Source multiple regression

PLS (partial least squares) multiple regression technique is used to estimate contributions of various polluting sources in ambient aerosol composition. The characteristics and performance of the PLS method are compared to those of chemical mass balance regression model (CMB) and target transformation factor analysis model (TTFA). Results on the Quail Roost Data, a synthetic data set generated as a basis to compare various receptor models, is reported. PLS proves to be especially useful when the elemental compositions of both the polluting sources and the aerosol samples are measured with noise and there is a high correlation in both blocks. 

Multivariate methods, on the other hand, resolve the major sources by analyzing the entire ambient data matrix. Factor analysis, for example, examines elemental and sample correlations in the ambient data matrix. This analysis yields the minimum number of factors required to reproduce the ambient data matrix, their relative chemical composition and their contribution to the mass variability. A major limitation in common and principal component factor analysis is the abstract nature of the factors and the difficulty these methods have in relating these factors to real world sources. Hopke, et al. (13.14) have improved the methods ability to associate these abstract factors with controllable sources by combining source data from the F matrix, with Malinowski s target transformation factor analysis program. (15) Hopke, et al. (13,14) as well as Klelnman, et al. (10) have used the results of factor analysis along with multiple regression to quantify the source contributions. Their approach is similar to the chemical mass balance approach except they use a least squares fit of the total mass on different filters Instead of a least squares fit of the chemicals on an individual filter. 

Comparison of the coefficients from the multiple regression analysis with available source emission data supports the validity of the models. 

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 ( ). 

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. 

It must be emphasized that the potential of multiple regression analysis to resolve sources of pharmacokinetic variations is much greater than has been realized by the particular canned1 model used previously. The technique itself is both sensitive and powerful. However, for multiple regression analysis to be used appropriately, a model must be developed that encompasses non-linear as well as linear relationships (JJ4). Error terms especially need to be appropriately modelled, rather than treated in a simply additive manner as in previous applications of this method. 

Baker (268) compared the responses of volunteers to EA 3580 administered as a dose per man or as a dose per unit of body weight. Four Indicators of effect were used accommodation for near vision, arm-hand steadiness, dynamic flexibility, and manual dexterity The general conclusion was that the use of the dose per unit of body weight may Increase variance, rather than control for extraneous sources of variation, when the purpose of a study is to establish the effects of a substance Itself The use of multiple-regression equations was suggested as an approach to the establishment of definitive Information on effects of chemicals. 

More refined forms of regression analyses have emerged to better quantify source—exposure and source—pathway—exposure relationships for lead. A particularly useful form is a variation on the multiple regression technique of structural equation modeling (SEM). Figme 9.1 shows interior dust, the principal Pb exposure pathway for infants and toddlers, arising from exterior Pb dusts, interior Pb paint, or secondary occupational ( take-home ) dusts. 

A number of correlation and regression analyses of differing complexity have been described for the Bunker Hill residents, principally for the site s childhood exposures. Table 23.4 describes two types of simpler analyses, the correlational matrix and a multiple regression model for log-transformed Pb source variables and geometric mean levels, notably the raw dust model... 

With increasing toxicity data of various kinds, more rehable predictions based on structure-toxicity relationships of toxic endpoints can be attempted [31-36]. Even the Internet can be used as a source for toxicity data, albeit with caution [37]. A number of predictive methods have been compared from a regulatory perspective [35]. Often traditional QSAR approaches using multiple Hnear regression are used [38]. Newer approaches include the use of neural networks in structure-toxicity relationships... 

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