Prospectus

# Linear & generalized linear models and linear algebra

Course
2022-2023

none

## Description

In the study of the effect of one or more explanatory variables on a response variable, linear regression and analysis of variance are important techniques. In linear regression we study how a quantitative variable, like the dose of a medicine, influences a quantitative response variable, like blood pressure. In analysis of variance we compare different groups with respect to a quantitative response, e.g. comparing the yields of different corn varieties. The statistical models that underlie these techniques are special cases of the linear model. In this course we discuss linear models with a thorough treatment of the matrix algebra for which the foundation is laid in the first two weeks.
Although linear models are widely used, sometimes alternatives are preferred. Therefore, we discuss how to check the assumptions underlying linear model: independent errors, with a normal distribution and constant variance. When the assumptions of normality and constant variance are violated, the wider class of generalized linear models may be employed. Examples discussed in this course are logistic regression for a binary response (assuming a binomial distribution), and log-linear models for counts (using a Poisson distribution). Data are still assumed to be independent. Emphasis will be on gaining understanding of the models, the kind of data that can be analyzed with these models, and with the statistical analysis of empirical data itself.
In the course we will first focus on the linear algebra which will be immediately followed by an exam after 2 weeks. Another exam on the remaining part (linear and generalized linear models) will take place at the end of the course.

## Course objectives

Students should understand the basic concepts of linear models (regression, ANOVA, ANCOVA) and generalized linear models, and the proper statistical inference methods. Students, when confronted with practical data for a linear or generalized linear model assuming independence should be able (1) understand the statistical analysis of the empirical data itself, (2) check for violations on the assumptions, and (3) perform a proper data analysis. Students should know the linear algebra, especially the matrix algebra, that is needed to understand Linear Models.

## Timetable

You will find the timetables for all courses and degree programmes of Leiden University in the tool MyTimetable (login). Any teaching activities that you have sucessfully registered for in MyStudyMap will automatically be displayed in MyTimeTable. Any timetables that you add manually, will be saved and automatically displayed the next time you sign in.

MyTimetable allows you to integrate your timetable with your calendar apps such as Outlook, Google Calendar, Apple Calendar and other calendar apps on your smartphone. Any timetable changes will be automatically synced with your calendar. If you wish, you can also receive an email notification of the change. You can turn notifications on in ‘Settings’ (after login).

For more information, watch the video or go the the 'help-page' in MyTimetable. Please note: Joint Degree students Leiden/Delft have to merge their two different timetables into one. This video explains how to do this.

## Mode of Instruction

Lectures and practicals (partly computer practicals, partly exercises).

## Assessment method

Assessment of a student will be based on a written exam in 2 parts (linear algebra and statistics).
Possibly a report on the case study in which students will be asked to analyze a practical data set or study a theoretical topic, will be part of the exam grade. This is yet to be decided upon.
The teacher will inform the students on how the inspection of and follow-up discussion of the exams will take place.

• Fox (2008). Applied Regression Analysis and Generalized Linear Models. Sage

• Faraway: Practical Regression and ANOVA using R. Text available as PDF at http://cran.r-project.org/doc/contrib/Faraway-PRA.pdf

• Faraway (2006). Extending the linear model with R. Generalized linear, mixed effects and nonparametric regression models. Chapman & Hall/CRC

## Registration

From the academic year 2022-2023 on every student has to register for courses with the new enrollment tool MyStudyMap. There are two registration periods per year: registration for the fall semester opens in July and registration for the spring semester opens in December. Please see this page for more information.

Please note that it is compulsory to both preregister and confirm your participation for every exam and retake. Not being registered for a course means that you are not allowed to participate in the final exam of the course. Confirming your exam participation is possible until ten days before the exam.

Extensive FAQ's on MyStudymap can be found here.

## Contact

Evert-jan.bakker[at] wur.nl
vahe.avagyan[at] wur.nl