Covariance-based Structural Equation Modeling: Foundations and Applications. Dr. Jörg Henseler. University of Cologne. Department of Marketing and Market ...
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
Dr. Jörg Henseler, University of Cologne, Department of Marketing and Market Research
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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
Dr. Jörg Henseler, University of Cologne, Department of Marketing and Market Research
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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).
Dr. Jörg Henseler, University of Cologne, Department of Marketing and Market Research
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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
Dr. Jörg Henseler, University of Cologne, Department of Marketing and Market Research
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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!
Dr. Jörg Henseler, University of Cologne, Department of Marketing and Market Research
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Theory Testing Covariance-based structural equation modeling facilitates three types of theory testing: strictly confirmatory alternative models model generating
Dr. Jörg Henseler, University of Cologne, Department of Marketing and Market Research
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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.
Dr. Jörg Henseler, University of Cologne, Department of Marketing and Market Research
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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
Consumer characteristics
Model 2
Product attributes
Behavior
Affect
Behavior
Consumer characteristics
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
Consumer characteristics
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.
Dr. Jörg Henseler, University of Cologne, Department of Marketing and Market Research
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Theory testing vs. prediction
Covariancebased SEM
Theory testing
PLS path modeling
Neural networks
Prediction
Dr. Jörg Henseler, University of Cologne, Department of Marketing and Market Research
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Thank you.
Dr. Jörg Henseler, University of Cologne, Department of Marketing and Market Research
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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)
Dr. Jörg Henseler, University of Cologne, Department of Marketing and Market Research
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