Visualization
plot(fit, type = "scree")
Scree plot with parallel analysis threshold
plot(fit, type = "loadings")
Factor loading heatmap
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semanticfa performs exploratory factor analysis on
language model embeddings of psychological scale items. Given item text,
it embeds each item, computes a similarity matrix, and extracts latent
factors — entirely from the text, with no human response data
required.
The package is designed to feel familiar to psych and
EFAtools users.
The package ships with the 50-item IPIP Big Five inventory and precomputed Qwen3-Embedding-8B embeddings (50 x 4096, rounded to 4 decimal places), so you can try it with zero setup:
library(semanticfa)
data(big5)
fit <- sfa(
big5$items,
nfactors = 5,
embeddings = big5$embeddings,
scoring = big5$scoring
)
print(fit)
#> Semantic Factor Analysis
#> Encoding: atomic
#> Embedding dim: 4096
#> Factors:5 (minres + oblimin)
#>
#> Diagnostics:
#> KMO: 0.971 (marvelous - higher is better)
#> TEFI: -27.7158 (lower is better)
#> RMSR: 0.0323 (good - lower is better)
#> CAF: 0.4120 (marginal - higher is better)
#>
#> Factor loadings:
#>
#> Loadings:
#> MR1 MR4 MR2 MR3 MR5
#> item_16 1.003
#> item_19 0.870
#> item_18 0.861
#> item_11 0.817
#> item_15 0.801
#> item_17 0.790
#> item_20 0.575
#> item_29 0.553 0.390
#> item_13 0.490
#> item_24 0.453 0.425
#> item_26 0.391 0.303
#> item_23
#> item_35 0.715
#> item_39 0.675
#> item_31 0.626
#> item_32 0.617
#> item_40 0.604
#> item_37 0.567
#> item_38 0.566 0.337
#> item_36 0.566
#> item_33 0.565
#> item_04 0.545
#> item_34 0.355 0.502
#> item_28 0.458 0.308
#> item_12 0.395 0.347
#> item_49 0.350
#> item_27 0.895
#> item_25 0.787
#> item_21 0.718
#> item_44 0.615 0.404
#> item_08 0.570
#> item_02 0.449
#> item_46 0.438 0.438
#> item_06 0.432
#> item_10 0.408 0.390
#> item_14 0.319
#> item_03 0.751
#> item_30 0.596
#> item_07 0.509
#> item_22 0.484
#> item_09 0.450
#> item_05 0.384
#> item_01 0.309 0.353
#> item_50 0.607
#> item_45 0.300 0.583
#> item_42 0.350 0.563
#> item_43 0.555
#> item_41 0.450
#> item_48 0.425
#> item_47 0.333
#>
#> MR1 MR4 MR2 MR3 MR5
#> SS loadings 6.423 5.320 4.114 3.189 2.742
#> Proportion Var 0.128 0.106 0.082 0.064 0.055
#> Cumulative Var 0.128 0.235 0.317 0.381 0.436
#>
#> Factor correlations (Phi):
#> MR1 MR4 MR2 MR3 MR5
#> MR1 1.000 0.684 0.607 0.576 0.540
#> MR4 0.684 1.000 0.538 0.581 0.555
#> MR2 0.607 0.538 1.000 0.465 0.447
#> MR3 0.576 0.581 0.465 1.000 0.398
#> MR5 0.540 0.555 0.447 0.398 1.000
#>
#> Variance accounted for:
#> MR1 MR4 MR2 MR3 MR5
#> SS loadings 9.240 8.619 6.284 5.612 4.842
#> Proportion Var 0.185 0.172 0.126 0.112 0.097
#> Cumulative Var 0.185 0.357 0.483 0.595 0.692
#> Proportion Explained 0.267 0.249 0.182 0.162 0.140
#> Cumulative Proportion 0.267 0.516 0.698 0.860 1.000When you omit nfactors, sfa() uses
embedding-adapted parallel analysis (random unit vectors in the
embedding dimension as the null):
fit_auto <- sfa(
big5$items,
embeddings = big5$embeddings,
scoring = big5$scoring
)
cat("Auto-detected factors:", fit_auto$factors, "\n")
#> Auto-detected factors: 5For a multi-method comparison, use sfa_nfactors(). Its
default runs parallel analysis alone (the conventional retention
default); request the battery explicitly, choosing among
"kaiser", "TEFI", "EKC",
"EGA", "MAP", and "semk" (the
calibrated learned rule, which reports a conformal interval alongside
its count):
sim <- sfa_similarity(big5$embeddings, encoding = "atomic_reversed",
scoring = big5$scoring)
nf <- sfa_nfactors(sim, big5$embeddings,
methods = c("parallel", "kaiser", "EKC"),
parallel_iter = 50)
print(nf)
#> Factor retention analysis (embedding-adapted)
#>
#> Method n_factors
#> parallel 5
#> kaiser 6
#> EKC 6
#> ------------------------
#> Consensus 6
#>
#> Eigenvalues: 29.62 1.92 1.74 1.48 1.27 1.01 0.93 0.88 0.78 0.70 ...When you want to see whether the matrix carries a crisp factor count
at all, sfa_cd() computes a comparison-data misfit profile
(see ?sfa_cd): a sharp elbow marks a real boundary, while
embedding similarity matrices typically decline smoothly instead.
