Enabling Propensity Score Analysis In Structural Equation Modeling: Advanced Topics In Causal Inference

Background and Purpose   Propensity score analysis (PSA) and structural equation modeling (SEM) are widely applied by social work researchers. PSA offers an approach to program evaluation when randomized controlled trials are infeasible, unethical, or when researchers need to draw causal inferences from survey, census, administrative, or other types of observational data. SEM enables researchers to study complex relationships, including those when some variables are latent. The underlying relationship, or structure, among variables is formulated as a model, and often articulated graphically through path diagrams. Despite ongoing and increasing use of PSA and SEM methods, few attempts have been made to combine PSA and SEM into a single approach. Insufficient attention to latent variables, measurement error, testing overidentification, and comparing parameters across groups are the weaknesses of PSA, but attention to these are among the strengths of SEMs.  Inadequate consideration of selectivity is a weak point of latent variable SEM, but is the key strength of PSA. This workshop addresses the problem of selection bias in non-experimental data by describing practical statistical and methodological tools that will enable social work researchers to conduct PSA in SEM and, as a result, take advantage of their complementary strengths.

Contents  The workshop covers the following topics: (a) examine the theoretical and methodological foundations of PSA and SEM, including the connections, similarities, and differences between the two approaches; (b) demonstrate two integrated models that incorporate specific PSA approaches (i.e., propensity score weighting [PSW] and propensity score subclassification [PSS]) with SEM models – both examples aim to test mediating effects using survey data, and the substantive research question concerns the direct impact of caregiver’s use of cash assistance program (i.e., AFDC) during childhood on child academic achievement and its indirect impact via child use of the same welfare program; and (c) discuss the importance of advancing knowledge about the adverse consequences of ignoring selection bias in observational studies and the need to promote rigor in causal inferences.

Pedagogical Techniques   Guided by the Neyman-Rubin counterfactual framework and Heckman’s scientific model of causality, this workshop builds on Kaplan’s (1999) pioneering work to develop procedures to apply PSW and PSS to SEM submodels that enable social worker researchers to draw causal inferences that simultaneously control for selection bias. Procedures of running PSA with SEM are demonstrated by using software packages of Stata and Mplus.

Significance   The workshop will demonstrate how to add analytic rigor to the applications of SEM and PSA.  This will be done for SEM by merging it with techniques of PSA that enable taking account of selectivity.  For PSA, the study will allow modeling with latent variables with measurement error in observed variables, testing a variety of parameters across groups, and performing overidentification tests.  The proposed approach will advance scientific knowledge about the importance of the strongly ignorable treatment assignment assumption embedded in studies of causal inference, and will promote rigor in social work research when this assumption is violated.