Introduction to structural equation modeling

Ned Kock

SEM techniques• Structural equation modeling (SEM) techniques

can be:– Covariance-based – e.g., those employed by the

statistical software analysis tool called LISREL.– Variance-based – e.g., those employed in partial least

squares (PLS) analysis.

• SEM techniques are known as second generation data analysis techniques.

• SEM allows for the modeling and testing of relationships among multiple independent and dependent constructs, all at once.

Constructs, indicators and paths• Construct

– This is a theoretical concept that is not directly measurable. Also known as latent variable.

• Indicator– Is a measurable variable used to represent a

construct (e.g., item on a questionnaire). Also referred to as manifest variable, item, and indicant.

• Path– Is the link between constructs, or from construct to

indicator. Also known as link, and often measured through a path coefficient.

Path coefficient Path coefficient between Y and X = standardized

partial regression of Y on X controlling for the effect of one (e.g., Z) or more variables.

Mathematical formula

X

Y

Z

Diagrammatic representation

Partial regression (standardized) of Y and X, controlling for Z.

Partial regression (standardized) of Y on Z, controlling for X.

Path coefficient example

R

W

E

Diagrammatic representation

Mathematical formula

Note: Hypothetical situation

0.10

0.36

Note: This is a simple linear regression model, where R, W and E are manifest variables.

W R EWealth - W 1Race - R 0.25 1Education - E 0.45 0.31 1Correlation matrix

Path coefficient between W and R controlling for E = 0.10

Endogenous vs. exogenous• Exogenous construct

– This is a construct that is independent of any other constructs.

– No other constructs point at it in an SEM diagram.– Also known as exogenous latent variable.

• Endogenous construct– This is a construct that depends on one or more

other constructs.– Is pointed at by one or more constructs in an SEM

diagram.– Also known as endogenous latent variable.

SEM model componentsConstruct (a.k.a. latent variable)

Exogenous construct (a.k.a. independent construct)

Indicator

Path

Interaction effect construct (a.k.a. moderating effect construct)

Source: Chin (2001)

Endogenous construct (a.k.a. dependent construct)

Path coefficient

Reflective measurement

• In this form of construct measurement, paths connecting construct to indicators are directed towards the indicators.

• The indicators are supposed to load strongly on the construct.

• Such constructs are often designated as latent constructs (or reflective latent constructs).

Reflective measurement example• Construct

– New product development team effectiveness

• Indicators (question-statements answered on a Likert-type scale)

1. The product met or exceeded volume expectations.

2. The product met or exceeded sales dollar expectations.

3. The product overall met or exceeded sales expectations.

Formative measurement

• In this form of construct measurement, paths connecting construct to indicators are directed towards the construct.

• The indicators are not assumed to have to load strongly on the construct.

• Such constructs are often designated as formative latent constructs.

• Only variance-based SEM techniques (e.g., PLS) can deal with formative latent constructs.

Formative measurement example• Construct

– Team electronic communication use• Indicators (question-statements answered on a Likert-type scale)

1. The team used e-mail to fellow team members (1 to 1).2. The team used e-mail to team distribution lists (1 to many).3. The team used team messaging boards or team discussion forums.4. The team used shared electronic files.5. The team used Lotus notes to facilitate sharing information among team

members.6. The team used electronic newsletters that covered project information.7. The team used auto routing of documents for team member and management

approval.8. The team used file transfer protocols (FTP) to attach documents to e-mails and

Web pages.9. The team used a Web page dedicated to this project.10. The team used a Web page for this project that contained project specs, market

research information, and test results.11. The team used voice messaging.12. The team used teleconferencing.13. The team used video conferencing14. The team used desktop video conferencing15. The team used attached audio files to electronic documents.16. The team used attached video files to electronic documents.

The SEM advantage• The ability to test multiple relationships at once

differentiates SEM techniques from several first generation regression techniques such as:– ANOVA.– MANOVA.– LOGIT.– Linear regression.

• Generally, first generation techniques allow for the analysis of a significantly more limited number of relationships between independent and dependent variables at once.

SEM techniques usage

Source: Gefen, Straub, & Boudreau (2000)

Notes: •Information & Management (I&M), Information Systems Research (ISR), and Management Information Systems Quarterly (MISQ) are top-tier journals in the field of information systems.•Wynne Chin, one of the developers of PLS-Graph (a widely used PLS-based SEM analysis tool), is an information systems researcher.•SEM tools are also widely used in other disciplines, mostly behavioral science research-based or related disciplines, for the causal modeling of multivariate datasets where complex webs of relationships between variables are tested.

Techniques comparison

Source: Gefen, Straub, & Boudreau (2000)

Techniques capabilities

Source: Gefen, Straub, & Boudreau (2000)

Acknowledgements

Adapted text, illustrations, and ideas from the following sources were used in the preparation of the preceding set of slides:

1. Gefen, D., Straub, D. W., & Boudreau, M-C. (2000). Structural equation modeling and regression: Guidelines for research practice. Communications of the AIS, 4(7), 1-76.

2. Kock, N. and Lynn, G. (2005), The E-collaboration Paradox: A Study of 290 New Product Development Teams, Proceedings of the 16th Information Resources Management International Conference, Khosrowpour, M. (Ed), Idea Group Publishing, Hershey, PA, pp. 444-448.

3. PLS-Graph User’s Guide, by W.W. Chin. Publisher: Soft Modeling Inc. (2001).

Final slide