Propensity Score Analysis of Complex Survey Data with Structural Equation Modeling: A Tutorial with Mplus

Abstract

Propensity score (PS) analysis aims to reduce bias in treatment effect estimates obtained from observational studies, which may occur due to non-random differences between treated and untreated groups with respect to covariates related to the outcome. We demonstrate how to use structural equation modeling (SEM) for PS analysis to remove selection bias due to latent covariates and estimate treatment effects on latent outcomes. Following the discussion of the design and analysis stages of PS analysis with SEM, an example is presented which uses the Mplus software to analyze data from the 1999 School and Staffing Survey (SASS) and 2000 Teacher Follow-up Survey (TFS) to estimate the effects teacher’s participation in a network of teachers on the teacher’s perception of workload manageability.

Keywords:

• causal inference
• latent confounders
• potential outcomes framework
• propensity score analysis
• propensity score weighting
• Rubin’s Causal model
• sensitivity analysis
• structural equation modeling

Notes

¹ Mplus code to estimate the ATE for this example is available on the online supplemental materials.

² The code for invariance testing of latent covariates is shown in Appendix 2.

³ In this case, auxiliary variables are not used in the analysis (see pp. 615–616 of the Mplus 8 manual).

⁴ In Mplus, this is accomplished by adding the STDY option to the OUTPUT: command (see p.800 of the Mplus 8 manual).

⁵ Appendix 3 shows the estimation of propensity scores, while appendices 4 and 5 shown balance evaluation.

⁶ Appendix 6 shows the Mplus code for invariance testing of the measurement model of the outcome.

⁷ Appendix 7 shows Mplus code for the multiple-group CFA to estimate the ATT.

⁸ Appendix 8 presents the Mplus code for multiple-group SEM with interactions.

⁹ Appendix 9 presents the code for sensitivity analysis.

¹⁰ The standardized factor loadings for the indicators of the latent confounders are shown in Appendix 1.

¹¹ The standardized factor loading estimates from CFA of workload manageability are shown in Appendix 1.