Estimating equation for approximate LASSO regression

Uses the bridge penalty with gamma = 1 + epsilon to approximate LASSO (L1 penalty). The true LASSO is not differentiable at zero, so an approximation is used.

Usage

ee_lasso_regression(
  theta,
  X,
  y,
  model,
  penalty,
  epsilon = 0.003,
  weights = NULL,
  center = 0,
  offset = NULL
)

Arguments

theta

Numeric vector of length p.

X

Numeric n-by-p design matrix.

y

Numeric vector of n observed outcome values.

model

Character string: "linear", "logistic", or "poisson".

penalty

Numeric scalar or vector of length p. Must be non-negative.

epsilon

Numeric approximation parameter. Default 0.003.

weights

Optional numeric vector of n weights. Default NULL.

center

Numeric scalar or vector. Default 0.

offset

Optional numeric vector of n offsets. Default NULL.

Value

A p-by-n matrix.

Examples

# A penalty vector gives one value per column of the design matrix. A scalar
# penalty would shrink the intercept along with the slopes.
#
# The approximate L1 penalty enters the estimating equation as its own
# derivative, and that derivative has unbounded slope at the penalty center.
# The estimating equation is therefore not differentiable there, so the
# bread matrix is undefined and the fit warns once that the sandwich
# variance should not be trusted here.
fit <- m_estimate(
  mpg ~ wt + hp,
  data = mtcars,
  .ee = ee_lasso_regression,
  model = "linear",
  penalty = c(0, 5, 5)
)
#> Warning: The estimating equation for the chosen penalized regression model is not always
#> differentiable. Therefore, the bread matrix is not always defined for finite
#> samples, and the sandwich should not be used to estimate the variance.
coef(fit)
#> (Intercept)          wt          hp 
#> 36.67817397 -3.58183470 -0.03452163