Rotate a loading matrix to a target using Procrustes alignment

PROCRUSTES() has been superseded by efa_procrustes(), which is the recommended interface going forward.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). Supplying this is useful when the same A is rotated repeatedly. S is used only when oblique_normalize = FALSE; if Kaiser normalization is requested, the cross-product must be recomputed on the normalized matrix.

T_init

Optional k x k nonsingular starting transformation matrix for the oblique solver. Its columns are normalized internally. 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()