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PHDH913 Introduction to longitudinal data analysis using mixed effects models

Course description for academic year 2024/2025

Contents and structure

Course information, material, videos, etc will be published on Canvas, which is the current learning platform at HVL.

The course is a 3-day course at Campus Kronstad:

Part 1:

Features of longitudinal data. Cross-sectional and longitudinal effects. How correlation comes into longitudinal data (use examples and methods to reveal correlation structures) and why standard methods do not suffice. Briefly introduce three regression strategies for accounting for correlated data. Comparing methods using real data example.

Part 2:

Define mixed effects models. Notions and notations. Simplest random intercept model. Going from a naive regression model to the random intercept model. Derive covariance matrix from the random intercept model. Show the consequences of ignoring correlation using naive regression modelling vs a random intercept model. Estimation of standard errors.

Part 3:

Going from the random intercept model to the random coefficient model. Correlation between random intercept and slope. Derive covariance matrix from the random coefficient model. Within and between subject variation in fixed effects. Missing data pattern. Distributions of random effects. Time varying vs time constant fixed effects - interpretation. Time-by-group interaction. Reporting of results.

Learning Outcome

After completing the course, the student will have the following total learning outcome:


The candidate …

  • can explain how longitudinal study designs introduce correlation into data
  • can explain why standard regression techniques are not appropriate for correlated data
  • can explain how linear mixed effects models can account for correlated data


The student …

  • can explore correlation structures in longitudinal data
  • can include random effects in linear models to account for correlated data
  • can derive variance-covariance matrix from random effects in linear models
  • can evaluate distributions of random effects in linear models
  • can explore within/between subject variation in fixed effects
  • can explore missing data patterns of fixed effects
  • can interpret time-dependent and time-constant regression coefficients
  • can evaluate the importance of a random effect by using likelihood ratio test
  • can use mixed effects models to estimate intra-cluster correlation
  • can compare observed vs estimated correlation matrix in linear models
  • can specify time-by-group interaction for estimating group-specific time associations
  • can report associations in terms of regression coefficients

General competence:

The student…

  • can evaluate data situations when linear mixed effects models are appropriate
  • can apply linear mixed effects models for longitudinal data
  • can report and interpret results based on linear mixed effects models

Entry requirements

Master's degree with 120 ECTS credits or equivalent in relevant academic fields.

Number of participants: The course requires a minimum of 5 and a maximum of 20 participants. The number of PhD students should preferably comprise at least 50% of the total number of participants.

Recommended previous knowledge

Basic statistics and linear regression modelling

Statistical language programming in Stata or other statistical software.

Teaching methods

Each day of the course consists of the following teaching methods:

  • Plenary lectures (2.5 hours)
  • Practical exercises in data lab with feedback from lecturer (3 hours)
  • Plenary summary of the learning goals of the day (0.5 hours)

Course dates can be found on the PhD programme's webpages

Compulsory learning activities

2 out of 3 assigned computer exercises must be approved. The exercises should be submitted through Canvas.



A written, individual assignment. The exam consists of real data problems, which the student needs to solve by using statistical software and course material.

Grading Pass / fail

New exam

If failing to pass, the student has the opportunity to hand in a new exam once.

Examination support material

All aids are permitted.

More about examination support material