Fast Log-Link Binomial Regression, Estimate Only (C++ Backend)

Fits a binary-response GLM with the log link (a relative-risk model), \(\log \mu_i = \log \Pr(Y_i = 1) = x_i^\top \beta\) (equivalently \(\mu_i = e^{x_i^\top \beta}\), constrained to stay below \(1 - 10^{-8}\) so it remains a valid probability), via Fisher scoring (IRLS) with a step-halving line search that rejects any Newton step whose resulting \(\eta_i = x_i^\top \beta\) would push \(\mu_i\) out of range or decrease the log-likelihood — the same boundary-constrained-line-search mechanism documented in full at fast_identity_binomial_regression_cpp (see that page for the IRLS/line-search mechanics, which are shared verbatim between the log and identity links here; only the link function itself, and hence the coefficient scale, differs). Regression coefficients are directly interpretable as log relative risks: \(e^{\beta_j}\) is the multiplicative change in \(\Pr(Y = 1)\) per unit change in covariate \(j\) — in contrast to fast_identity_binomial_regression_cpp's risk-difference scale, or a logit-link model's odds-ratio scale.

Usage

fast_log_binomial_regression_cpp(
  X,
  y_r,
  maxit = 100L,
  tol = 1e-06,
  fixed_idx = NULL,
  fixed_values = NULL,
  warm_start_beta = NULL,
  smart_cold_start = TRUE,
  warm_start_weights = NULL,
  warm_start_fisher_info = NULL,
  estimate_only = FALSE
)

Arguments

X: A numeric matrix of predictors, \(n \times p\); include an explicit intercept column if desired (no implicit intercept).
y_r: A binary (0/1) numeric vector of responses, length \(n\).
maxit: Maximum number of Fisher-scoring iterations.
tol: Convergence tolerance, on the relative norm of the coefficient update step.
fixed_idx: Optional integer indices of coefficients to hold fixed rather than estimate.
fixed_values: Optional values to fix the parameters named by fixed_idx at.
warm_start_beta: Optional starting values for coefficients. If provided, smart_cold_start is ignored.
warm_start_weights: Optional initial working weights for the first IRLS iteration.
warm_start_fisher_info: Optional initial Fisher Information matrix for the first IRLS iteration.

Value

A list with components b (estimated coefficients \(\hat\beta\), on the log-relative-risk scale), mu_hat (fitted probabilities, length \(n\)), working_weights (final IRLS weights), iterations, converged (logical), and fisher_information (the working-weights curvature matrix \(X^\top W X\)).

Usage

Arguments

Value

See also