Why is the lasso interesting?
The least absolute shrinkage and selection operator (lasso) estimates model coefficients and these estimates can be used to select which covariates should be included in a model. The lasso is used for outcome prediction and for inference about causal parameters. In this post, we provide an introduction to the lasso and discuss using the lasso for prediction. In the next post, we discuss using the lasso for inference about causal parameters.
The lasso is most useful when a few out of many potential covariates affect the outcome and it is important to include only the covariates that have an affect. “Few” and “many” are defined relative to the sample size. In the example discussed below, we observe the most recent health-inspection scores for 600 restaurants, and we have 100 covariates that could potentially affect each one’s score. We have too many potential covariates because we cannot reliably estimate 100 coefficients from 600 observations. We believe that only about 10 of the covariates are important, and we feel that 10 covariates are “a few” relative to 600 observations.