function. The factor loadings matrix is responsible for modeling spatial variation, while the common factors are responsible for modeling the temporal variation. One of the main advantages of our model with spatially structured loadings is the possibility of detecting similar regions associated to distinct dynamic factors. We also show that the new class outperforms a large class of spatial-temporal models that are commonly used in the literature. Posterior inference for fixed parameters and dynamic latent factors is performed via a custom tailored Markov chain Monte Carlo scheme for multivariate dynamic systems that combines extended Kalman filter-based Metropolis–Hastings proposal densities with block-sampling schemes. Factor model uncertainty is also fully addressed by a reversible jump Markov chain Monte Carlo algorithm designed to learn about the number of common factors. Three applications, two based on synthetic Gamma and Bernoulli data and one based on real Bernoulli data, are presented in order to illustrate the flexibility and generality of the new class of models, as well as to discuss features of the proposed MCMC algorithm.

Bayesian analysis of the multivariate geographical distribution of the socio‐economic environment in England

AbstractIn this paper we analyse the geographical distribution of the Indices of Deprivation 2004, a set of seven area‐based indices measuring multiple dimensions of socio‐economic status (SES) related to income, employment, education, health, access to services and housing, crime, and living environment in England at district level. We first study all the seven SES ‘domains’ separately using spatial hierarchical models to assess the level of underlying geographical structure in each of them. We then explore their joint relationships using a spatial factor model that extracts the information common and specific to the income, employment and education domains and regress the other domains on the extracted components. We use Bayesian inference throughout. Results show that all seven domains present strong spatial structure. The income, employment, education and health domains largely share the same information, which moderately overlaps with the crime and environment domains. The domain on access to services and housing is quite different from the others. The geographical patterns found in the latent common and specific factors are however difficult to interpret without further complementary information. Further investigation is required to identify plausible causal processes related to current economic and regional policies, and also to historic factors and their long‐lasting socio‐economic legacy. Copyright © 2007 John Wiley & Sons, Ltd.

Modelling the horizontal spatial structure of planktonic community in Lake Trasimeno (Umbria, Italy) using multivariate geostatistical methods

Spatial heterogeneity of ecological systems has been recognised in recent years as an important ecological feature of an ecosystem, rather than a mere statistical nuisance. However, although considerable interest has been paid to the development of statistical methods for the analysis of spatial environmental data, when in presence of more species or environmental variables common analyses still fail to recognise the necessity of a joint modelling of the whole correlation structure. In this paper, we propose to study the multivariate spatial autocorrelation of a plankton community by making explicit reference to a spatial linear factor model entailing a set of constraints for the spatial structure of the planktonic species. The data set examined come from an intensive 2-day sampling survey performed in July 1991 on Lake Trasimeno (Italy) to investigate the horizontal spatial heterogeneity and distribution of the planktonic community, from small (50 m) to large (1000–10,000 m) scale. The analysis revealed that zooplankton and phytoplankton essentially have different degrees of heterogeneity and different spatial structures which required separate modelling. On the other hand, the similarity of the spatial autocorrelation found within zooplankton and phytoplankton communities, indicates that at the investigated scales of observation the horizontal organisation of both components is not appreciably affected by species-specific behaviours. The analysis of the multivariate spatial patterns emerging from the mapping of the extracted factors suggested an interpretation of the distribution of macrozooplankton and phytoplankton assemblages in terms of planktonic responses to environmental factors of a lake-size scale.

Loglinear spatial factor analysis: an application to diabetes mellitus complications

AbstractThe investigation of spatial variation in disease rates is a standard epidemiological practice used to describe the geographic clustering of diseases which is helpful for making hypotheses about the possible ‘factors’ responsible for differences in risk. Up to the most recent statistical and computational developments, studies have almost entirely focused on the spatial modeling of univariate distributions of cases, that is, on the spatial modeling of single diseases. However, many diseases show similar patterns of geographical variation which may suggest the existence of common underlying risk factors, whether these are related to the environment, to particular local food habits, or to the clustering of a particular population (genetic origin). In this work, for multivariate categorical data pointwise geo‐referenced in a ‘geostatistical’ fashion, we propose a model for the study of the joint spatial variation of more diseases. Our approach is based on a hierarchical (generalized linear mixed) multivariate model where the underlying latent structure is given by a Gaussian geostatistical spatial factor model. The methodology proposed can be seen as an extension of the geostatistical linear model of coregionalization, and of the related ‘factorial kriging analysis’, to the case of geo‐referenced, in general multi‐way, contingency tables. An application of the proposed methodology is shown on an epidemiological data set coming from an extensive survey on diabetes mellitus patients which involved the majority of the family practitioners of the region of Umbria in central Italy in 1990. Attention is centered on the study of nephropathy and retinopathy, two of the chronic diabetic complications affecting life quality and expectancy. Copyright © 2004 John Wiley & Sons, Ltd.

Generalized common spatial factor model.

There are often two types of correlations in multivariate spatial data: correlations between variables measured at the same locations, and correlations of each variable across the locations. We hypothesize that these two types of correlations are caused by a common spatially correlated underlying factor. Under this hypothesis, we propose a generalized common spatial factor model. The parameters are estimated using the Bayesian method and a Markov chain Monte Carlo computing technique. Our main goals are to determine which observed variables share a common underlying spatial factor and also to predict the common spatial factor. The model is applied to county-level cancer mortality data in Minnesota to find whether there exists a common spatial factor underlying the cancer mortality throughout the state.

Specification searches in spatial econometrics: the relevance of Hendry’s methodology

This article brings together a number of new specification search strategies in spatial econometric modeling. In the literature, experimental results for several forward stepwise strategies aimed at remedying spatial dependence, have been reported. Essentially, these strategies boil down to the expansion of a spatial linear regression model with spatially lagged variables, conditional upon the results of misspecification tests. We investigate a Hendry-like specification strategy, starting from the spatial common factor model and subsequently reducing the number of spatially lagged variables on the basis of significance tests. The experimental simulations pertain to various small to large sample sizes, with spatial processes modeled on regular lattice surfaces. Our main conclusion is that the classical forward stepwise approach outperforms the Hendry strategy in terms of finding the true data generating process as well as in the observed accuracy of the estimators for spatial and non-spatial parameters. It also dominates concurrent forward stepwise strategies recently suggested in the literature.