The MIMIC model and formative variables:problems and solutions

Nick Lee & John W. Cadogan & Laura Chamberlain

Received: 28 September 2012 /Accepted: 5 January 2013 /Published online: 24 January 2013# Academy of Marketing Science 2013

Abstract The use of the multiple indicators, multiplecauses model to operationalize formative variables (the for-mative MIMIC model) is advocated in the methodologicalliterature. Yet, contrary to popular belief, the formativeMIMIC model does not provide a valid method of integrat-ing formative variables into empirical studies and we rec-ommend discarding it from formative models. Ourarguments rest on the following observations. First, muchformative variable literature appears to conceptualize a caus-al structure between the formative variable and its indicatorswhich can be tested or estimated. We demonstrate that thisassumption is illogical, that a formative variable is simply aresearcher-defined composite of sub-dimensions, and thatsuch tests and estimates are unnecessary. Second, despitethis, researchers often use the formative MIMIC model as ameans to include formative variables in their models and toestimate the magnitude of linkages between formative var-iables and their indicators. However, the formative MIMICmodel cannot provide this information since it is simply amodel in which a common factor is predicted by someexogenous variablesthe model does not integrate withinit a formative variable. Empirical results from such studiesneed reassessing, since their interpretation may lead to in-accurate theoretical insights and the development of untest-

ed recommendations to managers. Finally, the use of theformative MIMIC model can foster fuzzy conceptualiza-tions of variables, particularly since it can erroneously en-courage the view that a single focal variable is measuredwith formative and reflective indicators. We explain theseinterlinked arguments in more detail and provide a set ofrecommendations for researchers to consider when dealingwith formative variables.

Keywords Formativevariables .Measurement .Composites .

Indicators . Theory . Causality . Ontology . Philosophy

The idea that some observable indicators cause orform (the terminology is often used interchangeably, e.g.Diamantopoulos 2008; Diamantopoulos and Winklhofer2001; Edwards and Bagozzi 2000; Hardin et al. 2011; Jarviset al. 2003) a variable is now well-accepted in mainstreammarketing research and is known as the formative variableapproach. The formative approach is in sharp contrast to thereflective measurement model, which posits that observableindicators are reflective effects of latent variables (emphasisadded, Howell et al. 2007a p. 205). The formativemodel is notnew and was explicit in the measurement literature as early as1964 (Blalock, reprinted in 1972) and can be implied from atleast 1948 (MacCorquodale and Meehl 1948; Rozeboom1956). Although formative variable approaches are presentedin various ways in the literature (e.g. Bagozzi and Fornell1982; Blalock 1971, 1975; Bollen 1984, 1989; Bollen andLennox 1991; Hayduk 1987, 1996; MacCallum and Browne1993), the current acceptance in mainstream business researchis driven, in part, byDiamantopoulos andWinklhofers (2001)now seminal Journal of Marketing Research article, as well aswith the publication of an entire special issue of theJournal of Business Research on formative measurement(Diamantopoulos 2008) and special sections of Psychological

N. Lee (*) : L. ChamberlainMarketing, Aston Business School,Aston University, Birmingham B4 7ET, UKe-mail: n.j.lee@aston.ac.uk

L. Chamberlaine-mail: l.m.chamberlain1@aston.ac.uk

J. W. CadoganMarketing, Business School, Loughborough University,Loughborough LE11 3TU, UKe-mail: j.w.cadogan@lboro.ac.uk

AMS Rev (2013) 3:317DOI 10.1007/s13162-013-0033-1

Methods (Howell et al. 2007a; Bollen 2007; Bagozzi 2007)and MIS Quarterly on the same (e.g. Diamantopoulos 2011;Bollen 2011). In this context, formative variable approachesare increasingly used in marketing, management, and otherbusiness research fields (Edwards 2011; Diamantopoulosand Siguaw 2006; Hardin and Marcoulides 2011; Howellet al. 2007a).

While an appreciation of approaches to variable construc-tion other than the traditional reflective view of constructshas the potential to make a considerable contribution to thequality of marketing research (Rigdon et al. 2011), there aresignificant areas of disquiet around the formative model(e.g. Borsboom et al. 2003; Cadogan and Lee 2013;Edwards 2011; Franke et al. 2008; Howell et al. 2007a;Lee and Cadogan 2013; Wilcox et al. 2008). In particular,Hardin and Marcoulides (2011 pp. 2) point out that the sumtotal of the growing body of research on formative variablesis a series of disjointed and contradictory messages that arenot only confusing to consumers of this research but alsocould threaten the advancement of knowledge. Such con-cerns are perhaps summed up best by Hardin, et al. (2011pp. 282) when they say, the application of causal indicatorsas formative measures has become a panacea without a clearset of theoretical foundations underlying their use.

One area of particular concern is the general acceptanceof the use of the multiple indicators, multiple causes(MIMIC) model as a way of operationalizing formativemodels in typical applications (hereafter, the formativeMIMIC model). Methodological literature (e.g. Jarvis et al.2003; MacKenzie et al. 2005) recommends the use of theformative MIMIC model to solve the inherent problemsinvolved in using formative variables in empirical work.Not surprisingly, it is well established in the applied litera-ture (e.g. Bello et al. 2010; Ernst et al. 2011; Gregoire andFisher 2008). However, the current study argues that theMIMIC model is not appropriate for modeling formativevariables. Consequently, the findings of research studies thatrely on MIMIC models to assist in the use of formativevariables may need to be reassessed and reinterpreted.

In order to demonstrate the problems of the formativeMIMIC model, we present a conceptual discussion of forma-tive variables that clarifies a number of problematic contra-dictions and assumptions contained in the existing formativevariable literature. In doing so, we build on recent studiescritical of formative models (e.g. Bagozzi 2007; Edwards2011; Howell et al. 2007a; Wilcox et al. 2008; Hardin et al.2011; Hardin and Marcoulides 2011). However, unlike some(cf. Edwards 2011; Hardin and Marcoulides 2011), we stopshort of recommending the abandonment of formative mod-els. Rather, we provide a set of directions and recommenda-tions for applied researchers who wish to employ variablesconceptualized as formative in their research. In what follows,we explain the principles underpinning the reflective and

formative models and extend the discussion to include theformative MIMIC modeling approach. Building on issuesrelating to (a) the nature of formative variables, and in partic-ular, whether the formative variable represents a real entitythat is distinct from its defining indicators, (b) the causallinkage (or lack thereof) between a formative variables indi-cators and the formative variable itself, and (c) notions ofinterpretational confounding, we explain why the MIMICmodel does not provide a valid method of integrating forma-tive variables into empirical studies. We also discuss the issueof the conceptual compression of constructs that formativeMIMIC models encourage researchers to engage in, arguingthat theory advancement and the accumulation of knowledgewill benefit from recognizing the potential problems that suchcompression can bring to theory development. We concludeby reflecting on the practical implications of our assessment ofthe MIMIC models place in formative variable models andrecommend several avenues for further research.

