Simulační studie lasso regrese a elastic net regrese v přítomnosti skupinových efektů

This bachelor thesis is focused on the description and analysis of the properties of two penalty regression methods, lasso regression and elastic net regression. These two methods were proposed as an alternative to the ordinary least squares method, which has two shortcomings related to data prediction and variables selection from the model. Both methods provide a solution to these shortcomings, which is due to their ability to shrink the coefficients of particular variables towards zero. Their different approach to the selection of variables, as well as their different predictive accuracy is analysed through a simulation study. The aim of this thesis is to find out which of the methods provides better results within these two aspects. It also deals with the identification of specific situations in which the method works better and tries to justify what it is caused by. The analysis pays attention to situations in which groups of highly correlated variables are used. The naive version of the elastic net regression, that is used in the analysis, proved to be able to reveal the grouping effect of correlated variables. It is also better in dealing with situations, where the number of variables is much larger than the number of observations. This results in its better prediction ability, as well as in its more reliable control of the coefficients in the selection of variables.