Core Empirical Likelihood Estimator

Implements the core computational engine for empirical likelihood estimation under nonignorable nonresponse, including parameter solving, variance calculation, and diagnostic computation.

Usage

el_estimator_core(
  missingness_design,
  aux_matrix,
  aux_means,
  respondent_weights,
  analysis_data,
  outcome_expr,
  N_pop,
  formula,
  standardize,
  trim_cap,
  control,
  on_failure,
  family = logit_family(),
  variance_method,
  bootstrap_reps,
  start = NULL,
  trace_level = 0,
  auxiliary_means = NULL
)

Arguments

missingness_design

Respondent-side missingness (response) model design matrix (intercept + predictors).

aux_matrix

Auxiliary design matrix on respondents (may have zero columns).

aux_means

Named numeric vector of auxiliary population means (aligned to columns of aux_matrix).

respondent_weights

Numeric vector of respondent weights aligned with missingness_design rows.

analysis_data

Data object used for logging and variance (survey designs supply the design object).

outcome_expr

Character string identifying the outcome expression displayed in outputs.

N_pop

Population size on the analysis scale.

formula

Original model formula used for estimation.

standardize

Logical. Whether to standardize predictors during estimation.

trim_cap

Numeric. Upper bound for empirical likelihood weight trimming.

control

List of control parameters for the nonlinear equation solver.

on_failure

Character. Action when solver fails: "return" or "error".

family

List. Link function specification (typically logit).

variance_method

Character. Variance estimation method.

bootstrap_reps

Integer. Number of bootstrap replications.

auxiliary_means

Named numeric vector of known population means supplied by the user (optional; used for diagnostics).

Value

List containing estimation results, diagnostics, and metadata.

Details

Orchestrates EL estimation for NMAR following Qin, Leung, and Shao (2002). For data.frame inputs (IID setting) the stacked system in \((\beta, z, \lambda_x)\) with \(z = \mathrm{logit}(W)\) is solved by nleqslv::nleqslv() using an analytic Jacobian. For survey.design inputs a design-weighted analogue in \((\beta, z, \lambda_W, \lambda_x)\) is solved with an analytic Jacobian when the response family supplies second derivatives, or with numeric/Broyden Jacobians otherwise. Numerical safeguards are applied consistently across equations, Jacobian, and post-solution weights: bounded linear predictors, probability clipping in ratios, and a small floor on denominators \(D_i(\theta)\) with an active-set mask in derivatives. After solving, unnormalized masses \(d_i/D_i(\theta)\) are formed, optional trimming may be applied (with normalization only for reporting), and optional variance is computed via bootstrap when variance_method = "bootstrap".