Conceptualizing Variables: Problems and ... - University of Surrey

Conceptualizing Variables: Problems and Solutions Professor Nick Lee Professor of Marketing and Organizational Research Aston University (Birmingham, UK) Editor In Chief: European Journal of Marketing

Based on work with Professor John Cadogan, accepted for publication in the Journal of Business Research and Academy of Marketing Science Review Nick Lee and John Cadogan, forthcoming in Journ. Bus. Res. and AMS Review

Nick Lee and John Cadogan, forthcoming in Journ. Bus. Res. and AMS Review

Conceptualizing Variables General purpose of this talk: - To demonstrate some errors inherent in using popular variable forms in conceptual models. - To provide guidance on best practice.

Why?


A Dip into the Literature Diamantopoulos & Winklhofer (2001), “Index construction with formative indicators: an alternative to scale development,” J. Marketing Research. Petter et al. (2007), “Specifying formative constructs in information systems research,” MIS Quarterly. Diamantopoulos et al. (2008), “Advancing formative measurement models,” Journal of Business Research Treiblmaier et al. (2011) “Formative constructs implemented via common factors,” Structural Equation Modeling.


A Dip into the Literature Rindskopf and Rose (1988), “Some theory and applications of confirmatory second-order factor analysis,” Multivariate Behavioral Research. Goldberg (2006), “Doing it all Bass-Ackwards: The development of hierarchical factor structures from the top down,” Journal of Research in Personality. Wetzels et al. (2009), “Using PLS path modeling for assessing hierarchical construct models: guidelines and empirical illustration,” MIS Quarterly. Koufteros et al. (2009), “A paradigm for examining secondorder factor models employing structural equation modeling,” International J. of Production Economics.


A Dip into the Literature Edwards (2001), “Multidimensional constructs in organizational behavior research: an integrative analytical framework,” Organizational Research Methods. MacKenzie et al. (2005), “The problem of measurement model misspecification in behavioral and organizational research and some recommended solutions,” J. Applied Psychology. Bollen and Bauldry (2011), “Three Cs in measurement models: causal indicators, composite indicators, and covariates,” Psychological Methods.

MacKenzie et al. (2011), “Construct measurement and validation procedures in MIS and behavioral research: integrating new and existing techniques,” MIS Quarterly.


Latent variable with reflective indicators

λ1

ξ1

λ2

x1

x2

δ1

δ2

λ3

λ1

Creativity

λ2

Exciting......Dull

δ1

Fresh……Routine

δ2

Novel……Predictable

δ3

λ3 x3

δ3

xi = λiξ + δi Nick Lee and John Cadogan, forthcoming in Journ. Bus. Res. and AMS Review

Latent variable with formative indicators This model is inherently multidimensional

γ1

ζ



γ2

x1

x2

γ3 x3

γ1

ζ1

Socioeconomic

status

γ2

Education

Income

γ3 Occupational standing

η = γ1x1 + γ2x2 + … + γnxn + ζ Nick Lee and John Cadogan, forthcoming in Journ. Bus. Res. and AMS Review

Wells et al. (2011) MIS Quarterly

Web site quality

δ1

δ2

x1

x2

SEC

δ3

δ4

x3

x4

γ1

SEC: Security DD: Download Delay

DD

ζ1

Web site quality Dimensions

γ2

δ3

δ4

x3

x4

WSQ γ3 γ4

δ5

δ6

x5

x6 VAP

NAV

NAV: Navigability

VAP: Visual appeal


Wells et al. (2011) MIS Quarterly

Web site quality .23 ζ1

δ1

δ2

x1

x2

SEC

δ3

δ4

x3

x4

SEC: Security DD: Download Delay

DD

.14

Web site quality Dimensions

δ3

δ4

x3

x4

WSQ

.05 .73

δ5

δ6

x5

x6 VAP

NAV

NAV: Navigability

VAP: Visual appeal


Problems with the formative variable model: η = γ1x 1 + γ 2x 2 + … + γ nx n + ζ 1. Entity realism:

Since Eta (η) is defined as a composite: Then Eta is not a real separate entity from the indicators that define it. Eta has no meaning of its own. Eta is vague and imprecise, conceptually.


Problems with the formative variable model: η = γ1x 1 + γ 2x 2 + … + γ nx n + ζ 2. The γs are not causal relationships.

Eta is not a real separate entity from the indicators that define it: Cause and effect requires a cause and an effect (i.e., two separate entities). The gammas are simply weights to be defined by the researcher. NOT estimated. Different weights = different Eta variable.


Problems with the formative variable model: η = γ1x 1 + γ 2x 2 + … + γ nx n + ζ 3. Eta should not be used as a variable in a structural model. Eta is not a real separate entity from the indicators that define it:

For instance, if anything exogenous causes variance in Eta, it must operate through the indicators.


