Table 2 Regression model forms.
From: Secondary organic aerosol association with cardiorespiratory disease mortality in the United States
Model | Form | Description |
|---|---|---|
Single Pollutant (SP) | \({{{\boldsymbol{D}}}}={\beta }_{0}+{\beta }_{1}{{{\boldsymbol{P}}}}{{{{\boldsymbol{M}}}}}_{{{{\boldsymbol{i}}}}}+\mathop{\sum }\limits_{j=1}^{N}{\beta }_{j}^{{{\hbox{'}}}}{{{{\boldsymbol{C}}}}}_{{{{\boldsymbol{j}}}}}\) | Primary models evaluating association of PM2.5 or a component with mortality |
Single Pollutant-Adjusted for total PM2.5 (SP-adj) | \({{{\boldsymbol{D}}}}={\beta }_{0}+{\beta }_{1}{{{\boldsymbol{P}}}}{{{{\boldsymbol{M}}}}}_{{{{\boldsymbol{i}}}}}+{\beta }_{2}{{{\boldsymbol{P}}}}{{{{\boldsymbol{M}}}}}_{2.5}+\mathop{\sum }\limits_{j=1}^{N}{\beta }_{j}^{{{\hbox{'}}}}{{{{\boldsymbol{C}}}}}_{{{{\boldsymbol{j}}}}}\) | SP model with adjustment of components for total PM2.5 |
Residual (R) | \({{{\boldsymbol{D}}}}={\beta }_{0}+{\beta }_{1}{{{\boldsymbol{residua}}}}{{{{\boldsymbol{l}}}}}_{{{{\boldsymbol{i}}}}}+\mathop{\sum }\limits_{j=1}^{N}{\beta }_{j}^{{{\hbox{'}}}}{{{{\boldsymbol{C}}}}}_{{{{\boldsymbol{j}}}}}\) where residuali = PMi – mi × PM2.5 – bi and mi and bi are component-specific coefficients obtained from the regression: PMi = mi × PM2.5 + bi | Second adjustment model of PM2.5 components for total PM2.5 based on residuals from regressing total PM2.5 components on PM2.5 |
Multipollutant (MP) | \(\begin{array}{c}{{{\boldsymbol{D}}}}={\beta }_{0}+\{{\beta }_{1}{{{\boldsymbol{P}}}}{{{{\boldsymbol{M}}}}}_{{{{\boldsymbol{OA}}}}}\}+{\beta }_{2}{{{\boldsymbol{P}}}}{{{{\boldsymbol{M}}}}}_{{{{\boldsymbol{Sea}}}}{{{\boldsymbol{spray}}}}}+{\beta }_{3}{{{\boldsymbol{P}}}}{{{{\boldsymbol{M}}}}}_{{{{\boldsymbol{Soot}}}}}\\ \qquad\quad\,+{\beta }_{4}{{{\boldsymbol{P}}}}{{{{\boldsymbol{M}}}}}_{{{{\boldsymbol{N}}}}{{{{\boldsymbol{H}}}}}_{4}{{{\boldsymbol{N}}}}{{{{\boldsymbol{O}}}}}_{3}}+{\beta }_{5}{{{\boldsymbol{P}}}}{{{{\boldsymbol{M}}}}}_{{{{\boldsymbol{S}}}}{{{{\boldsymbol{O}}}}}_{4}}+{\beta }_{6}{{{\boldsymbol{P}}}}{{{{\boldsymbol{M}}}}}_{{{{\boldsymbol{Dust}}}}}+\mathop{\sum }\limits_{j=1}^{N}{\beta }_{j}^{{\prime} }{{{{\boldsymbol{C}}}}}_{{{{\boldsymbol{j}}}}}\end{array}\) | Model with 6 primary PM2.5 components including OA to evaluate their independent associations |
