sfa_congruence: Compare Semantic and Empirical Factor Structures

In semanticfa: Semantic Factor Analysis of Language Model Embeddings

Compare Semantic and Empirical Factor Structures

Description

Computes agreement metrics between a semantic factor analysis result and a reference factor structure (from empirical data or theory).

Usage

sfa_congruence(
  sfa_fit,
  target,
  metrics = c("tucker", "nmi", "ari", "frobenius", "disattenuated")
)

Arguments

sfa_fit	An object of class "sfa".
target	A psych::fa object, a loadings matrix, a named factor label vector (one per item), or a correlation/similarity matrix.
metrics	Character vector of metrics to compute. Supported: "tucker", "nmi", "ari", "frobenius", "disattenuated".

Details

The disattenuated metric applies Spearman's (1904) correction r/\sqrt{r_{xx'}r_{yy'}} to the correlation between the two matrices' item-pair values, estimating each matrix's reliability by a Spearman–Brown-corrected odd/even split-half of its lower-triangle entries. That reliability construction is this package's own device (values are capped at 1). When either split-half reliability is not positive — as the checkerboard sign pattern of "atomic_reversed" produces — the correction is undefined and NA is returned with a warning.

Value

A list of class "sfa_congruence" with one component per requested metric.

References

Hubert, L., & Arabie, P. (1985). Comparing partitions (adjusted Rand index). Journal of Classification, 2, 193–218. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/BF01908075")}

Strehl, A., & Ghosh, J. (2002). Cluster ensembles — a knowledge reuse framework for combining multiple partitions (geometric-mean normalized mutual information). Journal of Machine Learning Research, 3, 583–617.

Spearman, C. (1904). The proof and measurement of association between two things (disattenuation for unreliability). The American Journal of Psychology, 15(1), 72–101. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.2307/1412159")}

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