165 Environmetrics Research Article Received: 17 May 2008, Accepted: 25 November 2009, Published online in Wiley Online Library: 12 February 2010 (wileyonlinelibrary.com) DOI: 10.1002/env.1039 Multiplicative factor analysis with a latent mixed model structure for air pollution exposure assessment Margaret C. Nikolov a∗ , Brent A. Coull a , Paul J. Catalano a and John J. Godleski b A primary objective of current air pollution research is the assessment of health effects related to specific sources of air parti- cles, or particulate matter (PM). Because most PM health studies do not observe the activity of the pollution sources directly, investigators must infer pollution source contributions based on a complex mixture of exposure. Methods such as source apportionment and multivariate receptor modeling use standard factor analytic techniques to estimate the source-specific contributions from a large number of observed chemical components. In the interest of a more flexible source apportion- ment, we propose a multiplicative factor analysis with a latent mixed model structure on the latent source contributions. A factor analysis with multiplicative errors serves to maintain the non-negativity of the measured chemical concentrations. A mixed model on the latent source contributions provides for systematic effects on source contributions as well as an adjustment for residual correlation in the source-specific exposures. In a simulation study, we examine the impact of (1) accounting for meteorological covariates and (2) adjusting for temporal correlation in the exposures on the estimation of the source profiles and the source contributions. Finally, we explore the influence of meteorological conditions on source-specific exposures in an analysis of PM exposure data from an animal toxicology study. Copyright © 2010 John Wiley & Sons, Ltd. Keywords: latent variable; source apportionment; factor analysis; multiplicative error; mixed model 1. INTRODUCTION Evaluation of health effects associated with major sources of air pollution, such as power plants and motor vehicles, often relies on the characterization of complex air pollution exposures. In most health effects studies, investigators are unable to measure the activity of the pollution sources directly, and instead collect samples of ambient air, which reflect dynamic mixtures of source contributions. Methods such as source apportionment and multivariate receptor modeling use factor analytic techniques to estimate the contributions of a small number of pollution sources from the measured mixture components. While the exposure assessment literature contains a large amount of research that focuses on estimation of source-specific contributions (i.e., Koutrakis and Spengler, 1987; Kavouras et al., 2001; and for review see Seigneur et al., 1999; Hopke, 2003; Kim et al., 2004), little work has been done to explore the role of important factors that influence source activity in a formal way. For over a decade, researchers at the Harvard School of Public Health (HSPH) have been conducting animal toxicology studies to evaluate the mechanisms of morbidity and mortality associated with ambient air particulate matter (PM). As part of these studies, samples of Boston aerosol have been collected, concentrated, and analyzed for a series of elements and other chemical components. Source apportionment analyses of these exposure mixtures have indicated four major sources of Boston PM; resuspended road dust consisting mainly of the crustal elements (Si and Al), coal-fired power plants (S and SULF), oil combustion primarily for home heating (Ni and V), and motor vehicle exhaust (BC, OC, and EC) (Oh et al., 1997; Clarke et al., 2000; Batalha et al., 2002). Source apportionment methods used to analyze the Boston PM exposures characterize pollution sources strictly in terms of the source profiles and the source contributions. Presently, researchers seek to better characterize source activity. A primary research objective is to allow the unobserved source contributions to depend on systematic effects, such as meteorological conditions. Consider, for instance, the potential for temperature to influence source activity. During periods of low temperature, home heating typically increases, which results in elevated contributions from oil combustion. Under this scenario, incorporating information on temperature in the source apportionment model may provide for better characterization of the oil combustion pollution source. Extending source apportionment methods to allow for systematic effects, such as meteorology, on the source activities may lead to better estimation of the source profiles and, more importantly, the source contributions. ∗ Correspondence to: M. C. Nikolov, 603 Knollwood Road, Severna Park, MD 21146, U.S.A. E-mail: meg.nikolov@gmail.com a Margaret C. Nikolov, Brent A. Coull, Paul J. Catalano Department of Biostatistics, Harvard School of Public Health, Boston, MA 02115, U.S.A. b John J. Godleski Department of Environmental Health, Harvard School of Public Health, Boston, MA 02115, U.S.A. Environmetrics 2011; 22: 165–178 Copyright © 2010 John Wiley & Sons, Ltd.