sfa_anchor: Construct-Label and Centroid Anchoring

In semanticfa: Semantic Factor Analysis of Language Model Embeddings

Construct-Label and Centroid Anchoring

Description

Produces an item-by-construct similarity matrix — the embedding analogue of a factor-loading table. Similarities are computed in the raw, un-flipped embedding space: embeddings encode topic, not valence, so a reverse-keyed item is still topically close to its construct and no sign-alignment is applied. Each cell is a belonging strength: high means the item belongs to that construct (for forward and reverse items alike), low means it does not. Read it like a loadings matrix — a well-behaved item is high in its own construct's column and low in the others; an item whose largest value lands on a different construct is a semantic cross-loader and a candidate for review.

Usage

sfa_anchor(
  x,
  anchor = c("centroid", "label", "both"),
  labels = NULL,
  label_embeddings = NULL,
  embed = NULL,
  model = NULL
)

Arguments

x	An object of class "sfa" carrying theoretical factor labels (i.e. fit from items with a factor column).
anchor	One of "centroid" (default), "label", or "both".
labels	Optional construct labels for the label anchor: either a character vector (one per construct, in the order of unique(factors)) or a named vector mapping construct -> label text. Defaults to the construct names themselves.
label_embeddings	Optional precomputed numeric matrix of label embeddings (one row per construct; named rows are matched to constructs). Use when the sfa object was built from precomputed embeddings.
embed, model	Embedding backend and model for the label anchor. Default to the backend/model recorded on x.

Details

Two anchor types are available:

"centroid"

(default) Each construct's anchor is the mean of its own (un-flipped) item embeddings. An item's similarity to its own construct is computed leave-one-out (the item is excluded from its own anchor), mirroring a corrected item-total correlation. Self-contained — needs no construct text and works for any sfa object.

"label"

Each construct's anchor is the embedding of the construct's name (or a richer gloss supplied via labels). Requires an embedding backend or precomputed label_embeddings. Because it uses the raw item embeddings, it is independent of the encoding the fit happened to use.

Value

An object of class "sfa_anchor": a list with the requested centroid and/or label item-by-construct similarity matrices, plus constructs, factors, and codes.

References

Wulff, D. U., & Mata, R. (2025). Semantic embeddings reveal and address taxonomic incommensurability in psychological measurement. Nature Human Behaviour, 9(5), 944–954. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1038/s41562-024-02089-y")}

See Also

sfa_simplify, sfa

Examples

data(big5)
fit <- sfa(
  data.frame(code = big5$codes, item = big5$items,
             factor = big5$factors, scoring = big5$scoring),
  embeddings = big5$embeddings, scoring = big5$scoring, nfactors = 5)

# item-by-construct belonging matrix (read like a loadings table)
a <- sfa_anchor(fit, anchor = "centroid")
head(round(a$centroid, 2))

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