TY - JOUR

T1 - A Bayesian propensity score adjustment for latent variable modeling and MCMC algorithm

AU - Hoshino, Takahiro

N1 - Funding Information:
This work was supported by JPSP KAKENHI(187-30406).

PY - 2008/1/1

Y1 - 2008/1/1

N2 - The estimation of the differences among groups in observational studies is frequently inaccurate owing to a bias caused by differences in the distributions of covariates. In order to estimate the average treatment effects when the treatment variable is binary, Rosenbaum and Rubin [1983. The central role of the propensity score in observational studies for causal effects. Biometrika 70, 41-55] proposed an adjustment method for pre-treatment variables using propensity scores. Imbens [2000. The role of the propensity score in estimating dose-response functions. Biometrika 87, 706-710] extended the propensity score methodology for estimation of average treatment effects with multivalued treatments. However, these studies focused only on estimating the marginal mean structure. In many substantive sciences such as the biological and social sciences, a general estimation method is required to deal with more complex analyses other than regression, such as testing group differences on latent variables. For latent variable models, the EM algorithm or the traditional Monte Carlo methods are necessary. However, in propensity score adjustment, these methods cannot be used because the full distribution is not specified. In this paper, we propose a quasi-Bayesian estimation method for general parametric models that integrate out the distributions of covariates using propensity scores. Although the proposed Bayes estimates are shown to be consistent, they can be calculated by existing Markov chain Monte Carlo methods such as Gibbs sampler. The proposed method is useful to estimate parameters in latent variable models, while the previous methods were unable to provide valid estimates for complex models such as latent variable models. We also illustrated the procedure using the data obtained from the US National Longitudinal Survey of Children and Youth (NLSY1979-2002) for estimating the effect of maternal smoking during pregnancy on the development of the child's cognitive functioning.

AB - The estimation of the differences among groups in observational studies is frequently inaccurate owing to a bias caused by differences in the distributions of covariates. In order to estimate the average treatment effects when the treatment variable is binary, Rosenbaum and Rubin [1983. The central role of the propensity score in observational studies for causal effects. Biometrika 70, 41-55] proposed an adjustment method for pre-treatment variables using propensity scores. Imbens [2000. The role of the propensity score in estimating dose-response functions. Biometrika 87, 706-710] extended the propensity score methodology for estimation of average treatment effects with multivalued treatments. However, these studies focused only on estimating the marginal mean structure. In many substantive sciences such as the biological and social sciences, a general estimation method is required to deal with more complex analyses other than regression, such as testing group differences on latent variables. For latent variable models, the EM algorithm or the traditional Monte Carlo methods are necessary. However, in propensity score adjustment, these methods cannot be used because the full distribution is not specified. In this paper, we propose a quasi-Bayesian estimation method for general parametric models that integrate out the distributions of covariates using propensity scores. Although the proposed Bayes estimates are shown to be consistent, they can be calculated by existing Markov chain Monte Carlo methods such as Gibbs sampler. The proposed method is useful to estimate parameters in latent variable models, while the previous methods were unable to provide valid estimates for complex models such as latent variable models. We also illustrated the procedure using the data obtained from the US National Longitudinal Survey of Children and Youth (NLSY1979-2002) for estimating the effect of maternal smoking during pregnancy on the development of the child's cognitive functioning.

KW - Causal inference

KW - Covariance structure analysis

KW - Markov chain Monte Carlo methods

KW - Observational study

KW - Structural equation modeling

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U2 - 10.1016/j.csda.2007.03.024

DO - 10.1016/j.csda.2007.03.024

M3 - Article

AN - SCOPUS:35548979035

SN - 0167-9473

VL - 52

SP - 1413

EP - 1429

JO - Computational Statistics and Data Analysis

JF - Computational Statistics and Data Analysis

IS - 3

ER -