Beginning with the
closed-form ridge regression model (with L2-norm loss and penalty) and
advancing to more computationally-intensive methods (such as the lasso and
elastic net), the possibilities for penalized regression have progressed
dramatically in recent years.
While the methods required to fit these models appropriately require
large amounts of computation time, the improvements in prediction accuracy
outweigh this concern.
Quantitative Structure Activity/Property Relationship (QSAR/QSPR)
models are general methods used in the area of chemometrics
to predict a biological activity or property (such as toxicity) of a compound
based on p chemical descriptors of various types. In the context of chemometrics,
we analyze prediction problems calling for the concurrent selection of
predictors with fitting of the regression model. Model selection from among several
penalized regression models (with different loss and penalty functions) requires
the further assessment of the model utility. Models are included with consideration
for the range of predictors implemented by the researcher and for the type of
loss function desired. Programming
is implemented in the R environment to obtain and to assess the fitted models.