Fast Adjacent-Category Logit with Variance (C++)

Adjacent-category logit model fitting with full variance-covariance matrix.

Usage

fast_adjacent_category_logit_with_var_cpp(
  X,
  y,
  maxit = 100L,
  tol = 1e-08,
  smart_cold_start = TRUE,
  fixed_idx = NULL,
  fixed_values = NULL,
  optimization_alg = "lbfgs",
  warm_start_fisher_info = NULL,
  warm_start_params = NULL,
  warm_start_beta = NULL
)

Arguments

X

A numeric matrix of predictors.

y

A numeric vector of responses (categorical).

maxit

Maximum number of iterations. Fast Adjacent-Category Logit Regression with Variance, Direct MLE (C++ Backend)

Fits the same adjacent-category logit model as fast_adjacent_category_logit_cpp (see that page for the model, category-coding/remapping, parameter layout, and optimizer contract, all shared unchanged here) and additionally computes the observed-information-based variance-covariance matrix of the fitted parameters.

tol

Convergence tolerance.

smart_cold_start

Logical. If TRUE, use an initial OLS-based guess when starting from scratch (a "cold start") with no prior knowledge. This is ignored if a warm start is provided.

fixed_idx

Optional integer indices (into the c(alpha, beta) parameter layout described in Details) of parameters to hold fixed rather than estimate.

fixed_values

Optional values to fix the parameters named by fixed_idx at; must be the same length as fixed_idx.

optimization_alg

Optimization algorithm; see Details.

warm_start_fisher_info

Optional initial Fisher Information matrix (over the full c(alpha, beta) parameter vector) to warm-start curvature information.

warm_start_params

Optional starting values for the full parameter vector c(alpha, beta). If provided, smart_cold_start is ignored.

warm_start_beta

Optional starting values for just the covariate coefficients \(\beta\) (cut intercepts \(\alpha\) are still initialized separately). If provided, smart_cold_start is ignored.

Value

A list with all the components of fast_adjacent_category_logit_cpp (b, alpha, params, neg_loglik, converged), plus ssq_b_1 (equivalently ssq_b_j, the variance of the first covariate's coefficient), vcov (the full parameter variance-covariance matrix, or NULL if not converged), and fisher_information (the full observed information matrix at the fitted parameters, over all parameters regardless of fixed_idx).

Details

Variance computation. The observed Fisher information (the Hessian of the negative log-likelihood, via AdjacentCategoryLogitNegLogLik::hessian()) is evaluated at the fitted parameter vector over all n_alpha + p parameters (returned in full as fisher_information), then restricted to the free (non-fixed_idx) parameters and inverted via a rank-aware (symmetric_pseudo_inverse(), not a plain Cholesky/LDLT solve) inverse before being expanded back to full (n_alpha + p) x (n_alpha + p) size as vcov. The pseudo-inverse is used deliberately: adjacent-category fits can have an estimable treatment effect even when nuisance columns make the full information matrix rank-deficient, a case where a standard Cholesky/LDLT solve can report spurious success with an invalid (sometimes negative) variance rather than failing cleanly. vcov is only populated when converged is TRUE; otherwise it is NULL.

First-covariate variance shortcut. ssq_b_1 (aliased as ssq_b_j for interface consistency with the package's other fast_*_with_var_cpp functions) is the variance of \(\hat\beta_1\), the coefficient on the first column of X — by the package's usual convention, the treatment-effect column — extracted directly from the free-parameter covariance block rather than requiring the caller to index into the full vcov matrix; it is NA if that coefficient was fixed (via fixed_idx) or if its estimated variance is non-finite or non-positive.

Usage

Arguments

Value

Details

See also