Reflective and formative models and the MIMIC model

Figure 1 illustrates both the formative and reflective modelsof latent variables as they commonly appear in organiza-tional and measurement literature. Figure 1a depicts thereflective model and can be represented by the equation

xi lix di 1where the subscript i represents the ith indicator, refers tothe random error (or unique variance) for the ith indicator,and i indicates the loading of the ith indicator on the latentvariable , which is exogenous. Thus, each observableindicator xi is a function of the common latent variable and some unique error i. As Borsboom (2005) shows, thismodel is customary in psychological measurement and gen-eralizes to models such as item response theory, commonfactor analysis, confirmatory factor analysis, and classicaltest theory (Howell et al. 2007a).

There are at least two conceptualizations of the formativevariable model represented in general terms by Fig. 1b. Thespecification advocated in most of the literature on formativevariables (e.g. Bollen and Lennox 1991; Diamantopoulos2006; Diamantopoulos and Winklhofer 2001; Jarvis et al.2003) is

g1x1 g2x2 . . . gnxn z 2where the latent variable is endogenous and considered to bea function of some observable indicators x1 to xn with ireferring to the contribution of xi to . An error term is alsoincluded at the construct level. Error is not included at the itemlevel in this formative model and, while interpretation of theconstruct-level error term has been subject to some debate(Diamantopoulos 2006), it is generally recognized as

4 AMS Rev (2013) 3:317

representing the remaining causes of that are not captured byx1 xn. A second specification (Fig. 1c) is identical to Eq. (2)except that the formative variable (now labeled a composite

variable, C, and represented with a hexagon, see Grace andBollen (2008) is not missing any additional causes beyond x1 xn (i.e., =0):

C w1x1 w2x2 . . . wnxn 3Both Eqs. (2) and (3) share the property of being empir-

ically inestimable without an additional endogenous vari-able or variables (Bagozzi 2007), meaning that the andw valuesand thus and Care dependent on whichspecific endogenous variables are used to estimate the model(Heise 1972).

The specifications of Eq. (1), (2), and (3), as coveredabove, also unavoidably imply conceptual differences. Mostimportantly, Eq. (1) expresses how the indicators x vary as aconsequence of the variation in the latent variable . There-fore, the implication is that is of independent existence (i.e. itcan exist without the indicators). Conversely, Borsboom et al.(2003) state that the formative variable is dependent on thespecific formative indicators used in the model and, thus, thatit is impossible to make any claims that represents anindependent entity (see also Howell et al. 2007b). This is notnecessarily a problem per se, but it does have substantiveconsequences on how a formative variable can be modeledand interpreted (Borsboom 2005; Howell et al. 2007a). Whatis potentially problematic is that when researchers considerthe meaning of formative models, they may visualize a modelsuch as that presented in Fig. 1b and, drawing on their expe-riences of working with classical test theory models of latentvariables, conclude that the parameters are paths that implya causal relationship between the formative indicators and theformative variable. These parameters, the researcher assumes,need to be estimated empirically from data. However, modelssuch as those presented in Fig. 1b and c cannot be estimated asthey stand, simply because they are under-identified. This iswhere MIMIC models can be employed, since MIMIC mod-els are quite easy to identify empirically. Specifically, forma-tive MIMIC models as presented in Fig. 2 contain a focallatent variable (), some reflective indicators (the ys), andsome formative indicators (the xs), and so allow for theinclusion of formative variables when estimating conceptualmodels (Jarvis et al. 2003; Kline 2006). Indeed, the formativeMIMIC modeling approach is also presented as a way ofvalidating/developing formative measures.

(a) The reflective variable model

(b) The formative variable model

(c) The composite variable modelFig. 1 Alternative latent variable models. a The reflective variablemodel. b The formative variable model. c The composite variable model

Fig. 2 The formative MIMIC model

AMS Rev (2013) 3:317 5

Despite its mainstream acceptance, the MIMIC modelsuse in modeling formative variables raises difficult issues.First among these is the fact that the MIMIC model suffersfrom interpretational confounding (Burt 1976), whichHowell et al. (2007b pp. 245) consider to render formativemodels ambiguous, at best[which] can be a fatal flaw intheory testing. In simple terms, interpretational confound-ing means that the meaning of the formative variable one isinterested in studying is determined by the endogenousvariables that the formative variable is meant to predict,not the exogenous items that are supposed to measure it(Burt 1976; see Howell et al. 2007a for a full explication).

Beyond the latter issue, however, the use of the formativeMIMIC model is flawed because a fundamental assumptionis incorrect. Specifically, the notion that there is a causalstructure between the formative indicators and the focalvariable is incorrect. Rather, the loadings implied byFigs. 1b and 2 are not causal paths, they are simply weightsthat indicate the contribution that a researcher decides anindicator makes to a formative variable. Indeed, the forma-tive indicators and the formative focal variable are notdistinct entitiesthey are the same entity and so one cannotcause the other. Accordingly, it is up to the researcher tospecify the weight that a formative indicator has whendefining the formative variable. There is no need to try toestimate these contributions, since they are part of the con-struct definition and cannot be inferred by statistical means.

Furthermore, the use of the formative MIMIC modelbrings with it deep logical errors. Specifically, contrary toconventional understanding, a MIMIC model does not pro-vide a method of measuring a single focal variable simulta-neously using formative and reflective indicators. Rather,the MIMIC model simply models a reflective latent variablewith some exogenous predictors. The following discussionsexplain, in-depth, the reasoning behind these conclusions.

