A semi-automatic method to guide the choice of ridge parameter in ridge regression

A semi-automatic method to guide the choice of ridge parameter in ridge regression
Erika Cule, Maria De Iorio
(Submitted on 3 May 2012)

We consider the application of a popular penalised regression method, Ridge Regression, to data with very high dimensions and many more covariates than observations. Our motivation is the problem of out-of-sample prediction and the setting is high-density genotype data from a genome-wide association or resequencing study. Ridge regression has previously been shown to offer improved performance for prediction when compared with other penalised regression methods. One problem with ridge regression is the choice of an appropriate parameter for controlling the amount of shrinkage of the coefficient estimates. Here we propose a method for choosing the ridge parameter based on controlling the variance of the predicted observations in the model.
Using simulated data, we demonstrate that our method outperforms subset selection based on univariate tests of association and another penalised regression method, HyperLasso regression, in terms of improved prediction error. We extend our approach to regression problems when the outcomes are binary (representing cases and controls, as is typically the setting for genome-wide association studies) and demonstrate the method on a real data example consisting of case-control and genotype data on Bipolar Disorder, taken from the Wellcome Trust Case Control Consortium and the Genetic Association Information Network.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s