Particulate regression models

Multivariate regression models have been developed for apportioning the contributions of emission sources to airborne particulate organic matter. 

In developing a multiple regression model for apportioning sources of TSP in New York City, Kleinman, et al.(2) selected Pb, Mn, Cu, V and SO, as tracers for automotive sources, soil-related sources, incineration, oil-burning and secondary particulate matter, respectively. These were chosen on the basis of the results of factor analysis and a qualitative knowledge of the principal types of sources in New York City and the trace metals present in emissions from these types of sources. Secondary TSP, automotive sources and soil resuspension were found to be the principal sources of TSP in 1974 and 1975 ( ). 

For comparison purposes, regression parameters were computed for the model defined by Equations 6, 7, 8, and 10 and the model obtained by replacing In (1/R) in those equations by R. The dependent variable (y) is particulate concentration because it is desired to predict particulate content from reflectance values. Data from Tables I and II were also fitted to exponential and power functions where the independent variable (x) was reflectance but the fits were found to be inferior to that of the linear relationship. 

Particulate Functions. Table IV sunmarizes the regression results from exploring linear relationships between dust and trash levels in cotton. Exponential and power relationships were considered but the fits were found inferior to the linear case. The unexplained variation ranging from 1% to 9% suggest that a model leading to Equation 7 and 9 may indeed be an appropriate choice. 

The samples were analyzed for trace metals and sulfate as well as for three fractions of particulate organic matter (POM) using sequential extraction with cyclohexane (CYC), dichloromethane (DCM) and acetone (ACE). Factor analysis was used to identify the principal types of emission sources and select source tracers. Using the selected source tracers, models were developed of the form POM = a(V) + b(Pb) + - - -, where a and b are regression coefficients determined from ambient data adjusted to constant dispersion conditions. The models for CYC and ACE together, which constitute 90% of the POM, indicate that 40% (3.0 pg/m ) of the mass was associated with oil-burning, 19% (1.4 pg/m ) was from automotive and related sources and 15% (1.1 pg/m ) was associated with soil-like particles. 

Multiple Regression Source Apportionment Models for Airborne Particulate Organic Matter in New York City... 

Source Apportionment Models for the Cyclohexane-Soluble Fraction of Respirable Suspended Particulate Matter. Stepwise multiple regression analysis was used to determine the coefficients of the source tracers for the models proposed for CYC in equations (7)-(9). These models are shown in Table IV. As expected from the factor analyses, the coefficient for V, accounting for the greatest proportion of the variance of CYC, was fitted first into the equation. Equation (14) was the simplest and the F value was slightly higher than for equations (15) and (16). In addition, as will be discussed later in this paper, the coefficient for PB was in reasonable agreement with the ratio of CYC /PB for samples collected in the Allegheny Tunnel. 

Comparisons of the regression coefficients of the source tracer elements with available source emission data, as well as comparisons with estimated source emission data for total suspended particulate matter, provide evidence of the validity of the models. 

Keywords Bayes theorem conditional probability information entropy Kalman Filter Markov Chain Monte Carlo simulation model identifiability particulate matter regression problem reliability structural health monitoring... 

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