The nature of the latent variable: applicationto the formative model

While the idea of latent variables is elemental to measure-ment theory, it has long been subject to disagreement aboutwhether a latent variable is a proxy for a real entity that isunobservable, a convenient fiction to help us make senseof observable events such as behavior, or a simple numericaloperation (Borsboom, et al. 2003; see e.g.; Bagozzi 2007;Bollen 2002; Borsboom 2005; Borsboom and Mellenbergh2002; Edwards and Bagozzi 2000; MacCorquodale andMeehl 1948; Rozeboom 1956 for a brief picture of thedevelopment of perspectives on this issue). The situation isnot helped by the plethora of different terms used in theliterature (cf. Bollen 2002; e.g. Bagozzi 1982; DeVellis1991; Nunnally 1967). In fact, Bollen (2002 p. 608) argues

that we should ignore this metaphysical dilemma, as itnarrows the use of the concept of latent variables and raisesmetaphysical debatesit seems preferable to leave the realor hypothetical nature of latent variables as an open questionthat may well be unanswerable. This seems a strangelyequivocal position, and Borsboom et al. (2003 p. 204,emphasis in original) counter that latent variable theory isnot philosophically neutral and that the connection be-tween mathematical definitions of latent variables and em-pirical data requires anontological stance. Borsboom(2005, p. 58) provides a very clear definition in this regardwhen he states that the only possible stance which is con-sistent with both accepted theory of latent variables andcurrent practice is the view that the latent variable is a realentity which is assumed to exist independent of measure-ment. This is termed entity realism, in which the theoreticalentities that we propose as components of our theoriesactually correspond to entities in reality. Borsboom et al.(2003) give the example of electrons as theoretical entities(being as they are unobservable) and perhaps the HiggsBoson would be another topical example in more recenttimes. Entity realism would maintain that the theoreticalentity of an electron actually corresponds to a real particlealbeit one that is unobservable with our present capabil-ities. Entity realism would therefore maintain the samecorrespondence between the modeled entities in marketingtheories and actual entities that exist in reality.

Despite this, literature advocating and using formativevariables rarely provides an explicit discussion of the onto-logical stance taken by the researcher in terms of their viewof the formative variables they are studying. However, anumber of authors critical of the formative approach contendthat formative models fail to support a realist interpretation(e.g. Edwards 2011; Wilcox et al. 2008). Borsboom et al.(2003 pp. 208209) explain this clearly in relation to socio-economic status (SES), using measures of income, educa-tion, and place of residence as indicators, and conclude thatvariables of the formative kind are not conceptualized asdetermining our measurements, but as a summary of thesemeasurements[and as such]nowherehas it beenshown that SES exists independent of the measurements.This is problematic in light of current theory and practiceregarding formative variables, much of which seem to implythat formative variables (e.g. or C in Fig. 1b and c) aredifferent from the formative indicators (the xs). A particularproblem concerns the nature of the relationship between theitems and the corresponding formative latent variable.

Causality and the formative variable

Detailed discussion of causality is rare in formative litera-ture (see Bagozzi 2007; Edwards and Bagozzi 2000 for

6 AMS Rev (2013) 3:317

notable exceptions). However, the causal implications of theformative variable model are simply not consistent with theway the formative model seems to be used in practice, aswell as with the assumptions tacit in the formative liter-ature which appear to be drawn primarily from those ofreflective measurement (Borsboom et al. 2003; Hardinand Marcoulides 2011). Despite causality being basic tohuman thought (Pearl 2000 p. 331; see also Blalock 1972;Scriven 1966), the philosophy literature has seen consider-able debate regarding what it is for one variable or event tocause another (Sosa and Tooley 1993; Pearl 2000). Never-theless, whichever philosophical definition of causality isused, one must define when causal inferences from empiricaldata can be made. Bollen (1989) provides three causalityconditions that must be present to infer some form of causalrelationship between X and Y. Briefly, a causal link from X toY can be inferred from a data set if a) Y is isolated from allother possible causes other than X, b) there is an empiricalassociation R observed between X and Y, and c) X can bedetermined to come before Y. However, one other conditionis explicit in the philosophical discourse (Sosa and Tooley1993) and that is that both cause and effect must be separatematerial entities.

Similarly, Edwards and Bagozzi (2000 pp. 157158, seealso Wilcox et al. 2008) note that the latent variable must bedistinct from its measure to infer causality in a measurementmodel. With an entity realist view, this condition is notproblematic. Specifically, if entities exist in reality (e.g.electrons, the Higgs Boson, attitudes, etc.,), it is easy tosee that measurement items are separate entities from thelatent variable they are purported to measure. To illustratethis in a practical sense, consider a construct such as roleambiguity, which can be measured using indicators such asI feel certain about how much authority I have in myselling position (MacKenzie et al. 1998). It would be usualto conceptualize a response to such an item to vary as afunction of the unobservable role ambiguity phenomenon;salespeople who feel less ambiguous about their jobs willfeel more affirmation towards this item than those who aremore ambiguous. As such, role ambiguity occurs first andcauses the response to the item (Borsboom et al. 2003). Thisconceptualization is accurately modeled using a reflectivevariable model.

Alternatively, consider a variable such as AdvertisingExpenditure, one of Diamantopoulos and Winklhofers(2001 pp. 275) examples of a formatively-modeled variable.The measure of this consists of four items, each tapping atype of expenditure: Television (TV), Radio, Newspaper,and All Media. Consistent with Diamantopoulos andWinklhofer (2001) and Fornell and Booksteins (1982) def-inition of a formative approach, Advertising Expenditure isdefined as a composite of four different types of expenditurethat are tapped. But this also means that it cannot logically

be a phenomenon that exists, independent of the indicators.TV, Radio, Newspaper and All Media expenditure do notcause Advertising Expenditure, they are Advertising Expen-diture. The formative Advertising Expenditure latent vari-able does not possess the property of being distinct from itsindicators and has no meaning over and above the fourformative indicators. This lack of distinction between theindicators and the construct is explicit in the conceptualdefinition of formative measurement (e.g. Diamantopoulosand Winklhofer 2001) and, as such, we cannot justify acausal relationship between the indicator and the outcome(Borsboom et al. 2003).

