ness of individual components in multiple-component designs. West and Aiken (1997) and MacKinnon (2008) also consider the statistical method of mediational analysis that permits researchers to probe these issues, although in a less definitive manner.
Rubin’s potential outcomes model takes a formal mathematical/statistical approach to causal inference. Building on earlier work by Splawa-Neyman (1990), it emphasizes precise definition of the desired causal effect and specification of explicit, ideally verifiable assumptions that are sufficient to draw causal inferences for each research design. Rubin defines a causal effect as the difference between the outcomes for a single unit (e.g., person, community) given two different well-defined treatments at the identical time and in the same context. This definition represents a conceptually useful ideal that cannot be realized in practice.
Holland (1986) notes that three approaches, each with its own assumptions, can be taken to approximate this ideal. First, a within-subjects design can be used in which the two treatments (e.g., intervention, control) are given to the same unit. This design assumes (1) temporal stability in which the same outcome will be observed regardless of when the treatment is delivered and (2) causal transience in which the administration of the first treatment has no effect on the outcome of the second treatment. These assumptions will frequently be violated in research on obesity. Second, homogeneous units can be selected or created so that each unit can be expected to have the same response to the treatment. This strategy is commonly used in engineering applications, but raises concern about the comparability of units in human research—even monozygotic twins raised in similar environments can differ in important ways in some research contexts. The matching procedures used in the potential outcomes approach discussed below rely on this approach; they assume that the units can indeed be made homogeneous on all potentially important background variables. Third, units can be randomly assigned to treatment and control conditions. This strategy creates groups that are, on average, equal on all possible background variables at pretest so that the difference between the means of the two groups now represents the average causal effect. This strategy makes several assumptions (see Table 8-2; Holland, 1986; West and Thoemmes, 2010), including full treatment adherence, independence of units, no attrition from posttest measurement, and the nondependence of the response of a unit to a treatment on the treatment received by other units (or SUTVA, the stable unit treatment value assumption). The SUTVA highlights the challenges in community research of considering possible dependence between units and possible variation in each treatment across sites (Rubin, 2010). Well-defined treatment (and no-treatment) conditions that are implemented identically across units are a key feature of strong causal inference in Rubin’s perspective. Hernan and Traubman (2008) discuss the importance of this assumption in the context of obesity research. Beyond requiring this set of foundational assumptions, randomization has another subtle effect: it shifts the focus from a causal effect defined at the level of the individual to an