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Table 7 Model notation

From: Using electronic transaction data to add geographic granularity to official estimates of retail sales

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