Confirmatory Factor Analysis(CFA) and Structural Equation Modeling(SEM) with MPLUS

The course targets PhD students and faculty of universities and colleges who are seeking to improve their skills in quantitative research methods. The theme for the course is structural equation modeling.

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ECTS credits: 5
Level of course: Ph.D. course
Type of course: Elective for students in business or other social science disciplines.
Duration: 18-22th May 2015.
Location: Bodø.
Language: English.
Faculty: Bodø Graduate School of Business, Harstad University College and the University of Tromsø Business School take great pleasure in inviting you to the course Structural Equation Modeling.
Bodø Graduate School of Business, University of Nordland, Norway, is the institutional
course organizer.

Main faculty:

Professor Peter Schmidt, University of Giessen, Germany
Professor Eldad Davidov, Universitety of Zürich, Switzerland

Additional faculty:

Professor Tor Korneliussen, Bodø Graduate School of Business

Administrative coordinator:

Grete Ingemann Knudsen, Bodø Graduate School of Business


The goal of this course is to provide the course participants with the ability to understand publications using CFA and SEM and apply confirmatory factor analysis and structural equation modelling to their own data.


The course targets PhD students and faculty of universities and colleges who are seeking to improve their skills in quantitative research methods. The theme for the course is structural equation modeling.

This course deals with CFA and SEM in the context of social sciences. Examples are drawn from two of the most widely used and tested theories in the social sciences: the theory of planned behaviour of I.Aizen and the value theory of Shalom Schwartz. The course  gives an introduction to confirmatory factor analysis to develop and test measurement models within and between groups including cross-national comparisons. Furthermore we will deal with full structural equation models to test complex theories involving mediation and moderation. Topics are:

  1. Confirmatory factor analysis and Simultaneous Confirmatory Factor Analysis to test convergent and divergent validity of measurement instruments and develop scales.
  2. Multitrait Multimethod Models and Higher Order Confirmatory Factor Analysis to model more complex measurement models.
  3. Multigroup Confirmatory Factor Analysis to test invariance of measurements over groups and time points as a prerequisite for comparing regression coefficients and means over groups including approximate measurement invariance using Bayesian estimation and alignment. .
  4. Full Structural Equation Models with multiple indicators for the constructs.
  5. Mimic Models with formative and reflective indicators
  6.  Test of full vs. Partial mediation and Indirect and Total Causal effects in Full Structural Equation Models
  7. Test of Moderation in Full structural Equation Models and Moderated Mediation.

The course is oriented towards applications of the technique, but the basic concepts and theory are also dealt with. We recommend strongly that the participants bring their own data and prepare it according to the guidelines of MPLUS for organizing the input data.

By the end of this course the participants will be able to recognize in which situations the different model specifications are useful, to choose the method appropriate to the problem at hand, to apply the method using appropriate software, and to interpret the results. The practical classes in the afternoons comprise: computer laboratory, applications to social science data, and to some degree analysis and discussion of participants' data sets.

Themes covered in the course include:

• Overview of causality and empirical research
• Foundation of confirmatory factor analysis
• Model modification and the theory of testing
• Level of measurement equivalence and source of non-equivalence
• Structural equation models with latent variables and multiple indicators
• Specification, identification and estimation
• Mediation and moderation
• Multiple group comparison and interaction effects
• MIMIC models

Learning outcomes

After completing the course the student will have acquired knowledge and skills about structural equation modeling:


• Overview of causality and empirical research
• Overview of the logic of structural equation modeling including specification, identification and estimation
• Understand measurement models and conformative factor analysis in single and multiple groups
• Understand model modification and the strategy of theory testing


• Demonstrate an understanding of the basic theory and principles of structural equation modeling
• Formulate a simple SEM model and implement it using structural equation software
• Critically discuss and evaluate a SEM model, and be able to respecify it if necessary
• Critically assess research publications using structural equation modeling techniques

Organization and learning activities

This is an intensive course of one week with individual study required prior to and after the
meeting. The course integrates lectures by experts in the field with practical sessions.

Practical information

Registration deadline: 18th March 2015
To register, students should fill in an application form with attachments


Location and accommodation

The course will take place at the campus of University of Nordland, Bodø.
The course is free.
Participants will pay for hotel accommodation and travel themselves. We advise you to book accommodation early.


Participation and a paper. The paper delivered after the course week will be evaluated by the grades ‘passed’ or ‘non-passed’.

Course Outline

The course will show how a causal theory can be represented by a path diagram and translated into a structural equation model and how the model can be estimated and tested with the MPLUS computer program. In the first part we will deal with measurement models relating single or multiple indicators to latent variables. Furthermore, different specifications of measurement models are tested via confirmatory factor analysis as a special case of a structural equation model. Next we will combine both the structural and the measurement models. Topics include particularly the treatment of cross-cultural data with multiple-group modeling and MIMIC models. Special attention is given to the process of model modification and the topics of mediation and moderation. The course will be application oriented rather than technically oriented. We strongly recommend participants to bring their own data with them (e.g., survey data that needs to be analyzed). Time will be dedicated for consultation on Thursday afternoon, and some participants will have the opportunity to present their models on Friday, discuss problems they had faced and ask other participants and the teachers for possible solutions.

Exam and evaluation

Participation in lectures, performing the prepared exercises and a short report on an application of cfa or full SEM. Paper graded: pass/non pass.

Language of education: English

Course presenter:  Professor Peter Schmidt University of Giessen, Germany

Compulsory Literature

Brown, T. 2015, Confirmatory factor Analysis for applied Research , 2nd edition. New York and London: Guilford Press. Paperback.

Kline, R.B. 2011. Principles and Practices of structural equation modelling. 3 rd edition. New York and London. Guilford Press.Paperback.

Kelloway, E.K., 2014. Using Mplus for Structural Equation Modeling; Sage. Thosand Oaks. California.


Recommended literature:

J.Wang and X.Wang 2012. Structural Equation Modeling. Applications using Mplus. New York. J.Wiley.


Preliminary timetable







9.00 – 12.00
·  Confirmatory Factor Analysis: Specification




 Cross-loadings and Error Correlations

Ordinal data

Missing data

Multiple Group Confirmatory factor Analysis:

Configural, metric and scalar Invariance

Approximate measurement invariance

MTMM Models and Higher Order CFA 

Full Structural Equation Models

Full vs. Partial mediation.

Indirect and Total effects

MIMIC Models with formative and reflective indicators

Moderation and Nonlinearity in SEM Models

Multiple Group Structural Equation Modeling

Reporting CFA and SEM results

Presentation of Projects of the Participants using own data.






13.00 – 15.00


PC Lab


PC Lab


PC Lab


PC Lab