Inherent problems with operationalizing formativelatent variables

The inappropriateness of the MIMIC model for operationaliz-ing formative latent variables can be effectively shownwith anexample. To return to Advertising Expenditure, recall that it isdefined by four formative indicators: TV, Radio, Newspaper,and All Media. Imagine we have an industry-sourced data setthat includes TV, Radio, and Newspaper expenditure, butnothing else. Figure 3a shows our initial conceptual modelof Advertising Expenditure, which contains three observedformative indicators (TV, Radio, Newspaper) and one unob-served formative indicator (All Media) that is represented bythe error term, 1 (cf. Diamantopoulos 2006). As it stands, thismodel is not testable due to lack of identification. Thus, manytheorists (e.g., Diamantopoulos andWinklhofer 2001) suggestadding two or more reflective indicators of the construct (y1and y2) to enable identification, creating a MIMIC model. Inour example (see Fig. 3b), the reflective indicators chosen areMarket Share and Brand Image, both of which are likely to beshaped by the various Advertising Expenditure indicators.

Now we have the tools to identify the latent variablemodel and provide estimates, including one for the errorterm, and it might be assumed by some that the error termreturned (2 in Fig. 3b) corresponds to All Media, theunmeasured component of the Advertising Expenditure var-iable (1 in Fig. 3a). This assumption is a mistake. While thediagrammatic representation of the formative model of Ad-vertising Expenditure (Fig. 3a) appears to imply that the xsare causes of the Advertising Expenditure construct, as wehave pointed out, this is not the casethe indicators aresimply the expenses that need to be aggregated to calculateAdvertising Expenditure. The Fig. 3a diagram is merely aconvenient way of showing what indicators define the for-mative Advertising Expenditure variable and of visuallydifferentiating the formative variable from the reflectivevariable. In practice, though, researchers do erroneouslytry to estimate the parameters in formative variable mod-els and, in order to identify the model, will add endogenous

AMS Rev (2013) 3:317 7

variables to the formative model (e.g., Fig. 3b). Unfortu-nately, in such cases, the meaning of the focal latent vari-able, 2, is not theoretically grounded in the formative itemsbut is empirically grounded in the covariance between Mar-ket Share and Brand Image (see Howell et al. 2007a; Lee andCadogan 2013; Treiblmaier et al. 2011). The empirically-tested latent variable, 2 in Fig. 3b, is, therefore, not thesame conceptually as the theoretically-grounded 1 variablein Fig. 3a; it is simply the common factor (shared variance)

underlying the two reflective variables. In this case, we havea serious problem. If we draw conclusions from ourempirically-identified model (Fig. 3b), we may make themistake of thinking they can be applied to our conceptualmodel (Fig. 3a). This is not the case (Lee and Cadogan 2013)and if we make this mistake, we are in real danger of drawingerroneous conclusions.

To reinforce this point, it should be clear that the theo-retical meaning of Advertising Expenditure has no actual

(a) Advertising expenditure as a formative variable initial definition

(b) MIMIC model that is estimated

(c) Advertising expenditure as a formative variable modified definition

Fig. 3 Alternative advertisingexpenditure models.a Advertising expenditure as aformative variableinitialdefinition. bMIMIC model thatis estimated. c Advertisingexpenditure as a formativevariablemodified definition

8 AMS Rev (2013) 3:317

impact on the empirical value of the error term resultingfrom our model (Lee and Cadogan 2013). Imagine that wechange the definition of Advertising Expenditure to add afifth formative component (see Fig. 3c), corresponding toadvertising through Paid Word of Mouth without collect-ing new data. We still only have access to TV, Radio, andNewspaper expenditure data, but now the error term haschanged (31) and has two components, All Mediaand Paid Word of Mouth. If the MIMIC model for Adver-tising Expenditure (Fig. 3b) provides an accurate represen-tation of the theoretical Advertising Expenditure variable,Fig. 3bs error term (2) should change to include both AllMedia and Paid Word of Mouth, accommodating thechange in the conceptualization of Advertising Expenditure.However, as one can anticipate, simply changing Advertis-ing Expenditures formative composition, but not addingnew data, will not result in new estimates if Fig. 3b is rerun.The estimates will of course be identicalincluding themagnitude of 2. This is because the value of 2 returnedis not dependent on the conceptual meaning that researchersascribe to Advertising Expenditure. Rather, the 2 errorterm just represents unexplained variance from trying topredict the common factor of market share and brand imageusing TV, Radio, and Newspaper expenditures as exogenouspredictors. This explains why Borsboom et al. (2003) con-sider that a MIMIC model is not a formative latent variablemodel but is rather a reflective latent variable model (withall the associated entity realism foundations) predicted by aset of causes.

Theoretical directions for formative latent variablemodels: divorcing causal terminology from formativemodels

Perhaps one reason the formative MIMIC model is so preva-lent is the lack of clarity within the formative literature, withsome authors using formative (e.g. Diamantopoulos andWinklhofer 2001; Fornell and Bookstein 1982) and othersusing the term causal to refer to what seems to be the sametype of variable (e.g. Bollen 1989; Bollen and Lennox 1991;MacCallum and Browne 1993; see also Blalock 1972).Edwards and Bagozzi (2000 p. 162) go so far as to state thatthe formative model specifies measures as correlated causesof a construct, while Baxter (2009 p. 1370) writes that informative scalesthe indicators are independent causes ofthe construct being measured. Likewise, the literature criticalof formative models is not exempt from this confusion (e.g.Hardin et al. 2011). Yet, as we know, there is a tautology inconsidering formative indicators as causes of their latent var-iable (rather, the formative items define their variabletheysimply are the variable) and, as such, the terms formativeand causal cannot logically be interchangeable.

A problem that some have identified is working outwhether a formative indicator is really a formative indicator(i.e., a defining component of a variable) or rather if it is anexogenous cause of a variable (Cadogan and Lee 2013). Toillustrate, we borrow Diamantopoulos and Winklhofers(2001) example of Perceived Coercive Power. This latterlatent variable is measured using six items, each referring toa buyers perception of a suppliers ability to take a differenttype of action (Gaski and Nevin 1985) such as delaydelivery, or refuse to sell. It seems clear that these itemsare external causes of a distinct phenomenon of PerceivedCoercive Power as experienced by the buyer rather thanintegral components of it. Thus, these measurement itemsare not necessarily providing information on whether thebuyer really perceives the supplier to have coercive power.They are merely potential causes of such a perception. Thebuyers perception of whether the supplier has a lot or a littlecoercive power is less complicated and is a simple unidi-mensional perception in this regard (one that could beassessed using reflective items).

