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Analytical Jacobian for survey EL system (design-weighted QLS analogue)

Source: R/engines_el_impl_jacobian.R
el_build_jacobian_survey.Rd

Analytical Jacobian for survey EL system (design-weighted QLS analogue)

Usage

el_build_jacobian_survey(
  family,
  missingness_model_matrix,
  auxiliary_matrix,
  respondent_weights,
  N_pop,
  n_resp_weighted,
  mu_x_scaled
)

Details

Builds the block Jacobian \(A = \partial g/\partial \theta\) for the survey EL system with \(\theta = (\beta, z, \lambda_W, \lambda_x)\) and \(z = \operatorname{logit}(W)\). Blocks follow the design-weighted analogue of Qin, Leung, and Shao (2002) used in el_build_equation_system_survey(). Guarding policy matches the IID Jacobian:

  • cap eta: eta <- pmax(pmin(eta, get_eta_cap()), -get_eta_cap())

  • compute w <- family$linkinv(eta) and clip to [1e-12, 1-1e-12] when used in ratios

  • denominator floor: Di <- pmax(Di_raw, nmar_get_el_denom_floor()); multiply terms depending on d(1/Di)/d(.) by active = 1(Di_raw > floor)

The Jacobian uses the same score and second-derivative machinery as el_build_jacobian(); when family$d2mu.deta2 is missing, this function returns NULL and the solver falls back to numeric/Broyden Jacobians.