# Linear and Generalized Linear Models

Vak
2023-2024

## 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.
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.

Topics:

• Simple and multiple linear regression

• One and two-way ANOVA

• Pairwise testing and multiple comparisons

• Model assumptions and checking

• Linear models in matrix form

• Outliers, influential points, leverages

• Model selection and selection criteria

• Maximum likelihood

• Generalized linear models (logistic and Poisson regression)

## Course Objectives

After the completion of this course, students should be able to

• understand the basic concepts of linear models (regression, ANOVA, ANCOVA) and generalized linear models, and the proper statistical inference methods.

• apply the methods to model empirical data.

• formulate and check the underlying assumptions of the model.

• analyse data with R Studio, given practical data and a research question.

• interpret the results and form conclusions relevant for the actual problem.

## 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

Lecture sessions and mandatory computer practicals.

## Assessment method

• Computer practical (attendance compulsory) has to result in a pass.

• Written exam.

Ott and Longnecker (2016). An Introduction to Statistical Methods and Data Analysis.

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

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.

## Registration

It is the responsibility of every student 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

vahe.avagyan[at] wur.nl