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Introduction
Management researchers regularly face two important problems in their modelling endeavours.
The first problem
This relates to the conceptualising, specifying for and empirically estimating of indirect (mediation) effects where one moderator is continuous (e.g. a psychological construct) and a second simultaneous moderator is nominal (e.g. gender). Traditionally, researchers follow Baron and Kenny (1986) and adopt the logic of an antecedent variable (X) influencing an outcome (Y) via an intervening mediator variable (M). A “moderated mediation” model is one where a covariate (Z) moderates the mediation effect (MacKinnon et al., 2007). The mediated effect varies with the level of the covariate (Valeri and VanderWeele, 2013, p. 142; also see Edwards and Lambert, 2007, p. 4). Graphically, mediation is depicted in “Model 4” in Hayes (2013) and moderated mediation is conceptualised in, for instance, Models 8 or 59 in Hayes (2013). A high-profile case used by Kline (2011, p. 333) in explaining the problem is Lance’s (1988) study, which focused on the relationship between recall accuracy of a lecture script (Y), memory demand (X), complexity of social perception (Z) and an interaction effect (between X and Z). The model also included a mediator, namely, “recollection of behaviours mentioned in the script” (M).
However, testing mediation without simultaneously controlling for both a continuous and nominal moderator (for instance, gender, as in Lance, 1988) is neither easy nor without biases. Including both moderators enables investigating the complex pathways of co-influence. For instance, a continuous moderator may influence the mediation effect in Group A differently/dissimilarly than in Group B. This refers to the direction of effect, its shape and the lower/upper bounds. Here, we demonstrate how to conceptualise, specify and empirically test such double-moderated mediation models using our context case.
The second problem
This refers to the substantive, and untenable, assumptions implicitly made when identifying direct and indirect effects while modelling mediation (Baron and Kenny, 1986). The validity of commonly used analysis critically relies on safeguarding against the so-called sequential ignorability assumption (Imai et al., 2010a, 2010b). Safeguarding, explained simply, has two parts (Imai et al., 2010a, 2010b, p. 310): ensuring that there is no unmeasured confounder (meaning a...