Fast Poisson Regression with Variance Calculation (C++ Backend)

Fits the same Poisson log-link model as fast_poisson_regression_cpp (see that page for the full model and optimizer contract; always with estimate_only = FALSE), and additionally inverts the fitted Fisher information matrix (Eigen::LDLT on the free-coefficient submatrix, via compute_diagonal_inverse_entry) to report the variance of two coefficients.

Usage

fast_poisson_regression_with_var_cpp(
  X,
  y,
  j = 2L,
  warm_start_beta = NULL,
  smart_cold_start = FALSE,
  maxit = 100L,
  tol = 1e-8,
  fixed_idx = NULL,
  fixed_values = NULL,
  optimization_alg = "irls",
  warm_start_weights = NULL,
  warm_start_fisher_info = NULL
)

Arguments

X: A numeric matrix of predictor variables. It is assumed that an intercept column (e.g., a column of ones) is already included in X if desired.
y: A numeric vector of the response variable, expected to be nonnegative-integer counts.
j: The 1-indexed coefficient whose variance to compute in ssq_b_j. Defaults to 2.
warm_start_beta: Optional starting values for coefficients \(\beta\). If provided, smart_cold_start is ignored.
smart_cold_start: Logical. If TRUE and no warm_start_beta is supplied, use a Poisson-specific heuristic initial guess rather than a zero cold start.
maxit: Maximum number of iterations. Defaults to 100.
tol: Convergence tolerance. Defaults to 1e-8.
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.
optimization_alg: Optimization algorithm: "irls" (default), "lbfgs", or "newton_raphson".
warm_start_weights: Accepted but unused; see fast_poisson_regression_cpp Details.
warm_start_fisher_info: Optional initial curvature (information) matrix to warm-start the first iteration.

Value

A list containing the following components:

b, params: A numeric vector of the estimated Poisson regression coefficients \(\hat\beta\) (both aliases of the same vector).
ssq_b_j: The variance of the \(j\)-th coefficient estimator; NA if j indexes a fixed coefficient.
ssq_b_2: The variance of the second coefficient estimator specifically (typically the treatment effect), regardless of what j is; equal to ssq_b_j when j = 2. NA if the second column is a fixed coefficient.
mu: The fitted means \(\hat\mu_i\).
converged: A logical value indicating whether the final gradient norm was below tol (gradient_norm < tol); uniform across the "irls"/"lbfgs"/"newton_raphson" optimizers.
num_iter: The number of iterations performed.
score: The score vector at the fitted coefficients.
observed_information, fisher_information, information: Three aliases for the same \(X^\top W X\) curvature matrix (information_type is always "fisher").
hessian: The negative of that same matrix (the actual Hessian of the log-likelihood).
neg_loglik, neg_ll: The negative log-likelihood at the fitted coefficients (two aliases).
loglik: The log-likelihood (-neg_ll), or NA if neg_ll is non-finite.
hit_iteration_cap: A logical value, mutually exclusive with converged: TRUE iff the optimizer exhausted maxit iterations without meeting the gradient-norm convergence criterion.
gradient_norm: The norm of the score vector at the returned coefficients.

Usage

Arguments

Value

See also