PROCRUSTES: Rotate a loading matrix to a target using Procrustes...

In EFAtools: Fast and Flexible Implementations of Exploratory Factor Analysis Tools

Rotate a loading matrix to a target using Procrustes alignment

Description

PROCRUSTES() has been superseded by efa_procrustes(), which is the recommended interface going forward. It remains available and unchanged so existing code keeps working.

Usage

PROCRUSTES(
  A,
  Target,
  rotation = c("orthogonal", "oblique"),
  S = NULL,
  T_init = NULL,
  oblique_eps = 1e-05,
  oblique_maxit = 1000,
  oblique_max_line_search = 10,
  oblique_step0 = 1,
  oblique_normalize = FALSE,
  oblique_random_starts = 0,
  oblique_screen_keep = 2,
  oblique_triage_maxit = 25,
  oblique_triage_improve_tol = 0
)

Arguments

A	Numeric loading matrix to be aligned.
Target	Numeric target matrix with the same dimensions as A.
rotation	Character string, either "orthogonal" or "oblique".
S	Optional ⁠k x k⁠ cross-product matrix crossprod(A), kept for compatibility. It enters both the oblique criterion and its gradient, so any other matrix would minimize a different criterion: where S is used it is checked against crossprod(A) and must agree with it up to a relative tolerance of 1e-8. That check forms crossprod(A) itself, so passing S no longer avoids any work: omitting it gives the same result for slightly less. S is used, and therefore checked, only on the oblique path with more than one factor and oblique_normalize = FALSE; if Kaiser normalization is requested, the cross-product must be recomputed on the normalized matrix and S is ignored.
T_init	Optional ⁠k x k⁠ starting transformation matrix for the oblique solver. Its columns are normalized internally, and the normalized matrix must be well enough conditioned to define a proper factor correlation matrix: its smallest singular value must be at least 1e-4, the same floor the solver applies to every candidate it evaluates. If NULL (the default), the oblique solver is warm-started from the closed-form orthogonal Procrustes solution.
oblique_eps	Positive convergence tolerance for the projected-gradient norm in the oblique solver.
oblique_maxit	Non-negative integer. Maximum number of projected-gradient updates in the full oblique solver.
oblique_max_line_search	Non-negative integer. Maximum number of step-halving attempts after the initial line-search step.
oblique_step0	Positive initial step size for the oblique solver.
oblique_normalize	Logical; if TRUE, apply Kaiser row normalization to the loadings (only) in the oblique solver and back-transform the aligned loadings afterwards, leaving Target unnormalized (as in GPArotation::targetQ(normalize = TRUE)).
oblique_random_starts	Non-negative integer. Number of additional random starts used by the oblique solver.
oblique_screen_keep	Non-negative integer. Number of random starts retained after cheap objective screening and sent to triage optimization.
oblique_triage_maxit	Non-negative integer. Number of short optimization iterations used in the triage stage.
oblique_triage_improve_tol	Non-negative scalar. Relative improvement required for a triaged start to be promoted to full optimization.

Value

A list identical to the value of efa_procrustes(); see there for the components.

See Also

efa_procrustes()

EFAtools documentation built on Aug. 21, 2026, 5:16 p.m.