## Logistic lasso #

**lassologit**
is intended for classification tasks with binary outcomes.
**lassologit** maximizes the penalized log-likelihood:

where \(y_i\) is the binary outcome variable and \(\boldsymbol{x}_i\) is the vector of predictors. \(\boldsymbol{\beta}\) is the vector of parameters to be estimated. The last term in the objective function imposes a penalty on the absolute size of \(\boldsymbol{\beta}\) . The intercept \(\beta_0\) 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
\(\lambda\)
:

- The base program
`lassologit`

allows to select the tuning parameter as the value of \(\lambda\) that minimizes either \(AIC\) , \(BIC\) , \(AIC_c\) or \(EBIC\) . `cvlassologit`

supports \(K\) -fold cross-validation. \(\lambda\) may be selected as the value that minimizes the estimated deviance or miss-classification rate.`rlassologit`

implements theory-driven penalization for the logistic lasso (see e.g. Belloni, Chernozhukov & Wei, 2016).

Installation

Lassologithas been integrated intolassopackafter the first release. To get the latest lassologit version, simply installlassopack.