# Nonlinear Mixed-effect Models

### Daily programme

Duration and credits: one week, 2 ECTS (lectures) or 4 ECTS (lectures + returning the reports of the exercises)
Teaching language: English
Level: UEF students who have sufficient prior knowledge. External students and researchers from various fields, including statistics, forest and environmental sciences, pharmacy, mathematics and physics.
Course coordinator: Lauri Mehtätalo, lauri.mehtatalo@uef.fi
Responsible department: School of Computing
Prerequisites: Basics on linear models and mixed-effect models. Pre-course reading will be distributed prior to the course.
Learning outcomes: To understand the basics of nonlinear regression and nonlinear mixed-effect models. To be able to build and fit such model in R. In addition, the student understands the link of nonlinear models to linear and generalized linear models.

### Content

In linear models and linear mixed-effect models, the relationship between the response variable y and predictors x is described by a function that is linear in terms of parameters. In nonlinear models, the assumed function is not linear with respect to parameters. By wise selection of the transformations of x, the linear model is able to describe practically any relationship between y and x; therefore switching from linear to nonlinear model does not lead to better fit to the data. However, nonlinear models have other benefits: they can be built on the subject-matter theory about the process being modeled, with nice interpretations for the parameters, may have smaller number of parameters than the linear model, and may behave better in extrapolation. An example of a nonlinear relationship is the carbon flux of an ecosystem as a function of photosynthetically active radiation. Similar models are also used in other fields, such as pharmacokinetics, ecology and forest sciences. Also the generalized linear (mixed-effect) models can be seen as a special case of the nonlinear mixed-effect models. This one-week intensive course covers nonlinear models and nonlin-ear mixed-effect models from an applied point of view. We use real-data examples from forest sciences and ecology, and fit the models using R-software. The course starts with one-day overview of linear mixed-effect models.
Modes of study: Lectures, execises and homework
Teaching methods: The course consists of 4 hours of lectures every day and 4 hours for exercises. Participating to the intensive week only gives 2 cp. returning reports of the exercises gives an additional cp.
Study materials: Lecture notes (see http://cs.uef.fi/~lamehtat/textbook.htm, the chapters about nonlinear and generalized linear mixed-effect models). Pinheiro and Bates 2000. Mixed-effects models in S and S-Plus. Springer.
Evaluation criteria: Pass/fail based on the returned homework report.
Teacher: Lauri Mehtätalo (UEF)