Correlated Component Regression: Re-thinking Regression in the Presence of Near Collinearity

We introduce a new regression method—called Correlated Component Regression (ccr)—which provides reliable predictions even with near multicollinear data. Near multicollinearity occurs when a large number of correlated predictors and relatively small sample size exists as well as situations involving a relatively small number of correlated predictors. Different variants of ccr are tailored to different types of regression (e.g. linear, logistic, Cox regression). We also present a step-down variable selection algorithm for eliminating irrelevant predictors. Unlike pls-r and penalized regression approaches, ccr is scale invariant. ccr is illustrated in several examples involving real data and its performance is compared with other approaches using simulated data.