dot-rotation_se_jacobian: Rotation Jacobians for analytic rotation standard errors
In EFAtools: Fast and Flexible Implementations of Exploratory Factor Analysis Tools

.rotation_se_jacobian

R Documentation

Rotation Jacobians for analytic rotation standard errors

Description

Forward-difference the warm-started re-rotation map ⁠A -> (rotated loadings, Phi)⁠ over the unrotated loadings A to obtain the rotation Jacobians used by the analytic standard errors for rotated loadings (se = "information" in efa_fit()). The full nrow(A) * ncol(A) finite- difference loop runs in compiled code, re-solving the rotation from the converged transformation T_init at each perturbation; the caller forms ⁠J V J'⁠ in R.

Usage

.rotation_se_jacobian(
  A,
  T_init,
  method,
  param,
  normalize,
  oblique,
  eps,
  general_col = 0L
)

Arguments

`A`	Numeric matrix. The unrotated loading matrix at the solution.
`T_init`	Numeric matrix. The converged transformation that warm-starts each re-rotation.
`method`	Character scalar. The criterion family: one of `"cf"`, `"oblimin"`, `"geomin"`, `"bentler"`, `"bifactor"`.
`param`	Numeric scalar. The criterion's tuning argument (`kappa` for `"cf"`, `gam` for `"oblimin"`, `delta` for `"geomin"`); ignored for `"bentler"` and `"bifactor"`.
`normalize`	Logical scalar. Apply Kaiser normalization before rotation and reverse it after.
`oblique`	Logical scalar. Use the oblique (column-normalized) manifold; otherwise orthogonal.
`eps`	Numeric scalar. The forward-difference step on the loadings.
`general_col`	Integer scalar. For `method = "bifactor"`, the zero-based column holding the general factor in the (factor-reordered) reported solution; ignored by the other criteria.

Value

A named list with the Jacobian J_L (⁠pk x pk⁠), the re-rotated base_loadings, a validity flag, and – when oblique – the Jacobian J_Phi (⁠k^2 x pk⁠) and base_Phi.