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

Covariance-based Structural Equation Modeling: Foundations and Applications

Dr. Jrg Henseler

University of CologneDepartment of Marketing and Market Research

&

Radboud University NijmegenInstitute for Management Research

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

Family Tree of SEM

BivariateCorrelation

MultipleRegression

PathAnalysis

StructuralEquationModeling

ConfirmatoryFactor Analysis

ExploratoryFactor

Analysis

FactorAnalysis

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

Schematic Representation of aStructural Equation Model

Indicatorx1

1Indicator

x2

Indicatorx4

2Indicator

x5

1

2

1

Indicatory1

Indicatory2

1

2

structural model

measurement model of the latent exogenous variables

4

5

Indicatorx3

3

Indicatorx6

6

Indicatory3

3

measurement model of the latent endogenous variables

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

Symbols Used

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).

x1

1

1

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

The Idea of Estimating SEM

( ) Seapproximat

=

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

variablesobserved ofmatrix covariance sampleparameters model

variablesobserved ofmatrix covariance implied

:::

S

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

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

The Concept of "Fit" Revisited

Results from Correlation orRegression:

R = 0

Thus, no fit!

Example: A theory states that two variables are unrelated. We empirically test the theory.

Results from CBSEM:

= S

Thus, perfect fit!

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

Theory Testing

Covariance-based structural equation modeling facilitates three types of theory testing:

strictly confirmatory

alternative models

model generating

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

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.

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

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BehaviorAffect

Productattributes

Consumercharacteristics

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

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 is supported if its fit is not significantly worse.

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BehaviorAffect

Productattributes

Consumercharacteristics

BehaviorAffect

Productattributes

Consumercharacteristics

Model 1 Model 2

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

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.

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).

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BehaviorAffect

Productattributes

Consumercharacteristics

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

Example 1

Research question:

Does the analysis of whole bloodand dried blood spots lead to

equivalent conclusions in termsof 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.

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

Example 1

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Strictly confirmatory.

Theory: Measurement instruments have constant reliability, and both ways of conserving blood lead to equal conclusions (12=1).

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

Example 2

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1

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.

Alternative models.

SportSponsorship

Intensity

RelationshipQuality

EconomicValue

1

1

SportSponsorship

Intensity

RelationshipQuality

EconomicValue

1

Model 1:

Model 2:

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

Example 3

y1

y2

1

2

1

Instrumental Variable 2

y3 3

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WholesalerLoyalty

BrandLoyalty

ChannelSwitching

y7

y8

7

8

y9 9

y4

y5

4

5

y6 6

2

3

Instrumental Variable 1

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.

Model generating.

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

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

Theory testing vs. prediction

Neural networks

PLSpath modeling

Covariance-based SEM

PredictionTheory testing

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

Thank you.

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Dr. Jrg Henseler, University of Cologne, Department of Marketing and Market Research - 20 -

Available Software for Covariance-BasedStructural Equation Modeling / CFA

LISREL

AMOS (graphical interface)

EQS

MPLUS (includes latent class modeling)

Mx

R: sem package ...

Streams (meta-language for LISREL/EQS/MPLUS)

Covariance-based Structural Equation Modeling: Foundations and ApplicationsOverviewFamily Tree of SEMSchematic Representation of aStructural Equation ModelSymbols UsedThe Idea of Estimating SEMHow SEM and Traditional Approaches Are DifferentThe Concept of "Fit" RevisitedTheory TestingStrictly Confirmatory Theory TestingTheory Testing: Alternative ModelsTheory Testing: Model GeneratingExample 1Example 1Example 2Example 3ConclusionsTheory testing vs. predictionThank you.Available Software for Covariance-BasedStructural Equation Modeling / CFA