A primary objective of current air pollution research is the assessment of health effects related to specific sources of air particles, 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 apportionment, 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.