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Linear & generalized linear models and linear algebra


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 analysed with these models, and with the statistical analysis of empirical data itself.

The course consists of two days of a three-hours lecture (morning) and a three-hours practical (afternoon) per week, for 7 weeks. In week four, students will be asked to analyse a practical data set, and hand in a report in week five. There will be a written exam at the end of the course. Assessment of a student will be based on the case study report (1/3) and the written exam (2/3), with a minimum grade of 5 for the latter.

Literature – Fox (2008). Applied Regression Analysis and Generalized Linear Models. Sage – Faraway: Practical Regression and ANOVA using R. Text available as pdf at Faraway (2006). Extending the linear model with R. Generalized linear, mixed effects and nonparametric regression models. Chapman & Hall/CRC, – McCulloch, Searle & Neuhaus (2008) Generalized, linear and mixed models. Wiley Blackwell.

The last two texts will be used in the course on mixed and longitudinal modeling as well.