Performance of propensity score weighting in structural equation modeling

In order to make causal statements based on the results of a research study, one must eliminate any possible confounding variables. When a study does not randomize its participants into groups, the different treatment and control groups cannot be treated as equivalent at baseline, and a statistical correction must be undertaken to justify any subsequent causal statements. This dissertation evaluated the use of propensity score weighting in structural equation modeling to correct for non-equivalence by incorporating the propensity score weights into the loglikelihood equation and formulas for standard errors and test statistics. The use of propensity score weights together with structural equation models is appropriate for any non-randomized treatment study with latent variable outcomes. A series of simulations were conducted to assess the impact of several data-related and model-fitting-related variables. It was found that the method studied in this dissertation is a large-sample technique, requiring a sample size of at least 500 in order to produce unbiased treatment effect estimates; however, it was difficult to attain the nominal Type-I error rate even with a sample size of 5,000. A large amount of propensity score distribution overlap (~70%) is needed. Correctly specified propensity score models, or models with extra predictors, performed better than models that omitted confounding variables. An illustrative data analysis was used to show how to conduct this type of analysis on real data. It was shown that ignoring the non-equivalence of the groups led to an overestimation of the treatment effect estimate