Covariance-based Structural Equation Modeling: Foundations and ...

Covariance-based Structural Equation Modeling: Foundations and Applications

Dr. Jörg Henseler University of Cologne Department of Marketing and Market Research & Radboud University Nijmegen Institute for Management Research

Dr. Jörg Henseler, University of Cologne, Department of Marketing and Market Research

Overview 1. What is CBSEM? 2. How does CBSEM work? 3. What can CBSEM do for you? 4. Examples 5. Conclusions


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Family Tree of SEM Structural Equation Modeling

Confirmatory Factor Analysis

Path Analysis

Exploratory Factor Analysis

Multiple Regression Factor Analysis

Bivariate Correlation Dr. Jörg Henseler, University of Cologne, Department of Marketing and Market Research

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Schematic Representation of a Structural Equation Model structural model

δ1

Indicator x1

δ2

Indicator x2

δ3

Indicator x3

δ4

Indicator x4

δ5

Indicator x5

δ6

Indicator x6

measurement model of the latent exogenous variables

ξ1

ζ

η1 ξ2

Indicator y1

ε1

Indicator y2

ε2

Indicator y3

ε3

measurement model of the latent endogenous variables


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Symbols Used

x1

ξ1 ε1

Indicators are normally represented as squares. For questionnaire based research, each indicator would represent a particular question. Latent variables are normally drawn as circles. In the case of error terms, for simplicity, the circle is sometimes left off. Latent variables are used to represent phenomena that cannot be measured directly. Examples would be beliefs, intention, motivation. Arrow connections represent linear relationships; curved double-ended arrows denote covariances (or correlations).


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The Idea of Estimating SEM

Estimate the parameters so that the discrepancy between the sample covariance matrix and the implied covariance matrix is minimal.

Σ(θ )

approximate

=

S

Σ : implied covariance matrix of observed variables θ : model parameters S : sample covariance matrix of observed variables Dr. Jörg Henseler, University of Cologne, Department of Marketing and Market Research

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How SEM and Traditional Approaches Are Different  Multiple equations can be estimated simultaneously  Latent (unobservable) variables can be constructed  Non-recursive models are possible  Correlations among disturbances are possible  Formal specification of a model is required  Measurement and structural relations are separated, with relations among latent variables rather than measured variables  Assessing of model fit is not as straightforward  Model fit gets a different meaning


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The Concept of "Fit" Revisited Example: A theory states that two variables are unrelated. We empirically test the theory.

Results from Correlation or Regression:

Results from CBSEM:

R² = 0

Σ=S

Thus, no fit!

Thus, perfect fit!


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Theory Testing Covariance-based structural equation modeling facilitates three types of theory testing:  strictly confirmatory  alternative models  model generating


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Strictly Confirmatory Theory Testing In a strictly confirmatory situation, the researcher has formulated one single model and has obtained empirical data to test it. The model should be either accepted or rejected. Product attributes

Affect

Behavior

Consumer characteristics

The model is supported if its implied covariance-matrix does not differ significantly from the empirical covariance matrix.


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Theory Testing: Alternative Models The researcher has specified several alternative models (or competing models) and, on the basis of an analysis of a single set of empirical data, one of the models should be selected. Model 1

Product attributes

Affect


Model 2

Product attributes

Behavior

Affect

Behavior


Model 1 is supported if its fit is not significantly worse. Dr. Jörg Henseler, University of Cologne, Department of Marketing and Market Research

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Theory Testing: Model Generating The researcher has specified a tentative initial model. If the initial model does not fit the given data, the model should be modified and tested again using the same data. Several models can be tested. Finding of a model that fits the data well from a statistical point of view and additionally every parameter of the model can be given a substantively meaningful interpretation.

Product attributes

Affect

Behavior


The re-specification of each model may be theory driven or data driven. Although a model may be tested in each round, the whole approach is model generating, rather than model testing. Depending on the circumstances, the chances to identify the true model can be quite small (MacCallum 1986). Dr. Jörg Henseler, University of Cologne, Department of Marketing and Market Research

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Example 1

Research question:

Does the analysis of whole blood and dried blood spots lead to equivalent conclusions in terms of heroine consumption?

Garcia Boy, R.; Henseler, J.; Mattern, R.; Skopp, G. (2008). Determination of Morphine and 6-Acetylmorphine in Blood With Use of Dried Blood Spots. Therapeutic Drug Monitoring, Vol. 30, No. 6, pp. 733-739. Dr. Jörg Henseler, University of Cologne, Department of Marketing and Market Research

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Example 1

Strictly confirmatory. Theory: Measurement instruments have constant reliability, and both ways of conserving blood lead to equal conclusions (φ12=1). Dr. Jörg Henseler, University of Cologne, Department of Marketing and Market Research

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Example 2 Alternative models. Model 1:

ζ1

Relationship Quality

Sport Sponsorship Intensity

ζ1

Economic Value

ζ1

Model 2: Sport Sponsorship Intensity

Relationship Quality

ζ1

Economic Value

Wilson, B.; Henseler, J. The Mediating Role of Relationship Quality Impacting Sponsorship Effects on Perceived Economic Outcomes. ANZMAC Conference, December 4-6, 2006, Brisbane, Australia. Dr. Jörg Henseler, University of Cologne, Department of Marketing and Market Research

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Example 3

Wholesaler Loyalty

Instrumental Variable 1

y4

ε4

y5

ε5

y6

ε6

ζ1

ζ2

Channel Switching ζ3

Instrumental Variable 2

Brand Loyalty

y7

ε7

y8

ε8

y9

ε9

y1

ε1

y2

ε2

y3

ε3

Model generating. Eggert, A.; Henseler, J.; Hollmann, S. Who Owns the Customer? Disentangling Customer Loyalty in Indirect Distribution Channels. 17th International Colloquium in Relationship Marketing, September 16-19, 2009, Maastricht, The Netherlands. Dr. Jörg Henseler, University of Cologne, Department of Marketing and Market Research

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Conclusions  CBSEM lets you test entire theories.  CBSEM may help to develop sensometric theories.  CBSEM allows to explicitly model measurement error.  Caution: • CBSEM does not focus on explaining variance. • CBSEM does not focus on prediction.


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Theory testing vs. prediction

Covariancebased SEM

Theory testing

PLS path modeling

Neural networks

Prediction


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Thank you.


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Available Software for Covariance-Based Structural Equation Modeling / CFA  LISREL  AMOS (graphical interface)  EQS  MPLUS (includes latent class modeling)  Mx  R: sem package  ...  Streams (meta-language for LISREL/EQS/MPLUS)


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