Estimating equation for ridge regression — ee_ridge

Returns a p-by-n matrix of estimating equation contributions for ridge (L2-penalized) regression: $$\psi_i(\theta) = \{Y_i - g(X_i^T \theta)\} X_i - \frac{\lambda}{n} \theta$$

Usage

ee_ridge_regression(
  theta,
  X,
  y,
  model,
  penalty,
  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. Penalty terms scaled by n internally.
weights: Optional numeric vector of n weights. Default NULL.
center: Numeric scalar or vector. Center for the penalty. 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.
fit <- m_estimate(
  mpg ~ wt + hp,
  data = mtcars,
  .ee = ee_ridge_regression,
  model = "linear",
  penalty = c(0, 5, 5)
)
coef(fit)
#> (Intercept)          wt          hp 
#> 35.59224774 -2.98849397 -0.04013219