This paper presents methods for selecting grouped variables in regression for accurate prediction. The authors propose extensions of the lasso, LARS, and non-negative garrotte methods for factor selection, which outperform traditional stepwise backward elimination. These methods are studied for their similarities and differences, and simulations and real examples are used to illustrate their performance. The group lasso, group LARS, and group non-negative garrotte are introduced as natural extensions of the individual variable selection methods. The group lasso is shown to have a non-piecewise linear solution path, while group LARS has a piecewise linear solution path. The group non-negative garrotte is also considered. The paper also introduces a computationally efficient $ C_p $-criterion for selecting the final model on the solution paths. The methods are tested on simulation studies and a real example, showing that they outperform traditional methods in factor selection. The group lasso is computationally more expensive, while group LARS and the group non-negative garrotte are faster. The paper concludes that these group methods are more suitable for factor selection than individual variable selection methods.This paper presents methods for selecting grouped variables in regression for accurate prediction. The authors propose extensions of the lasso, LARS, and non-negative garrotte methods for factor selection, which outperform traditional stepwise backward elimination. These methods are studied for their similarities and differences, and simulations and real examples are used to illustrate their performance. The group lasso, group LARS, and group non-negative garrotte are introduced as natural extensions of the individual variable selection methods. The group lasso is shown to have a non-piecewise linear solution path, while group LARS has a piecewise linear solution path. The group non-negative garrotte is also considered. The paper also introduces a computationally efficient $ C_p $-criterion for selecting the final model on the solution paths. The methods are tested on simulation studies and a real example, showing that they outperform traditional methods in factor selection. The group lasso is computationally more expensive, while group LARS and the group non-negative garrotte are faster. The paper concludes that these group methods are more suitable for factor selection than individual variable selection methods.