Fit a GLM with elastic net regularization for a single value of lambda

Fit a generalized linear model via penalized maximum likelihood for a single value of lambda. Can deal with any GLM family.

Usage

glmnet.fit(
  x,
  y,
  weights,
  lambda,
  alpha = 1,
  offset = rep(0, nobs),
  family = gaussian(),
  intercept = TRUE,
  penalty.factor = rep(1, nvars),
  exclude = c(),
  lower.limits = -Inf,
  upper.limits = Inf,
  warm = NULL,
  from.glmnet.path = FALSE,
  save.fit = FALSE,
  control = glmnet.control()
)

Arguments

x: Input matrix, of dimension nobs x nvars; each row is an observation vector. If it is a sparse matrix, it is assumed to be unstandardized. It should have attributes xm and xs, where xm(j) and xs(j) are the centering and scaling factors for variable j respsectively. If it is not a sparse matrix, it is assumed that any standardization needed has already been done.
y: Quantitative response variable.
weights: Observation weights. glmnet.fit does NOT standardize these weights.
lambda: A single value for the lambda hyperparameter.
alpha: The elasticnet mixing parameter, with $0 \le \alpha \le 1$. The penalty is defined as $$(1-\alpha)/2||\beta||_2^2+\alpha||\beta||_1.$$ alpha=1 is the lasso penalty, and alpha=0 the ridge penalty.
offset: A vector of length nobs that is included in the linear predictor. Useful for the "poisson" family (e.g. log of exposure time), or for refining a model by starting at a current fit. Default is NULL. If supplied, then values must also be supplied to the predict function.
family: A description of the error distribution and link function to be used in the model. This is the result of a call to a family function. Default is gaussian(). (See family for details on family functions.)
intercept: Should intercept be fitted (default=TRUE) or set to zero (FALSE)?
penalty.factor: Separate penalty factors can be applied to each coefficient. This is a number that multiplies lambda to allow differential shrinkage. Can be 0 for some variables, which implies no shrinkage, and that variable is always included in the model. Default is 1 for all variables (and implicitly infinity for variables listed in exclude). Note: the penalty factors are internally rescaled to sum to nvars.
exclude: Indices of variables to be excluded from the model. Default is none. Equivalent to an infinite penalty factor.
lower.limits: Vector of lower limits for each coefficient; default -Inf. Each of these must be non-positive. Can be presented as a single value (which will then be replicated), else a vector of length nvars.
upper.limits: Vector of upper limits for each coefficient; default Inf. See lower.limits.
warm: Either a glmnetfit object or a list (with names beta and a0 containing coefficients and intercept respectively) which can be used as a warm start. Default is NULL, indicating no warm start. For internal use only.
from.glmnet.path: Was glmnet.fit() called from glmnet.path()? Default is FALSE.This has implications for computation of the penalty factors.
save.fit: Return the warm start object? Default is FALSE.
control: A fully resolved 17-key control list of the form returned by glmnet.control(). Default is glmnet.control() – current session state. This function does not resolve or validate the list; keys (thresh, maxit, trace.it, epsnr, mxitnr, big, etc.) are read directly. See ?glmnet.path for the same contract.

Value

An object with class "glmnetfit" and "glmnet". The list returned contains more keys than that of a "glmnet" object.

a0: Intercept value.
beta: A nvars x 1 matrix of coefficients, stored in sparse matrix format.
df: The number of nonzero coefficients.
dim: Dimension of coefficient matrix.
lambda: Lambda value used.
dev.ratio: The fraction of (null) deviance explained. The deviance calculations incorporate weights if present in the model. The deviance is defined to be 2*(loglike_sat - loglike), where loglike_sat is the log-likelihood for the saturated model (a model with a free parameter per observation). Hence dev.ratio=1-dev/nulldev.
nulldev: Null deviance (per observation). This is defined to be 2*(loglike_sat -loglike(Null)). The null model refers to the intercept model.
npasses: Total passes over the data.
jerr: Error flag, for warnings and errors (largely for internal debugging).
offset: A logical variable indicating whether an offset was included in the model.
call: The call that produced this object.
nobs: Number of observations.
warm_fit: If save.fit=TRUE, output of C++ routine, used for warm starts. For internal use only.
family: Family used for the model.
converged: A logical variable: was the algorithm judged to have converged?
boundary: A logical variable: is the fitted value on the boundary of the attainable values?
obj_function: Objective function value at the solution.

Details

WARNING: Users should not call glmnet.fit directly. Higher-level functions in this package call glmnet.fit as a subroutine. If a warm start object is provided, some of the other arguments in the function may be overriden.

glmnet.fit solves the elastic net problem for a single, user-specified value of lambda. glmnet.fit works for any GLM family. It solves the problem using iteratively reweighted least squares (IRLS). For each IRLS iteration, glmnet.fit makes a quadratic (Newton) approximation of the log-likelihood, then calls elnet.fit to minimize the resulting approximation.

In terms of standardization: glmnet.fit does not standardize x and weights. penalty.factor is standardized so that they sum up to nvars.