Table 7 Model notation
Notation | Definition |
|---|---|
\(\theta_{ijk}\) | Retail sales (estimand of interest) |
\(\varvec{x}_{{\varvec{ijk}}}\) | Vector of covariates from among \(EC_{ijk}\), \(POP_{ijk}\), \(QE\_ACC_{ijk}\), \(QE\_CON_{ijk}\), and \(QE\_RET_{ijk}\) (all on the log scale) and also an intercept |
\(\varvec{\beta}\) | Vector of coefficients |
\(q\) | Length of vectors \(\varvec{x}_{{\varvec{ijk}}}\) and \(\varvec{\beta}\) |
\(u_{ij}\) | Random effect to account for geographical division |
\(\tau^{2}\) | Variance of \(u_{ij}\) |
\(\varepsilon_{ijk}\) | Residual error at the state level |
\(\sigma^{2}\) | Variance of \(\varepsilon_{ijk}\) |
\(B\) | Posterior sample size |
\(b\) | Index for the posterior draws |