Thus, the relationship between the six items and thenotion of buyers perceptions of suppliers coercive papersatisfies a causal interpretation being as the phenomenon isindependent of its indicators, and one would expect theindicators to occur prior to their effects. Furthermore, thevariable Perceived Coercive Power satisfies an entity-realist standpoint.

Interestingly, Gaski and Nevins (1985) items could beargued to be formative components of a different variable,perhaps one capturing the suppliers Access to CoerciveTools, as opposed to causal indicators of the buyers per-ceptions of the Coercive Power of their suppliers. Ofcourse, these different variables may have separate antece-dents and consequences. By way of illustration, Table 1presents the two alternative variables and the three possiblemodels discussed here.

The previous discussion shows how conceptualizing aformative variable unavoidably defines it as nothing morethan its indicators. It is important to realize that this does notrun counter to statements such as that by Wilcox et al. (2008p. 1220) that constructs themselves, posited under a realistphilosophy of scienceare neither formative nor reflec-tive. Rather, defining a variable as formative places itoutside the entity realist stance (Borsboom et al. 2003), bydefining it as representing nothing more than its indicators.In other words, the constructs discussed by Wilcox et al.(2008) and others could never be formative as they representreal entities, independent of their measurement. Once oneposits an entity independent of the indicators, one is dealingwith a different construct and, therefore, can include thisconstruct in either reflective or causal models as shown inTable 1. However, the construct cannot simultaneously beconceptualized or modeled as formative.

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Table1

Illustratio

nof

differentlatent

variabletypes

Construct

Definition

Unitof

analysis

Item

sRelationshipof

itemsto

latent

variable

Ontologicalstatus

oflatent

variable

Perceivedcoercive

power

(see

GaskiandNevin1985)How

muchcapabilitythesupplier

hastogetthe

buyertodo

what

they

wouldnothavedone

otherwiseby

way

ofpunishment

(see

GaskiandNevin1985)

Buyer

(buyersperception

ofsuppliersability)

0=NoCapability

Item

scauselatentvariabletooccur.

I.e.buyersperceptionof

suppliersabilitycauses

buyerto

perceive

suppliertohave

high

coercive

power.W

hetherthe

itemsare

measuresis

questionable.

Latentvariableisahypo

thetical

real

entity.

4=Verymuchcapability

1.Delay

delivery

2.Delay

warrantyclaims

3.Takelegalaction

4.Refuseto

sell

5.Chargehigh

prices

6.Deliver

unwantedproducts

Accessto

coercive

tools

Abilityof

supplierto

take

differentactions

intheir

dealings

with

agivenfirm

.

Supplier(e.g.suppliers

ratingof

theirow

nability)0=NoCapability

Item

sform

latent

variable.I.e.the

supplierscoercive

power

isa

compositeof

theirability

totake

each

action

Latentvariableisan

abstraction

oftheem

piricaldata.

4=Verymuchcapability

1.Delay

delivery

2.Delay

warrantyclaims

3.Takelegalaction

4.Refuseto

sell

5.Chargehigh

prices

6.Deliver

unwantedproducts

Perceivedcoercive

power

(see

GaskiandNevin1985)How

muchcapabilitythesupplier

hastogetthe

buyertodo

what

they

wouldnothavedone

otherwiseby

way

ofpunishment

(see

GaskiandNevin1985).

Buyer

(buyersperception

ofsupplier)

1=StronglyDisagree

Item

sarecaused

bythelatent

variable.I.e.thecoercive

power

ofthesupplierinfluences

the

levelof

alltheitems

Latentvariableisahypo

thetical

real

entity.

5=StronglyAgree

1.Ibelieve

thissupplierhas

theability

toforcemyfirm

togo

alongwith

theirplans

whether

wewantto

ornot

2.Managersatmyfirm

doalmostanything

this

supplierwants,even

when

wedontwantto

3.Whenthissuppliersays

jum

p,weask

how

high

?

4.Weareafraid

oftheability

thissupplierhasto

hurtus

ifwedontgo

alongwith

theirplans.(etc.)

Partsof

thistableadaptedfrom

Diamantopoulos

andWinklhofer(2001 )

10 AMS Rev (2013) 3:317

Bollen and Bauldry (2011 p. 266; see also Bollen, 2011)also distinguish between causal, effect (their term for reflec-tive) and composite (their term for formative) models, statingthat the different types of variables have distinct theoreticalinterpretations, and careful consideration of the differencesamong them may inform the substantive understanding ofthe object under study. Bollen is not the first to make thisdistinction. Over 60 years ago, MacCorquodale and Meehl(1948 p. 103) conceptualized a distinction between abstrac-tive and hypothetical variables which is essentially thesame thing. An abstractive variable is defined as simply aquantity obtained by a specified manipulation of the valuesof empirical variables; it will involve no hypothesis as to theexistence of nonobserved entities. Such a variable does notrepresent a nonobservable phenomenon and is defined by itsobservable indicators (as in the Advertising Expenditureexample) and is therefore appropriately constructed as aformative composite (e.g. Bollen 2011). A hypothetical var-iable on the other hand is defined as referring to processesor entities that are not directly observed (although they neednot be in principle unobservable)the truth of the empiricallaws is a necessary but not a sufficient condition for the truthof these conceptions (MacCorquodale and Meehl 1948p. 104). Clarifying which type of variable one is dealingwith for all variables in a given model is vitally impor-tant to the validity of the models representation of theunderlying theory. However, such decisions can concealtraps for the unwary researcher.

Clarifying the constructs implied in a formative MIMICmodel

Despite the logic of the above discussion, researchers inapplied settings sometimes make the error of assuming thata MIMIC model allows them to essentially do two things atthe same timethat is, measure a single construct in twoways, both formatively and reflectively. Unfortunately, thisis not the case, and the formative and reflective modelsimply two separate constructs. For example, Cadogan etal. (2008) provide an example of a situation where research-ers have assumed that the focal construct in a MIMIC model( in Fig. 2) can be measured using both formative indica-tors (the xs) and reflective indicators (the ys). For instance,one of their focal constructs (1) is the quality of the firmsmarket information generation process, and the formativeapproach to its assessment involves measuring direct indi-cators of information generation quality, such as the speedof information generation, the quantity of information gen-erated, etc., while the reflective measures ask respondentsabout the effectiveness and efficiency of the generationprocess and the firms satisfaction with the generation pro-cess (see Fig. 4a).

