Linear Statistical Models

Prof. Hans Jørn Juhl (HJJ) and Prof. Joachim Scholderer (SCH), Aarhus University, School of Business and Social Sciences, Department of Business Administration.

The course will introduce participants to the three statistical modelling approaches that dominate in the social sciences: the general linear model, linear mixed models (multi-level models) and structural equation modelling. The course will be an intensive five-day course, consisting of the following modules:

Day 1: The general linear model

  • Simple, multiple and multivariate regression models
  • Regression with transformed variables
  • Correlation and causation
  • Hypothesis testing, the iid assumption and consequences of its violation
  • Overfitting and the bias-variance trade-off
  • Suppression and mediation
  • PROC GLM lab: SAS exercises

Day 2: Linear mixed models I

  • Nested units of observation
  • Fixed and random effects
  • Random intercepts and slopes
  • Variance components
  • Multi-level models
  • Model comparison strategies
  • PROC MIXED lab: SAS exercises

Day 3: Linear mixed models II

  • Longitudinal data
  • Parameterisation of fixed and random effects
  • G-side versus R-side covariance structures
  • Common types of covariance structures
  • Consequences of misspecification
  • Model comparison strategies
  • PROC MIXED lab: SAS exercises

 Day 4: Structural equation modelling I

  • Latent variables and measurement error
  • Confirmatory factor analysis
  • Model identification
  • Maximum likelihood estimation
  • Goodness-of-fit tests and descriptive fit indices
  • Model comparison strategies
  • PROC CALIS lab: SAS exercises

Day 5: Structural equation modelling II

  • Path analysis
  • Model identification
  • Direct, indirect and total effects
  • Structural equation models with latent variables
  • Multi-group models and measurement invariance
  • Model comparison strategies
  • PROC CALIS lab: SAS exercises


All participants are expected to obtain the course literature before the beginning of the course: 

  • Graham, J. M. (1996). Congeneric and (essentially) tau-equivalent estimates of score reliability: What they are and how to use them. Educational and Psychological Measurement, 66, 930-944.
  • Kaplan, D. (2009). Structural equation modelling: Foundations and extensions (2nd Ed.). Thousand Oaks, CA: Sage.
  • Kreft, I. & De Leeuw, J. (1998). Introducing multilevel modeling. Thousand Oaks, CA: Sage.
  • Littell, R. C., Pendergast, J. & Natarajan, R. (2000). Modelling covariance structure in the analysis of repeated measures data. Statistics in Medicine, 19, 1793-1819.
  • SAS Institute (2011). SAS/STAT 9.3 user’s guide (Chapters 26, 41, 58). Cary, NC: SAS Institute (
  • Rucker, D. D., Preacher, K. J., Tormala, Z. L. & Petty, R.E. (2011). Mediation analysis in social psychology: Current practices and new recommendations. Social and Personality Psychology Compass, 5/6, 359-371.
  • Singer, J. D. (1998). Using SAS PROC MIXED to fit multilevel models, hierarchical models, and individual growth models. Journal of Educational and Behavioral Statistics, 24, 323-355.
  • Steenkamp, J.-B. E. M. & Baumgartner, H. (1998). Assessing measurement invariance in cross-national consumer research. Journal of Consumer Research, 25, 78–90.

Instruction methods
Lectures (20 hours) and lab exercises (10 hours)

The techniques introduced in this course will be demonstrated using SAS. All participants are expected to obtain and install the SAS system before the beginning of the course and familiarise themselves with basic operations (library references, data import and export, variable transformations, general syntax rules).

Time and place
23-27 June 2014. Aarhus University, School of Business and Social Sciences, Department of Business Administration, Bartholins Allé 10, DK-8000 Aarhus C. Room: 1325-242.

Teaching language

We expect a prior knowledge in methodology and statistics that is equivalent to that obtained during a BSc in Economics and Business Administration as taught at Aarhus University (consisting of the courses Statistics I, Statistics II, Philosophy of Science I, Philosophy of Science and Methodology II—Quantitative Methods, Philosophy of Science and Methodology III—Qualitative Methods). In addition, we expect that all participants have a basic understanding of matrix algebra.

The total number of participants is limited to 25. Since the course is mandatory for all PhD students enrolled in the Business Administration programme of the Graduate School of Business and Social Sciences, Aarhus University, all applicants enrolled in this programme will be admitted. The remaining places will be distributed on a first-come-first-served basis among applicants who are enrolled in other PhD programmes and who can document that they have mastered the prerequisites.  

2 May 2014 to: Lisbeth Widahl, Aarhus University, School of Business and Social Sciences, Department of Business Administration, Bartholins Allé 10, DK-8000 Aarhus C (preferably by email: The application form can be downloaded from the right-hand side of this web page. Please note that your application/registration is binding.

PhD students from other programmes/universities will be charged a fee that covers meals during the course (for information, please contact Lisbeth Widahl, Participants are required to find their own accommodation.

5 ECTS points for active participation and submission of written solutions to the course exercises.

Exam form
Each participant will submit solutions to exercises in which linear mixed models and structural equation modelling are applied to empirical data sets. The assignments will be evaluated in terms of pass or fail. Deadline for submission is 31 August 2014.

Further information
Please contact Prof. Hans Jørn Juhl or Prof. Joachim Scholderer