Abstract
This paper presents a causal explanation of formative variables that unpacks and clarifies the generally accepted idea that formative indicators are ‘causes’ of the focal formative variable. In doing this, we explore the recent paper by Diamantopoulos and Temme (AMS Review, 3(3), 160-171, 2013) and show that the latter misunderstand the stance of Lee, Cadogan, and Chamberlain (AMS Review, 3(1), 3-17, 2013; see also Cadogan, Lee, and Chamberlain, AMS Review, 3(1), 38-49, 2013). By drawing on the multiple ways that one can interpret the idea of causality within the MIMIC model, we then demonstrate how the continued defense of the MIMIC model as a tool to validate formative indicators and to identify formative variables in structural models is misguided. We also present unambiguous recommendations on how formative variables can be modelled in lieu of the formative MIMIC model.
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Notes
Note, Model 6 in Diamantopoulos and Temme (2013) is clearly cited as Bollen and Bauldry’s (2011) idea in Lee et al. (2013), and is not presented as “our” idea. In the latter, we use Model 6 as a speculative example of how other researchers might attempt to deal with the fundamental issues we point out, just as we use the logarithmic and multiattribute utility function examples (again, neither of which is our idea). While Diamantopoulos and Temme (2013) might accurately reproduce that model (although see the caveats pointed out later), it is not relevant to the present paper. As such, it is not part of this discussion. That said, we wonder why, while discussing Bollen and Bauldry’s (2011) suggested model, Diamantopoulos and Temme (2013) do not also operationalize the other potential examples in the same section in Lee, Cadogan, and Chamberlain (2013).
Unfortunately, Diamantopoulos and Temme’s (2013) Model 6 is not clearly specified (e.g. we do not know how the composites in the model are created). Thus, aside from the issues we highlight in the previous footnote (which mean we are uninterested in the Model 6), we would be unable to discuss Model 6 even if we were to be interested in it.
By this we mean that it is necessary for there to be two separate events/entities for a cause-effect relation to exist. In other words, one thing cannot cause itself. This is fundamental to Hume’s accounts of cause (see A Treatise of Human Nature (e.g. Hume 1985) and An Enquiry Concerning Human Understanding) (e.g. Hume 2008).
In a similar way, Markus and Borsboom (2013) suggest that the formative model could represent formal causation, which Aristotle defines as describing the form of the final result (i.e., the shape, or appearance of the thing). However, this type of cause does not seem to represent the definitions of formative variables quoted herein as accurately as the material cause interpretation does.
If it was the same entity, then ‘alcoholization’ would just be another name for ‘total amount consumed’. That said, we certainly agree with the principle that the same indicators could be used in different model definitions. Indeed we suggest exactly that in Lee et al. (2013). Interestingly, we are criticised by Diamantopoulos (2013, p. 35 original emphasis), for using “these same indicators as items defining a composite of a different construct”. Diamantopoulos (ibid) later says “I leave it to the reader to decide for himself/herself the utility of this exercise”. However, it seems that Diamantopoulos has come around to the idea, since he co-opts it in Diamantopoulos and Temme (2013).
Diamantopoulos (2013, p. 33) cites himself in attempting to overcome this conceptual impossibility by saying that “how a particular MIMIC model should be interpreted ‘depends on the conceptual interpretation attacked [sic] to the relationships between η, the xs and the ys’ (Diamantopoulos 2011, p. 346, original emphasis)”. As should now be apparent, this line of thinking only makes sense if one is erroneously attempting to simultaneously invoke material and efficient causal interpretations onto the MIMIC model. Interestingly, Diamantopoulos (2013) criticizes Lee et al. (2013) for advocating that formative models are not subject to empirical testing using the MIMIC model. Key pillars of Diamantopoulos (2013, p. 35) criticisms of our arguments against the formative MIMIC are that it is wrong to set up a situation where “your auxiliary theory cannot be refuted (because it cannot be tested)” and that it is problematic that by rejecting the formative MIMIC model, we “provide no opportunity for assessing whether” the combination rules that we decide on for the creation of the formative variable “are indeed reasonable”. Diamantopoulos’ stance on this front, then, appears to be at odds with his argument that it is up to a researcher’s conceptual interpretation as to whether a MIMIC model contains a formative variable. We clearly show in the above that the conceptualization of a MIMIC model as a formative variable model is flawed, since it amounts to the same thing as a basic efficient cause model of antecedents – whatever terminology one places on it.
Probably the most logical definition.
That is, one could decide not to interpret the items as entities that form, in a material sense, a focal variable.
Possibly, equation 1 is the origin of all the confusion in the minds of formative MIMIC model advocates. If one assumes that material causation is what a formative variable is, but then superimpose Eq.1 onto that definition, as Diamantopoulos and Winklhofer (2001) do (themselves borrowing from Bollen [e.g. Bollen and Lennox 1991] and collegues), then one will end up with the problems outlined here, and a belief that the MIMIC model can be used to model formative variables. We advocate eliminating Eq. 1 from the formative variable definition.
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Lee, N., Cadogan, J.W. & Chamberlain, L. Material and efficient cause interpretations of the formative model: resolving misunderstandings and clarifying conceptual language. AMS Rev 4, 32–43 (2014). https://doi.org/10.1007/s13162-013-0058-5
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DOI: https://doi.org/10.1007/s13162-013-0058-5