Generalizations of the Linear Model

Linear models form the core of traditional statistical inference. Linear regression and ANOVA are the two work horses of the 20th century. Nevertheless, with the advent of more complex data, these two approaches have become too limiting. Extensions of the linear model have been extremely successful to balance model complexity and computational demand, combining the good computational aspects of the linear model with the modelling requirements from practitioners. In this course we consider the linear model, focusing on regression and ANOVA. Crucial assumptions underlying these models are (i) independent observations, (ii) linear covariate effects, (iii) more observations than unknown and (iv) normal error. We consider mixed effect models, to deal with departures of the independence assumption. Then we consider generalized additive models to model departures of linearity. To deal with high-dimensional data we consider regularized regression approaches, such as the LASSO and generalized linear models as well.

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This course is not offered in the academic year 2018/19