equations

Model 1 CVD

$$ \[\begin{aligned} & \text{cvd\_deaths}_{ijk} \sim \text{Poisson}(\text{pop\_in\_agegrp}_{ijk} \rho_{ijk}) \\ & \log(\rho_{ijk}) = \beta_0 + \beta_1 \text{scale(pm25)}_{ijk} + u_{\text{age\_group}_i} + u_{\text{year}_j} + u_{\text{GEOID}_k} + \log(\text{pop\_in\_agegrp}_{ijk}) \end{aligned}\] \[\begin{aligned} & u_{\text{age\_group}_i} \sim \text{Normal}(0, \sigma^2_{\text{age\_group}}) \\ & u_{\text{year}_j} \sim \text{Normal}(0, \sigma^2_{\text{year}}) \\ & u_{\text{GEOID}_k} \sim \text{Normal}(0, \sigma^2_{\text{GEOID}}) \end{aligned}\]

$$

Model 2 CVD

$$ \[\begin{aligned} & \text{cvd\_deaths}_{ijk} \sim \text{Poisson}(\text{pop\_in\_agegrp}_{ijk} \rho_{ijk}) \\ & \log(\rho_{ijk}) = \beta_0 + \beta_1 \text{scale(pm25)}_{ijk} + \beta_2 \text{scale(maxairtemp)}_{ijk} \\ & \quad + u_{\text{age\_group}_i} + u_{\text{year}_j} + u_{\text{GEOID}_k} + \log(\text{pop\_in\_agegrp}_{ijk}) \end{aligned}\] \[\begin{aligned} & u_{\text{age\_group}_i} \sim \text{Normal}(0, \sigma^2_{\text{age\_group}}) \\ & u_{\text{year}_j} \sim \text{Normal}(0, \sigma^2_{\text{year}}) \\ & u_{\text{GEOID}_k} \sim \text{Normal}(0, \sigma^2_{\text{GEOID}}) \end{aligned}\]

$$

Model 3 CVD \[ \begin{aligned} & \text{cvd\_deaths}_{ijkl} \sim \text{Poisson}(\text{pop\_in\_agegrp}_{ijkl} \rho_{ijkl}) \\ & \log(\rho_{ijkl}) = \beta_0 + \beta_1 \text{scale(pm25)}_{ijkl} + \beta_2 \text{scale(maxairtemp)}_{ijkl} + \beta_3 \text{scale(mhhi)}_{ijkl} \\ & \quad + \beta_4 \text{scale(p\_below\_pov)}_{ijkl} + \beta_5 \text{scale(speakeng)}_{ijkl} + \beta_6 \text{scale(pwhite)}_{ijkl} \\ & \quad + \beta_7 \text{scale(pblack)}_{ijkl} + \beta_8 \text{scale(phisp)}_{ijkl} \\ & \quad + u_{\text{age\_group}_i} + u_{\text{year}_j} + u_{\text{GEOID}_k} \\ & \quad + \log(\text{pop\_in\_agegrp}_{ijkl}) \end{aligned} \]