Multivariate Receptor Models for Spatially Correlated Multipollutant Data

The goal of multivariate receptor modeling is to estimate the profiles of major pollution sources and quantify their impacts based on ambient measurements of pollutants. Traditionally, multivariate receptor modeling has been applied to multiple air pollutant data measured at a single monitoring site or measurements of a single pollutant collected at multiple monitoring sites. Despite the growing availability of multipollutant data collected from multiple monitoring sites, there has not yet been any attempt to incorporate spatial dependence that may exist in such data into multivariate receptor modeling. We propose a spatial statistics extension of multivariate receptor models that enables us to incorporate spatial dependence into estimation of source composition profiles and contributions given the prespecified number of sources and the model identification conditions. The proposed method yields more precise estimates of source profiles by accounting for spatial dependence in the estimation. More importantly, it enables predictions of source contributions at unmonitored sites as well as when there are missing values at monitoring sites. The method is illustrated with simulated data and real multipollutant data collected from eight monitoring sites in Harris County, Texas. Supplementary materials for this article, including data and R code for implementing the methods, are available online on the journal web site.

[1]  Mikyoung Jun,et al.  Non‐stationary Cross‐Covariance Models for Multivariate Processes on a Globe , 2011 .

[2]  Alessio Pollice,et al.  Major PM10 source location by a spatial multivariate receptor model , 2011, Environmental and Ecological Statistics.

[3]  C. F. Sirmans,et al.  Nonstationary multivariate process modeling through spatially varying coregionalization , 2004 .

[4]  R. Henry.  Receptor Model Applied to Patterns in Space (RMAPS)Part II–Apportionment of Airborne Particulate Sulfur from Project MOHAVE , 1997 .

[5]  P. Hopke.  An introduction to receptor modeling , 1991 .

[6]  William F. Christensen,et al.  Incorporating Time-Dependent Source Profiles Using the Dirichlet Distribution in Multivariate Receptor Models , 2010, Technometrics.

[7]  P. Paatero,et al.  PM source apportionment and health effects: 1. Intercomparison of source apportionment results , 2006, Journal of Exposure Science and Environmental Epidemiology.

[8]  R. Henry,et al.  Extension of self-modeling curve resolution to mixtures of more than three components: Part 2. Finding the complete solution , 1999 .

[9]  Alessio Pollice,et al.  Recent statistical issues in multivariate receptor models , 2011 .

[10]  Peter Guttorp,et al.  Multivariate Receptor Modeling for Temporally Correlated Data by Using MCMC , 2001 .

[11]  R. Henry.  Receptor Model Applied to Patterns in Space (RMAPS) , 1997 .

[12]  Werner Alfred Stahel,et al.  Linear unmixing of multivariate observations: a structural model , 2002 .

[13]  Tatiyana V. Apanasovich,et al.  Cross-covariance functions for multivariate random fields based on latent dimensions , 2010 .

[14]  R. Henry.  History and fundamentals of multivariate air quality receptor models , 1997 .

[15]  Philip K. Hopke,et al.  Recent developments in receptor modeling , 2003 .

[16]  P. Paatero.  Least squares formulation of robust non-negative factor analysis , 1997 .

[17]  Brent A. Coull,et al.  Multiplicative factor analysis with a latent mixed model structure for air pollution exposure assessment , 2011 .

[18]  P. Hopke.  Receptor modeling in environmental chemistry , 1985 .

[19]  Peter Guttorp,et al.  Locating major PM10 source areas in Seoul using multivariate receptor modeling , 2004, Environmental and Ecological Statistics.

[20]  Peter Guttorp,et al.  Multivariate receptor models and model uncertainty , 2002 .

[21]  P. Paatero,et al.  Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values† , 1994 .

[22]  T. Gneiting,et al.  Matérn Cross-Covariance Functions for Multivariate Random Fields , 2010 .

[23]  William F. Christensen,et al.  Accounting for Dependence in a Flexible Multivariate Receptor Model , 2002, Technometrics.

[24]  M. Goulard,et al.  Linear coregionalization model: Tools for estimation and choice of cross-variogram matrix , 1992 .

[25]  David D Billheimer,et al.  Compositional receptor modeling , 2001 .

[26]  J. Schmee.  An Introduction to Multivariate Statistical Analysis , 1986 .

[27]  Paul J Catalano,et al.  An informative Bayesian structural equation model to assess source-specific health effects of air pollution. , 2007, Biostatistics.

[28]  Ronald C. Henry,et al.  Extension of self-modeling curve resolution to mixtures of more than three components: Part 3. Atmospheric aerosol data simulation studies☆ , 1990 .

[29]  William F. Christensen,et al.  Dirichlet based Bayesian multivariate receptor modeling , 2008 .

[30]  M. Fraser,et al.  Source identification and apportionment of volatile organic compounds in Houston, TX , 2006 .

[31]  C. Spiegelman,et al.  Correspondence estimation of the source profiles in receptor modeling , 2004 .

[32]  Eun Sug Park,et al.  A computation saving jackknife approach to receptor model uncertainty statements for serially correlated data , 2007 .

[33]  Anja Vogler,et al.  An Introduction to Multivariate Statistical Analysis , 2004 .

[34]  Haotian Hang,et al.  Inconsistent Estimation and Asymptotically Equal Interpolations in Model-Based Geostatistics , 2004 .

[35]  Ronald C. Henry,et al.  Bilinear estimation of pollution source profiles and amounts by using multivariate receptor models , 2002 .

[36]  Jeff W. Lingwall,et al.  Iterated confirmatory factor analysis for pollution source apportionment , 2006 .