What effect does increasing λ have on bias in the lasso model?

In the context of the lasso regression model, increasing the regularization parameter, denoted as λ (lambda), has a significant impact on the bias of the model's parameter estimates. As λ increases, the lasso method applies stronger penalties to the coefficients associated with the predictor variables. This results in more coefficients being shrunk towards zero, effectively leading to simpler models with fewer predictors retained.

This penalization helps in reducing variance, particularly in overfitting scenarios, but it does so at the expense of increasing bias. With higher λ values, the model may become overly simplistic as it may ignore potentially significant predictors, leading to parameters that are systematically different from the true values—hence increasing bias.

In scenarios where λ is small, the lasso might approximate a least squares solution, keeping bias closer to zero while potentially allowing for more variance. However, as λ grows larger, the tendency towards bias increases due to the enforced parameter shrinkage. This trade-off between bias and variance is a cornerstone in statistical modeling, particularly relevant in the lasso framework, making the assertion that increasing λ increases bias in the parameters a correct conclusion.