A propensity score adjustment for multiple group structural equation modeling

Takahiro Hoshino, Hiroshi Kurata, Kazuo Shigemasu

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


In the behavioral and social sciences, quasi-experimental and observational studies are used due to the difficulty achieving a random assignment. However, the estimation of differences between groups in observational studies frequently suffers from bias due to differences in the distributions of covariates. To estimate average treatment effects when the treatment variable is binary, Rosenbaum and Rubin (1983a) proposed adjustment methods for pretreatment variables using the propensity score. However, these studies were interested only in estimating the average causal effect and/or marginal means. In the behavioral and social sciences, a general estimation method is required to estimate parameters in multiple group structural equation modeling where the differences of covariates are adjusted. We show that a Horvitz-Thompson-type estimator, propensity score weighted M estimator (PWME) is consistent, even when we use estimated propensity scores, and the asymptotic variance of the PWME is shown to be less than that with true propensity scores. Furthermore, we show that the asymptotic distribution of the propensity score weighted statistic under a null hypothesis is a weighted sum of independent χ1 2 variables. We show the method can compare latent variable means with covariates adjusted using propensity scores, which was not feasible by previous methods. We also apply the proposed method for correlated longitudinal binary responses with informative dropout using data from the Longitudinal Study of Aging (LSOA). The results of a simulation study indicate that the proposed estimation method is more robust than the maximum likelihood (ML) estimation method, in that PWME does not require the knowledge of the relationships among dependent variables and covariates.

Original languageEnglish
Pages (from-to)691-712
Number of pages22
Issue number4
Publication statusPublished - 2006 Dec 1
Externally publishedYes


  • Causal inference
  • M estimation
  • Observational study
  • Structural equation modeling
  • Two step estimation
  • Unconfoundedness

ASJC Scopus subject areas

  • Psychology(all)
  • Applied Mathematics


Dive into the research topics of 'A propensity score adjustment for multiple group structural equation modeling'. Together they form a unique fingerprint.

Cite this