sfa_leximax: Leximax: Rotate Factor Axes Toward the Construct Lexicon

In semanticfa: Semantic Factor Analysis of Language Model Embeddings

Leximax: Rotate Factor Axes Toward the Construct Lexicon

Description

Chooses, among the orientations that reproduce a fitted factor solution identically, the one whose factors sit closest to real construct terms. The optimizer alternates naming (the full sfa_name() selection rule on the current pattern matrix) with oblique target rotation toward the retrieved terms' predicted loading profiles, from multiple deterministic starts, until the retrieved term tuple recurs. The recurrent states are the candidate solutions (a fixed point is the one-state case), and the recurrent state with the highest nameability wins, with ties broken by start order and then iteration. The winner is re-named through the canonical blocked pool path and those labels are authoritative.

Usage

sfa_leximax(
  x,
  Phi = NULL,
  lexmap = NULL,
  model = NULL,
  pool = NULL,
  instruction = NULL,
  n_random = 10L,
  seed = 42L,
  col_scale = c("unitmax", "z"),
  rotation = c("oblique", "orthogonal"),
  normalize = FALSE,
  max_iter = 30L,
  block_size = 50000L,
  baseline = NULL,
  baseline_sd = NULL,
  ...
)

Arguments

x	An sfa() fit, a psych::fa fit, or a pattern matrix.
Phi	Factor correlations when x is a plain matrix (default identity).
lexmap	An sfa_lexmap() for the instrument's items. Required when x is a matrix; built automatically from an sfa fit.
model, pool, instruction	Passed to sfa_lexmap() when it must be built.
n_random	Number of seeded random orthonormal starts appended to the oblimin, varimax, and geominQ starts (default 10).
seed	Base seed for the random starts (default 42).
col_scale	Target column scaling: "unitmax" (default) or "z".
rotation	"oblique" (default) or "orthogonal".
normalize	Kaiser row normalization inside the target rotation.
max_iter	Iteration cap per start (default 30).
block_size	Passed to sfa_lexmap() when it must be built.
baseline, baseline_sd	Optional per-pool-word null mean and standard deviation for surprise scoring, passed through to sfa_nameability(). Default NULL scores raw target cosines.
...	Passed to the embedding backend via sfa_lexmap().

Details

Also available as rotate = "leximax" in sfa().

Value

An object of class sfa_leximax: loadings, Phi, Th, A0, labels (with the canonical retrieved labels and leave-one-out candidate sets), criterion, per_factor, start, iteration, history, converged.

semanticfa documentation built on Sept. 2, 2026, 1:07 a.m.