Multipollutant OA (MP OA) | \(\begin{array}{c}{{{\boldsymbol{D}}}}={\beta }_{0}+\{{\beta }_{1}{{{\boldsymbol{P}}}}{{{{\boldsymbol{M}}}}}_{{{{\boldsymbol{SOA}}}}}+{\beta }_{2}{{{\boldsymbol{P}}}}{{{{\boldsymbol{M}}}}}_{{{{\boldsymbol{POA}}}}}\}+{\beta }_{3}{{{\boldsymbol{P}}}}{{{{\boldsymbol{M}}}}}_{{{{\boldsymbol{Sea}}}}{{{\boldsymbol{spray}}}}}\\ \,+{\beta }_{4}{{{\boldsymbol{P}}}}{{{{\boldsymbol{M}}}}}_{{{{\boldsymbol{Soot}}}}}+{\beta }_{5}{{{\boldsymbol{P}}}}{{{{\boldsymbol{M}}}}}_{{{{\boldsymbol{N}}}}{{{{\boldsymbol{H}}}}}_{4}{{{\boldsymbol{N}}}}{{{{\boldsymbol{O}}}}}_{3}}+{\beta }_{6}{{{\boldsymbol{P}}}}{{{{\boldsymbol{M}}}}}_{{{{\boldsymbol{S}}}}{{{{\boldsymbol{O}}}}}_{4}}\\ \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!+{\beta }_{7}{{{\boldsymbol{P}}}}{{{{\boldsymbol{M}}}}}_{{{{\boldsymbol{Dust}}}}}+\mathop{\sum }\limits_{j=1}^{N}{\beta }_{j}^{{\prime} }{{{{\boldsymbol{C}}}}}_{{{{\boldsymbol{j}}}}}\end{array}\) | Multipollutant composition model as in MP but with refinement of OA (OA subdivided into SOA and POA) |
Multipollutant SOA (MP SOA) | \(\begin{array}{c}{{{\boldsymbol{D}}}}={\beta }_{0}+\big\{{\beta }_{1}{{{\boldsymbol{P}}}}{{{\boldsymbol{M}}}}_{{{{\boldsymbol{SO}}}}{{{\boldsymbol{A}}}}_{{{\boldsymbol{BVOC}}}}}+{\beta }_{2}{{{\boldsymbol{P}}}}{{{\boldsymbol{M}}}}_{{{{\boldsymbol{SO}}}}{{{\boldsymbol{A}}}}_{{{\boldsymbol{AVOC}}}}}\\ \qquad\qquad+{\beta }_{3}{{{\boldsymbol{P}}}}{{{\boldsymbol{M}}}}_{{{{\boldsymbol{POA}}}}}\big\}+{\beta }_{4}{{{\boldsymbol{P}}}}{{{\boldsymbol{M}}}}_{{{{\boldsymbol{Sea}}}}{{{\boldsymbol{spray}}}}}+{\beta }_{5}{{{\boldsymbol{P}}}}{{{\boldsymbol{M}}}}_{{{{\boldsymbol{Soot}}}}}\\ \qquad\qquad\qquad\;\;+{\beta }_{6}{{{\boldsymbol{P}}}}{{{\boldsymbol{M}}}}_{{{{\boldsymbol{N}}}}{{{\boldsymbol{H}}}}_{4}{{{\boldsymbol{N}}}}{{{\boldsymbol{O}}}}_{3}}+{\beta }_{7}{{{\boldsymbol{P}}}}{{{\boldsymbol{M}}}}_{{{{\boldsymbol{S}}}}{{{\boldsymbol{O}}}}_{4}}+{\beta }_{8}{{{\boldsymbol{P}}}}{{{\boldsymbol{M}}}}_{{{{\boldsymbol{Dust}}}}}+\mathop{\sum }\limits_{j=1}^{N}{\beta }_{j}^{\prime} {{{\boldsymbol{C}}}}_{{{\boldsymbol{j}}}}\end{array}\) | Multipollutant composition model as in MP OA but with refinement of SOA into SOA from oxidation of VOCs that are predominantly biogenic (BVOC) and anthropogenic (AVOC) in origin. |
