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Fast Logistic Regression with Targeted Variance (C++ Backend)

Source: R/helper_glm_fit.R
fast_logistic_regression_with_var_cpp.Rd

Fits the same logistic regression model as fast_logistic_regression_cpp (see that page for the full model and log-odds-ratio interpretation) and additionally computes the variance of two coefficients — the caller-selected j-th coefficient and, separately, the 2nd coefficient (the package's usual treatment-effect position) — via a targeted diagonal-entry inversion of the working-weights Fisher information, rather than a full matrix inverse. Unlike fast_logistic_regression_cpp, maxit and tol are not exposed here: they are fixed internally at 100 iterations and 1e-8 tolerance.

Usage

fast_logistic_regression_with_var_cpp(
  X,
  y,
  j = 2L,
  warm_start_beta = NULL,
  smart_cold_start = FALSE,
  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 binary (0 or 1).

j

1-based index (into X's columns) of the coefficient to compute ssq_b_j for. 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 an OLS-based initial guess rather than a zero cold start.

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"; see .normalize_optimizer_algorithm.

warm_start_weights

Optional initial IRLS working weights for the first iteration.

warm_start_fisher_info

Optional initial Fisher Information matrix to warm-start curvature information.

Value

A list with components b/params (estimated coefficients \(\hat\beta\), identical to each other), ssq_b_j/ssq_b_2 (the two targeted coefficient variances described in Details), score (the score vector at \(\hat\beta\)), observed_information/fisher_information/ information (three aliases for the same working-weights curvature matrix, tagged information_type = "fisher"), hessian (the negative of that matrix), neg_loglik/neg_ll (aliases for the negative log-likelihood), loglik (its negation), converged (logical, gradient_norm < tol, uniform across optimizers), num_iter, hit_iteration_cap (logical, mutually exclusive with converged), and gradient_norm.

Details

Variance computation. The working-weights Fisher information \(X^\top W X\) is restricted to the free (non-fixed_idx) parameters; ssq_b_j and ssq_b_2 are each obtained via a single targeted diagonal-entry inversion (compute_diagonal_inverse_entry()) at the free-parameter position corresponding to j and to column 2, respectively — NA if the relevant coefficient is out of range or was itself fixed via fixed_idx. ssq_b_2 is always computed (when ncol(X) >= 2) regardless of what j is, so a caller interested in the treatment effect's variance does not need to pass j = 2 explicitly.

See also

fast_logistic_regression_cpp for the estimate-only variant and the full model documentation.