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A Propensity Score Adjustment for Multiple Group Structural Equation Modeling

Published online by Cambridge University Press:  01 January 2025

Takahiro Hoshino ,
Hiroshi Kurata  and
Kazuo Shigemasu
Takahiro Hoshino*
Affiliation:
The University of Tokyo
Hiroshi Kurata
Affiliation:
The University of Tokyo
Kazuo Shigemasu
Affiliation:
The University of Tokyo
*
Requests for reprints should be sent to Takahiro Hoshino, Department of Cognitive and Behavioral Science, The University of Tokyo, 4-3-5 yanaka, Taito-ku, Tokyo, 110-0001, Japan. E-mail: [email protected]
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Abstract

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 χ12 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.

Keywords

causal inferencestructural equation modelingobservational studytwo step estimationM estimationunconfoundedness
Type
Original Paper
Information
Psychometrika , Volume 71 , Issue 4 , December 2006 , pp. 691 - 712
Copyright
Copyright © 2007 The Psychometric Society

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