Due to the difficulty in achieving a random assignment, a quasi-experimental or observational study design is frequently used in the behavioral and social sciences. If a nonrandom assignment depends on the covariates, multiple group structural equation modeling, that includes the regression function of the dependent variables on the covariates that determine the assignment, can provide reasonable estimates under the condition of correct specification of the regression function. However, it is usually difficult to specify the correct regression function because the dimensions of the dependent variables and covariates are typically large. Therefore, the propensity score adjustment methods have been proposed, since they do not require the specification of the regression function and have been applied to several applied studies. However, these methods produce biased estimates if the assignment mechanism is incorrectly specified. In order to make a more robust inference, it would be more useful to develop an estimation method that integrates the regression approach with the propensity score methodology. In this study we propose a doubly robust-type estimation method for marginal multiple group structural equation modeling. This method provides a consistent estimator if either the regression function or the assignment mechanism is correctly specified. A simulation study indicates that the proposed estimation method is more robust than the existing methods.
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