title: Using a latent variable model with non-constant factor loadings to examine PM2.5constituents related to secondary inorganic aerosols.
abstract: Factor analysis is a commonly used method of modelling correlated multivariate exposure data. Typically, the measurement model is assumed to have constant factor loadings. However, from our preliminary analyses of the Environmental Protection Agency's (EPA's) PM2.5fine speciation data, we have observed that the factor loadings for four constituents change considerably in stratified analyses. Since invariance of factor loadings is a prerequisite for valid comparison of the underlying latent variables, we propose a factor model that includes non-constant factor loadings that change over time and space using P-spline penalized with the generalized cross-validation (GCV) criterion. The model is implemented using the Expectation-Maximization (EM) algorithm and we select the multiple spline smoothing parameters by minimizing the GCV criterion with Newton's method during each iteration of the EM algorithm. The algorithm is applied to a one-factor model that includes four constituents. Through bootstrap confidence bands, we find that the factor loading for total nitrate changes across seasons and geographic regions.
authors.affiliation: Department of Biostatistics, University of Michigan, Ann Arbor, USA.
authors.forename: Zhenzhen
authors.initials: Z
authors.lastname: Zhang
authors.affiliation: Department of Environmental Health Sciences, University of Michigan, Ann Arbor, USA; Department of Epidemiology, University of Michigan, Ann Arbor, USA.
authors.forename: Marie S
authors.initials: MS
authors.lastname: O'Neill
authors.affiliation: Department of Biostatistics, University of Michigan, Ann Arbor, USA.
authors.forename: Brisa N
authors.initials: BN
authors.lastname: Sánchez
keywords: EM algorithm; P-spline; PM2.5 constituents; factor model; generalized cross-validation; non-constant factor loading; tensor product spline basis