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Fig. 3.12 Coefficient path of the parameters for the Sonar dataset
3.5.2 Uncertainty Quantification
Here, we will discuss uncertainty quantification for the LASSO under the logistic
model, by way of application on the Sonar dataset.
3.5.2.1 Refit-LASSO
We applied the refit-LASSO method on the Sonar dataset. We carried out 100
cross-validation runs with randomized partitions to check the behavior of variable
selection. We considered variables as important if they appeared to be non-zero
in 50 or more runs. We illustrate the selection of important variable in Fig. 3.13.
Then we applied logistic regression on the important variables. We used the glm
package in R for model fitting. The corresponding refit-LASSO estimates are given
in Table 3.3.
3.5.2.2 Bootstrap
We applied the bootstrap method on the Sonar dataset with 1000 bootstrap
replicates. The procedure works identically as outlined in Sect. 3.4.2, except that
for the Sonar dataset, the response variable follows a Bernoulli distribution, so
that for model fitting (and refitting), we need to work with the binomial response