Estimation of Average Total Effects in Quasi-Experimental Designs : Nonlinear Contraints in Structural Equation Models
This thesis focuses on estimating and testing average total effects in quasi-experimental designs based on the stochastic theory of causal effects (Steyer, et al., in press). Three issues are investigated that are crucial for statistical inference about average total effects in quasi-experimental designs: (1) Interactions between covariates and the treatment variable, (2) stochasticity of covariates and the resulting nonlinearity of the hypothesis of no average total effect, and (3) heterogeneity of residual variances. It is shown that the standard error for the average total effect estimator of the general linear model and of sample mean-centered covariates is often biased if there are interactions between covariates and the treatment variable and if the covariates are stochastic. Assuming a joint distribution is necessary for developing unbiased standard errors for estimators of the average total effect. Therefore, structural equation models with nonlinear constraints of estimated parameters are studied for the implementation of generalized analysis of covariance and compared to different standard error corrections in the general linear model, for instance, robust standard errors based on heteroscedasticity-consistent estimators (White, 1980) and adjusted standard errors for regression estimates (Schafer & Kang, 2008). The results of a simulation study confirm the adequacy of appropriately specified structural equation models with nonlinear constraints for the analysis of average total effects in observational studies and confirm the augmentation approach implemented in EffectLite (Steyer & Partchev, 2008). It is shown that the adjusted standard errors for regression estimates are unbiased under all considered conditions and that the statistical power of our Wald-test statistic for the nonlinear constraint is comparable overall to the tests based on the adjusted standard errors for all simulated data sets with medium and large sample sizes.