Upon rumination, however, it seems obvious that assum-ing that the formative and reflective items measure the samething is flawed. On the one hand, we have shown that theaggregate of the measured and unmeasured xs in a MIMICmodel is not the same thing as the common factor under-pinning the ys; this is evidenced by the fact that the forma-tive variable in a MIMIC model can change (e.g., bychanging the number of and/or breadth of conceptual cov-erage of the xs), but the conceptual meaning of the reflectiveconstruct measured by the ys will remain the same. As such,when the MIMIC model is used in formative variable mod-els, the single focal construct might be better thought of asbeing two variables (see Fig. 4b); on the one hand, there isthe aggregate of the formative indicators (1)the forma-tive variable the researcher wishes to assess with the xs and,on the other hand, there is the unidimensional reflective con-struct (2) that is the common factor underpinning the ys.

In Cadogan et al.s (2008) case, for instance, the 1construct (quality of the firms market information gen-eration process) could be considered different from, andperhaps causally linked to, the reflective construct (2)capturing managers overall assessment of whether theirfirms market information generation processes are ofhigh or low quality. It is plain to see that 1 and 2are different thingsalthough they may be related (in thesense that there may be some kind of causal relationshipbetween the two variables), they should not be confusedas being the same variable. Indeed, even if 1 is a causeof 2 (as depicted in Fig. 4b), it is only one of severalcauses of 2, indicating that 1 and 2 may have verydifferent causal relationships with other variables andmay not be good proxies for each other (certainly notgood enough to act as surrogates for each other in causalmodels).

Giving different constructs the same name is confusingand potentially dangerous for scientific progress. This isshown in the case of socio-economic status (SES), whichis a single label that has been applied to multiple differentvariables. For example, Blalock (1975) conceptualizes SESin two ways. First, Blalock (1975 p. 365) defines what hecalls the usual notion of socio-economic status as being aninternal evaluation of others by a judge, where objectivepropertiesin part determine the subjective evaluationswhich confer status. SES here is a hypothetical entity,possibly influenced by causal indicators (interestingly, clear-ly this is not the usual notion of SES as it has developedsince). Later, Blalock (1975 p. 365) conceptualizes a differ-ent construct as the combination of positions or group orcategory memberships that [a person] occupies. Blalock(1975) also labels this second construct as SES, even thoughit is clearly a different variable from the initial usual notionof SES. In fact, Blalocks (1975) second definition appearsconsistent with an abstractive conceptualization, using a

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composite of formative indicators (ironically, it appears thislatter conception has become the usual notion of SES sinceBlalocks work).

This is not a simple semantic difference. In fact, eachconceptualization of SES refers to a different concept, de-spite the common name, and this difference has importantimplications for any associated theoretical models and em-pirical operationalizations. Wilcox et al. (2008) point outhow reviews of the SES literature have shown inconsisten-cies that have led to non-comparable results across studies,which is a serious issue for scientific progress. Note that thisis not necessarily due to inherent problems with the differentvariable models, but one of a) inconsistent conceptualizationin the first place and b) inadequate information presented instudies about how that construct was conceptualized. Clearinformation in this regard would have allowed researchers to

decide which type of SES they wished to incorporate intheir theories, and forced them to justify why, allowingfuture work to build more consistently.

In light of the above, one can sympathize with Howell etal.s (2007a, 2007b; see also Wilcox et al., 2008) contentionthat formative indicators are not measures at all. Instead,abstractive (i.e., formative composite) variables are used inmodels because they provide some shorthand or convenientsummary of the empirical data which is useful for somepurpose, rather than to measure some underlying hypotheticalentity.

With the above in mind, one could therefore term thisprocess of using formative variables constructing a variablerather than measuring a construct. It can be argued that suchabstractive formative composites are useful to the extent thatthey provide clear and consistent definitions and quantitative

a) The focal formative variable, 1, in a formative MIMIC model

b) The focal formative variable, 1, and a conceptually distinct entity, 2

c) 1 and 2 in a causal model

Fig. 4 Multiple variablesunderpinning the MIMICmodel. a The focal formativevariable, 1, in a formativeMIMIC model. b The focalformative variable, 1, and aconceptually distinct entity, 2.c 1 and 2 in a causal model

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operationalizations (see Lee and Cadogan 2013). In fact, suchapproaches are common in clinical research settings where,among other things, they are used to diagnose various con-ditions and assess key indicators of health (e.g., Torrance et al.1996). Correspondingly, in a marketing context, there is surelyno major problem with using a formative composite such asAdvertising Expenditure as long as we are clear on how thecomposite is operationalized.

The practical implications of the clarificationof the formative MIMIC model

Our clarification of the formative MIMIC model, as dis-cussed above, is a useful one in a number of ways. Inparticular, it forces the researcher to think more clearlyabout exactly what their variables represent. Of relevancehere is Bollens (2011; Bollen and Bauldry 2011) aforemen-tioned work on different types of indicators. Specifically,Bollen and Bauldry (2011) differentiate three different kindsof indicator: composite (i.e. formative), effect (i.e. reflec-tive), and a new kind of indicator, the causal indicator. Thedistinction between causal and composite (formative) indi-cators appears to be founded on the idea that causal indica-tors have conceptual unity, whereas composite indicatorscan be an arbitrary combination of variables. However,Bollen and Bauldry (2011) state that the distinctions be-tween these indicators can be blurred and that theoreticalframing of the analysis is the most important way of deter-mining the different variable types.