The encoding argument controls how embeddings become a
similarity matrix:
sim_ar <- sfa_similarity(big5$embeddings, "atomic_reversed", big5$scoring)
sim_sq <- sfa_similarity(big5$embeddings, "squid", big5$scoring)
#> Warning: 'scoring' has reverse-keyed items but is ignored for encoding =
#> "squid": this method is keying-free by design. Use "atomic_reversed" for keyed
#> sign-flipping.
sim_mcp <- sfa_similarity(big5$embeddings, "mean_centered_pearson", big5$scoring)
#> Warning: 'scoring' has reverse-keyed items but is ignored for encoding =
#> "mean_centered_pearson": this method is keying-free by design. Use
#> "atomic_reversed" for keyed sign-flipping.
cat("atomic_reversed range:", range(sim_ar[lower.tri(sim_ar)]), "\n")
#> atomic_reversed range: -0.7766852 0.9381671
cat("squid range: ", range(sim_sq[lower.tri(sim_sq)]), "\n")
#> squid range: -0.2671767 0.8269712
cat("mean_centered_pearson:", range(sim_mcp[lower.tri(sim_mcp)]), "\n")
#> mean_centered_pearson: 0.3938766 0.9382228The ranges show what each encoding does to the sign structure.
Sign-flipping (atomic_reversed) manufactures strong
negatives by turning reverse-keyed items into anti-topic vectors, and
SQuID’s questionnaire-mean centering recovers a modest negative range.
Mean-centered Pearson tracks the raw cosines, which stay positive for
these items.
plot(fit, type = "scree")Scree plot with parallel analysis threshold
plot(fit, type = "loadings")Factor loading heatmap
The $loadings component works directly with
psych functions:
# Run human-data EFA (not run — requires response data)
human_fit <- psych::fa(response_data, nfactors = 5, rotate = "oblimin")
# Compare
psych::factor.congruence(fit$loadings, human_fit$loadings)For NMI, ARI, Frobenius, and disattenuated correlation:
cong <- sfa_congruence(fit, big5$factors, metrics = c("nmi", "ari"))
print(cong)
#> Factor structure congruence
#>
#> NMI: 0.527 (moderate - higher is better)
#> ARI: 0.402 (weak - higher is better)Pass any embedding model’s output via embeddings=:
# With sentence-transformers (requires reticulate + Python).
# The default model is "Qwen/Qwen3-Embedding-0.6B"; larger models such as
# "Qwen/Qwen3-Embedding-4B" (8 GB RAM) or "Qwen/Qwen3-Embedding-8B" (16 GB RAM)
# recover factor structure more accurately.
emb <- sfa_embed(my_items, embed = "sbert", model = "Qwen/Qwen3-Embedding-0.6B")
fit <- sfa(my_items, embeddings = emb, scoring = my_scoring)
# Or bring your own function
my_embedder <- function(texts) {
# ... your embedding logic ...
# must return a numeric matrix (n_items x dim)
}
fit <- sfa(my_items, embed = my_embedder, scoring = my_scoring)These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.