ABSTRACT: Causality in statistical models is a topic of intense interest in contemporary research. Counterfactural definitions of causality, selectivity effects as confounders, and propensity scoring are just a few of the issues that are part of current debates. Each of these issues is relevant to Sructural Equation Models (SEMs), but they have received less attention than warranted in the SEM literature. For instance, in my 1989 Structral Equations with Latent Variables , I have a separate chapter devoted to causality in SEMs and the preceding causal issues are given minimal attention. In this talk I will discuss how some of these issues in current causality discussions mesh with SEMs and how consideration of these issues would alter the causality chapter that I wrote two decades ago.

ABSTRACT: Standardization is a useful method for confounder adjustment through stratification. It has been frequently used in epidemiologic research. For many confounding variables, stratification does not work well because data will be so sparse. In that case parametric model-based standardization is used. Recently, a new causal model called marginal structural model was proposed and its nonparametric standardization interpretation was given. I will discuss the relationship between the doubly robust estimator and those parametric model-based and nonparametric marginal structural model standardization methods. The doubly robust estimator is the estimator of the causal parameter of interest which is consistent when either the parametric outcome regression model or the propensity score model is correct. I also give doubly robust estimators in different target populations.

ABSTRACT: Estimation of average treatment effects under unconfoundedness or exogenous treatment assignment is often hampered by lack of overlap in the covariate distributions. This lack of overlap can lead to imprecise estimates and can make commonly used estimators sensitive to the choice of specification. In such cases researchers have often used informal methods for trimming the sample. In this paper we develop a systematic approach to addressing such lack of overlap. We characterize optimal subsamples for which the average treatment effect can be estimated most precisely, as well as optimally weighted average treatment effects. Under some conditions the optimal selection rules depend solely on the propensity score. For a wide range of distributions a good approximation to the optimal rule is provided by the simple selection rule to drop all units with estimated propensity scores outside the range $[0.1,0.9]$.

ABSTRACT: A causal effect may be defined as a comparison among the potential outcomes that would be realized if different treatments could be applied to the same individual. Literature on causal inference has emphasized methods for estimating average causal effects in a population. Generalizing this idea, we define a semiparametric model that allows average causal effects to vary in relation to a set of analytic variables. This marginal causal model (MCM) is similar to the marginal structural model of Robins et al., but we apply a different estimation strategy based on imputation of the missing potential outcomes. Imputed values are generated under a second model that accounts for confounding variables and, possibly, estimated propensities of treatment; the latter may help to reduce bias when the imputation model is wrong. Coefficients of the MCM are estimated by solving a set of imputed estimating equations, with asymptotic standard errors computed by a sandwich formula.