# BIN303 Estimation of variance components - animal and plants

Credits (ECTS):5

Course responsible:Gunnar Klemetsdal

Campus / Online:Taught campus Ås

Teaching language:Engelsk

Course frequency:BIN303 will intentionally be given every second year.

Nominal workload:125 hours of study, including colloquia and participation in study groups for 25 hours.

Teaching and exam period:The course version is given first time in 2024, in the spring paralell.

Variance components are needed for prediction of breeding values.The course will give the basis for understanding of likelihood, log likelihood, first and second order derivatives of log likelihood, for determination of maximum likelihood (ML) estimates of effects, in addition to their precision through the Fisher information matrix. Moreover, first and second order derivatives will be combined through the Newton-Raphson method for iterative estimation of variance components. A simple model will be used initially, to introduce the mixed linear (pl)animal model. Then, restricted maximum likelihood (REML) estimates of variance components will be introduced through a model transformation, and estimates will be obtained through "average information", i.e. the methodology that is used in state-og-the-art R-packages, built on likelihood. This summes up the course by allowing to estimate variance components in a variety of linear models, e.g. with several random effects, in multivariate models and in models used to analyse longitudinal data, while R and matrix algebra will be used to solve the assignments in the first half of the course.

### Learning outcome

Knowledge

You will get knowledge on theory for estimation of variance components in mixed linear models via REML.

Skills

You will be able to calculate REML-variance components with R, by use of matrix algebra and by use of a R-package.

General competence

In general, the course will give you competence in data handling, programming, linear algebra, and estimation theory; and some understanding of plant and animal breeding programs

• Every second week lecture with assignments in R, that will be worked through in detail the following week. Self-study of literature. Estimation of variance components on own, realistically huge datasets. Presentation for students and teacher.
• Teacher goes through all assignments and participate in all colloquia. Advice will be given for term papers and assignments.
• Primarilly BIN301, but at least good knowledge in matrix algebra and linear models.
• Evalutation will be made of the term paper, showing results of calculations of variance components in real data with state of the art R-program.

• Evaluated by teacher and external sensor.
• Participation in colloquia.

Presentation of calculation of variance components in an own data set, of size relevant for plant or animal breeding organizations.

Commenting/being opponent to other participants' presentations.

• Approximately 12.5 hours colloquium/lectures and 12.5 hours of exercises.
• Special requirements in Science