The Stata package lassologit is intended for classification tasks with binary outcomes. lassologit maximizes the penalized log-likelihood:
where is the binary outcome variable and is the vector of predictors. is the vector of parameters to be estimated. The last term in the objective function imposes a penalty on the absolute size of . The intercept is (by default) not penalized.
lassologit implements the coordinate descent algorithm of Friedman, Hastie & Tibshirani (2010, Section 3). For further speed improvements, we also utilize the strong rule proposed in Tibshirani et al. (2012).
Like lassopack, lassologit consists of three programs which correspond to three approaches for selecting the tuning parameter :
- The base program
lassologitallows to select the tuning parameter as the value of that minimizes either , , or .
cvlassologitsupports -fold cross-validation. may be selected as the value that minimizes the estimated deviance or miss-classification rate.
rlassologitimplements theory-driven penalization for the logistic lasso (see e.g. Belloni, Chernozhukov & Wei, 2016).