Iterated confirmatory factor analysis for pollution source apportionment

Abstract

SUMMARYMany approaches for pollution source apportionment have been considered in the literature, most of which are based on the chemical mass balance equations. The simplest approaches for identifying the pollution source contributions require that the pollution source profiles are known. When little or nothing is known about the nature of the pollution sources, exploratory factor analysis, confirmatory factor analysis, and other multivariate approaches have been employed. In recent years, there has been increased interest in more flexible approaches, which assume little knowledge about the nature of the pollution source profiles, but are still able to produce nonnegative and physically realistic estimates of pollution source contributions. Confirmatory factor analysis can yield a physically interpretable and uniquely estimable solution, but requires that at least some of the rows of the source profile matrix be known. In the present discussion, we discuss the iterated confirmatory factor analysis (ICFA) approach. ICFA can take on aspects of chemical mass balance analysis, exploratory factor analysis, and confirmatory factor analysis by assigning varying degrees of constraint to the elements of the source profile matrix when iteratively adapting the hypothesized profiles to conform to the data. ICFA is illustrated using PM 2:5 data from Washington D.C., and a simulation study illustrates the relative strengths of ICFA, chemical mass balance approaches, and positive matrix factorization (PMF).

Evaluation of a Modified Receptor Model for Solving Multiple Time Resolution Equations: A Simulation Study

“…The agreement between the simulated and modeled contributions and profiles was evaluated for each data set by calculating the average absolute error (AAE) (Christensen and Gunst, 2004;Christensen et al, 2006;Lingwall and Christensen, 2007). Unlike other model performance statistics, such as the root mean square error (RMSE), the AAE gives the amplitude of average error without being pulled by the large one (Javitz et al, 1988;Willmott and Matsuura, 2005).…”

“…This assessment was achieved by using synthetic data as in several previous studies (Miller et al, 2002;Brinkman et al, 2006;Christensen et al, 2006;Lingwall and Christensen, 2007;Hemann et al, 2009;Vedal et al, 2009;Habre et al, 2011).…”

PM source apportionment and health effects: 1. Intercomparison of source apportionment results

“…CFA has been used in the pollution source apportionment setting by CFA models (e.g., Yang, 1994;Gleser, 1997;Christensen and Sain, 2002). A recent modification of CFA is the iterated confirmatory factor analysis (ICFA) approach, which can take on aspects of chemical mass balance analysis, exploratory factor analysis, and CFA by assigning varying degrees of constraint to the elements of the source profile matrix when iteratively adapting the hypothesized profiles to conform to the data (Christensen et al, 2004). This approach attempts to maximally utilize a priori source profile information to reduce indeterminacy and enhance interpretability in a multivariate receptor modeling scenario.…”

Receptor modeling of C<sub>2</sub>–C<sub>7</sub> hydrocarbon sources at an urban background site in Zurich, Switzerland: changes between 1993–1994 and 2005–2006

“…Depending on the degree of prior knowledge of the sources, a chemical mass balance (CMB; composition of the emission sources is known), a multivariate receptor model (no a priori knowledge) or a hybrid model in between these extreme cases is most appropriate (Hopke, 1988;Wåhlin, 2003;Christensen , 2006). The first multivariate source apportionment studies were based on the elemental composition of particulate matter (e.g.…”