Unfortunately, Bollens (2002; 2011; Bollen and Bouldry,2011) work appears to place the definitional focus on theindicators rather than the latent variable and does not take anexplicit ontological stance on the nature of latent variables. Itis not clear whether, in a causal indicator model, the indicators(i.e., the xs) are separate entities from the focal variable () norwhether the variable is a real entity. Yet, if the ontologicalstatus of the focal variable is clarified (i.e., if the researcherspecifies whether the variable is a real entity or not, andwhether the xs are separate entities from the variable), it ishard to see where the difficulties in distinguishing the differenttypes of indicators that are cited by Bollen and Bauldry (2011)could lie. In particular, invoking an entity-realism perspectivefor a given variable and a set of xs immediately rules out aformative (composite) approach and, as a result, any x iden-tified must be exogenous causes of the , or covariates.However, if does not exist as a separate entity from the xs,then the model is a composite (formative) one.

Of course, if one does clarify that does exist as aseparate entity, this begs the question of why the causalitems are necessary, and whether one is not better servedby simply using the reflective model to develop a measure.In fact, it seems likely that the causal variable model offered

by Bollen and Bauldry (2011) would rarely offer any advan-tages over a reflective model, apart from the situation inwhich it is impossible to develop a reflective measurementmodel. Such situations could arise when one only has lim-ited access to data or is using secondary data, where thereare no logical reflective measures of the construct. Ofcourse, this would bring up the potential for interpretationalconfounding again, and there is always the inherent questionregarding the validity of proxy measures of this kind.

When it comes to the question of how to model formativeindicators without using a MIMIC model, Diamantopouloset al. (2008) give some alternatives, some of which involvereplacing formative indicators of the construct with endog-enous reflectively-measured latent variables. Alternatively,Cadogan et al. (2008) offer the aforementioned example ofmodeling the quality of market information generation as aformative construct, taking into account complex relation-ships between the indicators and construct (e.g. interactionsbetween indicators), an idea implied also by Blalock (1982).None of these approaches solves the conceptual problemsraised presently, that the formative latent variable is not anindependent entity. However, Howell et al. (2007a pp. 214215; see also Wilcox et al. 2008) suggest a number of otheroptions for dealing with sets of formative indicators, includ-ing principal components analysis, weighted averages, andpartial least squares. Ultimately, they conclude that model-ing formative indicators as separate constructs is the mostreasonable course of action.

Bollen and Bauldry (2011 p. 268) suggest the use of themodel shown in Fig. 5 for composite variables. This modelshows the use of a separate composite for each outcomevariable (yi) and avoids the assumption that a single forma-tive composite completely mediates the entire effect of theindicators (the xs) on all of the outcomes (ys). The modelalso allows different weights to be used for each composite,optimizing the predictive ability of the model for eachoutcome.

The literature on clinical measurement also offers at leastone interesting alternative, given that it has dealt with sim-ilar issues for many years (Fayers and Hand 2002; e.g.Torrance et al. 1996). Indeed, the statement most symp-tomscan combine and interact in various ways, and we areconfronted by the problem of how to use them in a single

Fig. 5 Formative composite model (Bollen and Bauldry 2011 pp. 268)

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model (Fayers and Hand 2002 p. 239) sums up exactly theproblem outlined above concerning formative indicators.Fayers and Hand (2002 pp. 246) come to the same conclu-sion as Howell et al. (2007a) that both simple summationand weighted sums are less easy to justify and suggest amethod based on the maximum of the observed variables,citing a model proposed by Blalock (1982) in which y (thevalue of the composite/formative variable of interest) isdefined as a function of a number of x indicators as follows:

log 1 y X

bj log 1 xj

: 4

Here, the value of y is high if any one of the x variables islarge, which is likely to be more appropriate than a simplesum in many situations. However, the choice of the weights in this equation is vital and provides a significantpart of the definition of the concept itself. Yet as Fayers andHand (2002 pp. 247) state, this is not a data analyticproblem, but one of definition. In other words, the re-searcher must in some way define these weights and notleave it to the data analysis process, just as some commen-tators have suggested regarding the formative compositemodel (Lee and Cadogan 2013).

There are various ways to engage with this problem. Forexample, one could ask members of the population to bemeasured to give their opinions of the importance of eachcomponent (e.g., through a preliminary survey) or academicexpert analysis could be used. These methods share muchwith Rossiters (2002; 2011) thoughts on content validity.Ryan and Farrar (2000) also suggest that conjoint analysismay be used to provide information on the relative values ofdifferent attributes. The information could then be used toweight various items using Eq. (4). All of these approachesare fundamentally different from those embedded in mar-keting research at present, which rely on the empirical datato either test hypotheses about the measure (reflective mod-els, where such an approach is justifiable) or to define thevariable itself (the current perspective on formative models,which can be approximated by a partial least squaresapproach).

Health economics also offers the multiattribute utilityfunction approach (e.g. Feeney 2006), which Fayers andHand (2002) note is broadly analogous to Eq. (4), but morecomplex and flexible. In brief, this approach is in twostages. Subjects of interest fill in a standard questionnaireof the relevant items. An index is then computed from thesescores using a multiattribute utility function (MAUF). Inessence, this function weights the different items andcombines them to create a single score, and the form ofthe function defines the interaction between the items, be itlinear, multiplicative, or multi-linear (Feeney 2006). Thefunction must be derived from a prior survey of the popu-lation to determine preference scores for each of the items.

The more complex the function and the larger the set ofitems, the more difficult and demanding this is and generallyaround seven attributes are considered to be the maximum(Feeney 2006). Such approaches appear to be challengingand time consuming in the marketing context but may beappropriate in many situations. For example, service qualitylooks to be a concept which is ideally suited to such anapproach.

Nevertheless, in many situations where formative indica-tors are used in organizational research, complex approachessuch as Eq. (4) or the MAUF would seem unnecessary. Forexample, the advertising expenditure example would seemto refer to a situation where a simple sum is appropriate. Inmost situations, given the definition used here, advertisingexpenditure is neither complex nor abstract; it is simply anamount of moneya concrete variable (Rossiter 2002).Thus, if no more detailed conceptualization is provided, thevalue of advertising expenditure is the simple sum of theindicators.

