NMAK16018U  Structural Equation Models

Volume 2017/2018

MSc Programme in Statistics


The course is an introduction to latent variable models. We introduce Item Response Theory (IRT) models, focusing mainly on the Rasch model, Confirmatory Factor Analysis (CFA) models, and Structural Equation Models (SEM’s). The exercises will be a mixture of theoretical problems and data analysis. The course covers the following topics:

  • General measurement models (including Rasch model and CFA)
  • Conditional and marginal estimation
  • Model identification
  • Evaluation of model fit
  • Path analysis
  • Causal inference
  • Structural equation models
  • Measurement error in covariates
  • An introduction to implementations of the methodology in R. 
Learning Outcome


At the end of the course the student will have knowledge about different types of latent variable models, and will have the knowledge to

  • Explain the assumptions underlying the models
  • Interpret the parameters of the models
  • Discuss model identification and be able to determine if two models are identical



The student will acquire skills necessary for applying latent variable models to real data, decide on which model to use and which analysis to perform. The student will have the skills to utilize theoretical results in the practical analysis, including how complex models can be specified.


At the end of the course the students will have the competence to

  • Evaluate the fit of measurement models (including Rasch model and CFA)
  • Estimate the parameters of structural equation models
  • Use latent variable models to adjust for measurement error in covariates
Statistik 2 or similar knowledge of statistics. Linear algebra and the multivariate normal distribution are essential prerequisites. Some experience with the use of R or SAS is recommended.
4 hours of lectures and 2 hours of presentation and discussion of a weekly assignment per week for 7 weeks.
7,5 ECTS
Type of assessment
Oral examination, 30 minutes without preparation
Every week a few statistical problems will be given. Students will in turn present solutions in class followed by a plenary discussion of these solutions. The student's own solutions will form the basis of the first part of the oral examination. The second part will be devoted to a general discussion of the contents of the course.
All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
Several internal examiners

Same as ordinary.

Criteria for exam assesment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.

  • Category
  • Hours
  • Lectures
  • 28
  • Exercises
  • 14
  • Preparation
  • 164
  • Total
  • 206