Illogical model: antecedent modeled as antecedent to formative variable δ1

δ2

x2

γ1

ζ

x1

ξ1

γ4



γ2

x4

x5

γ3 δ3

x3

x6

ξ1 = Antecedent latent η = Formative x4, x5, x6 = variable with reflective variable Formative indicators x1, x2 and x3 Nick Lee and John Cadogan, forthcoming in Journ. Bus. Res. and indicators AMS Review

ξ1 = Antecedent latent variable with reflective indicators x1, x2 and x3

δ1

x1

λ1

y1, y2, and y3 = Observed formative indicators

γ1

y1

η= Composite variable

ζ2 w1 Ζ1=0

δ2

x2

λ2 λ3

δ3

x3

ξ1

γ2

w2 y2

γ3

ζ3

η

w3 y3

ζ4


Endogenous formative measures - examples Iacouvou et al. 2009. Selective status reporting in information systems projects: a dyadic-level investigation. MIS Quarterly Vosgerau et al. 2008. Can inaccurate perceptions in businessto-business (B2B) relationships be beneficial? Mark. Science Hoeteker & Mellewigt 2009. Choice and performance mechanisms: matching alliance governance to asset type. Strategic Management Journal Dowling 2009. Appropriate audit support system use: the influence of auditor, audit team, and firm factors. Accounting Review Im & Rai 2008. Knowledge sharing ambidexterity in long-term interorganizational relationships. Management Science Nick Lee and John Cadogan, forthcoming in Journ. Bus. Res. and AMS Review

McFarland et al. 2008. Supply chain contagion. J. Marketing ζ1=0 H: (+) but ns Industry tenure

Supply chain contagion

Information exchange

(–) & sig.

Recommending Promises

Threats Ingratiation Inspirational appeals


McFarland et al. 2008. Supply chain contagion. J. Marketing ζ1=0 Environmental uncertainty

H: (+), find (+) & sig

Supply chain contagion

Information exchange Recommending Promises None are sig.

Threats Ingratiation Inspirational appeals


Exogenous formative variable

x1 x2

γ1 γ2 γ3

λ1

γ4

η1

η2

λ2 λ3

x3

γ3

γ2 x2 x3

λ1

γ1

x1

η2 γ4

λ2 λ3

y1

δ1

y2

δ2

y3

δ3

y1

δ1

y2

δ2

y3

δ3


Exogenous formative variable: MIMIC model

x1 x2

γ1

λ1

γ2

η1

γ3

x3

y4

γ4

η2

λ2 λ3

y1

δ1

y2

δ2

y3

δ3

y5


Exogenous formative variable: MIMIC model

x1 x2

γ1

λ1

γ2

η1

γ3

x3

y4 Possible causes of η1

y5

γ4

η2

λ2 λ3

y1

δ1

y2

δ2

y3

δ3

Η1 = Common factor underlying y4 and y5


Higher-order reflective models δ1

δ2

x1

x2 η1

λ1

ξ1

λ2

x1

δ1

x2

δ2

λ1

ξ1

δ4

x3

x4

λ2

λ3 λ3 x3

δ3

δ3 Reflective 2nd-order Latent variable = ξ1: 1 , 2 and 3, are reflective 1st order latent variables

η2 δ5

δ6

x5

x6 η3


Hedhli and Chebat (2008) J Bus Res Shopping Mall Equity δ5

δ6

x5

x6

δ1 δ1δ2

x1

x2

CON

δ2δ3

δ4

δ3

δ4

δ5

δ6

x3

x4

x3

x4

x5

x6

ENV

QP

QS

Awareness ζ3

ζ4

ζ5

ζ6

ζ2 Mall Equity ζ1

Mall Image

CON: Convenience ENV: Environment QP: Quality of Products QS: Quality of Services Nick Lee and John Cadogan, forthcoming in Journ. Bus. Res. and AMS Review

Multi-item reflective measures revisted: - Measures represent a single dimension (describe the same single entity). - And are conceptually interchangeable (can remove a measure with no loss of meaning – are redundant).

- They do not capture unique facets of construct (a single dimension is unidimensional).


Higher-order reflective models ηs reflect a unidimensional construct (ξ1) Higher-order model is redundant.

δ1 δ1

δ2

x1

x1

x2

δ2 x2

η1 λ1

δ3

δ4 x3

x3 ξ1

λ2 λ3

δ3

x4 η2

ξ1

δ4 x4

δ5

δ6

δ5

x5

x6

x5 δ6

η3

x6


Alternatives to higher-order reflective models ηs are distinct constructs – there is no unidimensional variable that they reflect

δ1

δ2

x1

x2 ζ1

η1 Model the ηs separately.

δ3

δ4

x3

x4 ζ2

η2 δ5

δ6

x5

x6 η3

ζ3


Alternatives to higher-order reflective models If the aim of modeling higher-order reflective constructs is to simplify the model, then a formative approach might make sense. However, remember that you should not use formative variables as endogenous, and there are also problems with using them as exogenous.

Model the ηs separately.

δ1

δ2

x1

x2 ξ1

γ1 ζ

η1

δ3

δ4

x3

x4

γ2 γ3

ξ2 δ5

δ6

x5

x6 ξ3


What are higher-order reflective models? ηs discriminate and are different constructs

ξ1 an unmeasured antecedent; or contains other reasons for shared variance between ηs.

x1

δ2

x2

λ1

λ2

ξ1

λ3 δ3

x3

ξ1 = Unmeasured antecedent to the ηs.

δ2

x1

x2 ζ1

η1 γ1

δ1

δ1

δ3

δ4

x3

x4

γ2 γ3

ζ2

η2 δ5

δ6

x5

x6

ζ3 Model the ηs η3 separately. Nick Lee and John Cadogan, forthcoming in Journ. Bus. Res. and AMS Review

What are higher-order reflective models? ηs discriminate and are different constructs

ξ1 could be hiding causal relationships between the ηs.

δ1

δ2

x1

x2 η1

Model the ηs separately.

δ3

δ4

x3

x4

γ1

η2

γ2

δ5

δ6

x5

x6 η3


Implications If it’s Multidimensional Think again Stronger models will emerge More realistic recommendations Nick Lee and John Cadogan, forthcoming in Journ. Bus. Res. and AMS Review