Many of the alternative approaches to the treatment offormative indicators discussed above share the standpointthat it is fundamentally the researcher, sometimes usinginformation from the research population, who determinesthe nature of a formative variable by conceptualizing itsformative components and their relationship to the singlevariable score. In other words, when constructing a forma-tive variable, the researcher is making a statement that thesecomponents form this composite in this manner. Allowingthe data to determine the nature of a formative compositelatent variable in a flexible manneras estimating aformative MIMIC model or even using partial least squaresas some formative literature (e.g. Diamantopoulos andWinklhofer 2001; Edwards and Bagozzi 2000) doesis fun-damentally unsound (Lee and Cadogan 2013). Also bear inmind that if different researchers use different weights tocreate a formative variable score, even if they may use thesame formative indicators and the same data, then the varia-bles they create are not equivalent and cannot be compared ortreated as though they have the same conceptual or empiricalmeaning.

We would advocate that researchers who wish to employvariables conceptualized as formative in their research mod-els avoid using the MIMIC model to operationalize forma-tive variables. In fact, the MIMIC model is not needed ifresearchers follow the guidelines below:

(a) Use predefined weights for formative indicators thatare explicitly part of the construct definition.

(b) Specify the weights using some explicit prior theory(e.g., the weights are all the same) or use some empir-ical method to determine the weights (e.g., a survey ofkey informants, Delphi method, or utility functionmethods).

14 AMS Rev (2013) 3:317

(c) Use these weights to create a single composite score forthe formative variable, using a standard algorithm thatis also explicitly part of the construct definition.

(d) Use the single composite score to test theoretical mod-els (e.g., to identify patterns of covariance between thecomposite score and other variables). The analysismethod in this case could be anything capable ofdealing with quantitative measurements.

(e) Critically, bear in mind that the composite score is not ameasure of a single real entity and so any observedcovariance between the formative composite and anothervariable runs the risk of being rather uninformative (seeFig. 6a), since the covariance () may hide the truerelationships between the indicators that create the com-posite score and the other variable (see Fig. 6b).

(f) Accordingly, theory development will be greatly en-hanced if the formative indicators are modeled in anexplicit causal model, whereby the potential interrela-tionships between the indicators themselves and be-tween the individual indicators and other variables inthe model (such as ) are specified.

Conclusions and questions for further research

This article addresses the problematic use of the MIMICmodeling approach when applied to formative variables andoffers some possible solutions.We demonstrate that the MIM-ICmodel is not doing its intended job since it does not provide

a way for researchers to operationalize formative variables inempirical research models. We explain why this is so bydrawing on various arguments, including those that look atthe nature of the causal relationship between the formativeindicators and the formative focal variable and by invokingthe entity-realist position, which we show does not hold forformative variables. Formative latent variables are defined asabstractive composites of empirical variables, with no inde-pendent meaning of their own, and as such the idea of a causalrelationship between an indicator and a formative variable isshown to be tautological. Ultimately, the onus is on the re-searcher, not the data, to define formatively-constructed latentvariables by way of various modeling approaches such as themultiattribute utility function.We also highlight the dangers invisualizing formative variables using the MIMIC model ap-proach; in some cases, it can encourage researchers to developfuzzy or confused conceptual understanding of their variables.

The arguments advanced in this paper have implications formarketing researchers who wish to use formative variablemodels in their work. First of all, researchers should avoidusing the MIMIC model when they are dealing with formativevariables. However, this decision will naturally requireresearchers to seriously consider whether the entity-realist po-sition is appropriate for the variables they are dealing with. Thisfundamental conceptual task is likely to lead to some interestingconclusions regarding many of our foundational marketingvariables, as well as when conceptualizing new ones. Further,when using formative composites, researchers will have to bevery clear in their definitions of such variables in order that they

a) A formative composite variable, C, and its covariance with another variable, : true relationships hidden

b) Possible inter-relationships between the xs, and relationships between the xs and

Fig. 6 Alternative models ofthe relationship between itemsand constructs. a A formativecomposite variable, C, and itscovariance with anothervariable, : true relationshipshidden. b Possible inter-relationships between the xs,and relationships between thexs and

AMS Rev (2013) 3:317 15

are to be of use across different contexts and studies. Formativemodelers must also take care in explicitly understanding thematch between their conceptual definitions and operationaldecisions (e.g. setting the beta weights when using Eq. [4]),and the ideas presented herein should help many begin.

Borsboom et al. (2004) are right to point out the dangers oftreating collections of distinct attributes as if they were actualreal entities (by naming them and using them as constructs inmodels); yet, Howell et al. (2007a) suggest that this may bejustifiable if one can show that the component parts of theformative variable exhibit similar relationships to antecedentsand consequences. Most important is that a formative variableshould be constructed for a sound reason, over and aboveusing the individual components. This reason should not bethat it represents an entity separate to its component items(because it has been shown that in such a case it cannot bydefinition be formative), but that using a single variable makeslogical sense and provides an important benefit to the re-searcher, outweighing any possible advantages one may getby testing individual components separately. The benefits of asingle variable can include prediction, description, parsimony,interpretability, and thus the possible increased practical in-fluence of a model. But, they should always be balancedagainst the potential obfuscation of individual important rela-tionships. Even so, more work clearly is needed in this regard.

Finally, it should be clear that this paper does not argue thatformative models are somehow inferior to reflective models.Instead, the formative model should be considered as a differentform of thinking about a variable which may be completelyappropriate in many situations. It seems to be the case that thetheoretical idea of a latent variable as an abstraction of itsempirical indicators (cf. MacCorquodale and Meehl 1948)has been generally ignored, even while the discussion of for-mative indicators has essentially implied exactly this type oflatent variable. In part, this may be due to what Hayduk (1987;1996; see also Rossiter, 2002) refers to as the entrenched factoranalytic thought patterns inherent in reflective measurementtheories. Yet, as Blalock (1975 p. 372) stated over 30 yearsago, we should not confuse our own convenience with thetheoretical adequacy of our underlying models. It is to behoped that this paper may encourage marketing researchers togive more consideration to the conceptualization and empiricalrealization of formative variables, since such consideration willplay an important role in assisting researchers in their efforts todevelop coherent theories.

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The MIMIC model and formative variables: problems and solutionsAbstractReflective and formative models and the MIMIC modelThe nature of the latent variable: application to the formative modelCausality and the formative variableInherent problems with operationalizing formative latent variablesTheoretical directions for formative latent variable models: divorcing causal terminology from formative modelsClarifying the constructs implied in a formative MIMIC modelThe practical implications of the clarification of the formative MIMIC modelConclusions and questions for further researchReferences