# Linear & generalized linear models and linear algebra

Year: 2017-2018 4433LAGLMY Dr. Gerrit Gort English Yes 9 400 Semester 1, Block II
• Yes Elective choice
• Yes Contractonderwijs
• Yes Exchange
• Yes Study Abroad
• No Evening course
• Yes A la Carte
• No Honours Class

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### Course 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 linear models. In this course we discuss linear models with a thorough treatment of the matrix algebra.

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 are logistic regression for a binary response (assuming a binomial distribution), or log-linear models for counts (using a Poisson distribution). Data are still assumed to be independent. Analysis of dependent data will be discussed in the course on mixed and longitudinal modeling. 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.

### 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 (2), and perform a proper data analysis. Students should acquaint themselves with the basics of linear algebra, especially the matrix algebra that is needed to understand Linear Models.

### Mode of Instruction

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

### Time Table

For the course days, course location and class hours check the Time Table under the tab “StatSci Students -> Program Schedule” at http://www.math.leidenuniv.nl/statisticalscience

### Assessment method

Assessment of a student will be based on written exam (2/3), a case study report (1/3), and an oral presentation of the case study report (pass/ fail).

Case study report: In week four, students will be asked to analyze a practical data set or study a theoretical topic. A report should be handed and the student will give a 15 minutes short oral presentation on the topic of his or her report.

Date information about the exam and resit can be found in the Time Table pdf document under the tab “Masters Programme” at http://www.math.leidenuniv.nl/statscience. The room and building for the exam will be announced on the electronic billboard, to be found at the opposite of the entrance, the content can also be viewed here http://info.liacs.nl/math/.

• 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

Enroll in Blackboard for the course materials and course updates.

To be able to obtain a grade and the ECTS for the course, sign up for the (re-)exam in uSis ten calendar days before the actual (re-)exam will take place. Note, the student is expected to participate actively in all activities of the program and therefore uses and registers for the first exam opportunity.

Exchange and Study Abroad students, please see the Prospective students website for information on how to apply.

### Contact information

gerrit [dot] gort [at] wur.nl

### Remarks

• This is a compulsory course in the Master’s programme of the specialisation Statistical Science for the Life & Behavioural sciences.