Although it is possible to conduct CACE-type analyses that rely on empirical model fitting and parametric assumptions (e.g., Muthén & Brown, 2009), we focused on a more widely practiced CACE approach in which empirical model fitting and parametric assumptions are not central to identification of causal treatment effects (see Jo, Stuart, Mackinnon, & Vinokur, under review). In this approach, to estimate the latent engagement status of the control group and to test for moderation effects on random assignment, several underlying assumptions are critical to the validity of the analytic framework (Angrist, Imbens, & Rubin, 1996; Jo, 2002a). These assumptions are that(a) possible outcomes for each individual are unrelated to the potential outcomes for other individuals; (b) intervention condition assignment is random; (c) there are no “defiers,” meaning there are no participants who do the opposite of the instructions given; (d) in the intervention group there are participants who comply, therefore the average causal effect of assignment to intervention on the actual receipt of services is not zero; and (e) for noncompliers, intervention assignment does not predict outcomes. This last assumption,
