What are some challenges or limitations of ridge regression?

2 Losing interpretability

Another challenge of ridge regression is that it reduces the interpretability of the model coefficients. Unlike ordinary least squares, which gives unbiased estimates of the coefficients, ridge regression gives biased estimates that depend on the value of alpha. This means that you cannot directly interpret the coefficients as the effect of each predictor on the response variable. Moreover, ridge regression does not perform variable selection, meaning that it keeps all the predictors in the model, even if some of them are irrelevant or redundant. This can make the model harder to understand and explain.

3 Dealing with multicollinearity

A third challenge of ridge regression is that it does not completely solve the problem of multicollinearity, which occurs when some of the predictors are highly correlated with each other. Multicollinearity can cause instability and high variance in the model coefficients, making them sensitive to small changes in the data. Ridge regression can reduce the variance of the coefficients by shrinking them towards zero, but it cannot eliminate the correlation among them. Therefore, ridge regression may not be the best option if you want to identify the causal relationships among the predictors and the response variable.

4 Comparing with other methods

A final challenge of ridge regression is that it may not be the best method for every situation. Depending on your data and your goals, you may want to consider other methods that offer different advantages or disadvantages. For example, lasso regression is another technique that adds a penalty term to the sum of squared errors, but this penalty term, also known as the L1 norm, shrinks some of the coefficients to exactly zero, performing variable selection. This can make the model more sparse and interpretable, but also more biased and less stable. Another example is elastic net regression, which combines both L1 and L2 norms, allowing for both shrinkage and selection of the coefficients. This can balance the trade-offs between bias and variance, but also adds another parameter to tune.

5 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?