Erratum to: A Two-Step Bayesian Approach for Propensity Score Analysis: Simulations and Case Study

Erratum to: PSYCHOMETRIKA 2012 DOI10.1007/s11336-012-9262-8

In Equation (19) of the paper, the denominator m should be deleted. In the BPSA-1 hybrid approach, we view the treatment effect estimate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\hat{\gamma}$\end{document} as the posterior mean of γ based on the posterior distribution of propensity score model parameters rather than the frequentist-based mean of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\hat{\gamma}_{j}$\end{document} as shown in Equations (14) and (15). We utilize the total variance formula to estimate the variance of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\hat{\gamma}$\end{document} in BPSA-1. Then

(16)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathit{Var}(\hat{\gamma})=E\bigl\{\mathit{Var}(\hat{\gamma}\mid \eta)\bigr\} + \mathit{Var}\bigl\{E(\hat{\gamma}\mid\eta)\bigr\}. $$\end{document}

From Equation (16) to (18) with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\hat{\gamma}_{1}$\end{document} replaced by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\hat{\gamma}$\end{document} we obtain the corrected Equation (19)

(19)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathit{Var}(\hat{\gamma})=m^{-1}\sum_{j=1}^m \hat{\sigma}^2_j+(m-1)^{-1}\sum_{j=1}^m \Biggl(\hat{\gamma}_j-m^{-1}\sum_{j=1}^m \hat{\gamma}_j\Biggr)^2. $$\end{document}

All the results presented in the tables are correct and based on this variance expression.