5.11 Dealing with correlated predictors
Highly correlated predictors can lead to collinearity issues and this can greatly increase the model variance, especially in the context of regression. In some cases, there could be relationships between multiple predictor variables and this is called multicollinearity. Having correlated variables will result in unnecessarily complex models with more than necessary predictor variables. From a data collection point of view, spending time and money for collecting correlated variables could be a waste of effort. In terms of linear regression or the models that are based on regression, the collinearity problem is more severe because it creates unstable models where statistical inference becomes difficult or unreliable. On the other hand, correlation between variables may not be a problem for the predictive performance if the correlation structure in the training and the future tests data sets are the same. However, more often, correlated structures within the training set might lead to overfitting.
Here are couple of things to do if collinearity is a problem:
We can do PCA on the training data, which creates new variables removing the collinearity between them. We can then train models on these new dimensions. The downside is that it is harder to interpret these variables. They are now linear combinations of original variables. The variable importance would be harder to interpret.
As we have already shown in the data preprocessing section, we can try variable filtering and reduce the number of correlated variables. However, this may not address the multicollinearity issue where linear combinations of variables might be correlated while they are not directly correlated themselves.
Method-specific techniques such as regularization can decrease the effects of collinearity. Regularization, as we will see in the later chapter, is a technique that is used to prevent overfitting and it can also dampen the effects of collinearity. In addition, decision-tree-based methods could suffer less from the effects of collinearity.