Statistical Modelling with Regression Methods

Aim

The course is intended to give the knowledge and understanding of different regression methods with applications, i.e., give the students the statistical tools to analyze response variables with different predictors. Models and methods in two different situations will be considered: i) classical statistical modelling, i.e., small number of variables with large number of observations, which leads to different types of regression models, and ii) high dimensional models, when the number of predictors is larger than the number of observations, which leads to prediction and classification algorithms for high dimensional data.By the end of the course, the student should be able to:

• know the sampling properties of point estimators used in regression models as well as principles and assumptions behind different estimation techniques applied,
• list and understand the assumptions behind standard parametric and model inference in the regression models,
• assess the fit of a regression model to data and know how to identify and diagnose potential problems,
• identify and develop regression modelling strategies suitable for large sample as well as for high-dimensional settings,
• explain how the multiple linear regression can be generalized to handle a response variable that is categorical or a count variable,
• use generalized linear models to analyze data, interpret the analyzes and discuss the adequacy of the methods,
• motivate the needs for and benefits of resampling methods in regression modelling, in particular cross-validation, for estimation of the model predictive accuracy,
• understand the need of mixed linear models and use these in statistical analyses,
• critically evaluate regression models in some real-world applications based on the above context.

Content

Linear models and ANOVA. Multiple linear regression. Model validation and diagnostic strategies. Non-linear regression. Generalized linear models and logistic regression. Regression methods for high dimensional data (Ridge, Lasso). Mixed linear models. Repeated measurements. Partial least squares and principal component regression.