alterlab-sem-psychometrics

name	alterlab-sem-psychometrics
description	Fits and evaluates measurement models — confirmatory factor analysis, full structural equation models, exploratory factor analysis, item response theory, and multi-group measurement invariance — using the verified Python stack: semopy (model syntax =~ / ~ / ~~, Model.fit, inspect(std_est=True), calc_stats for CFI/TLI/RMSEA), factor_analyzer (EFA, KMO, Bartlett, ConfirmatoryFactorAnalyzer), and pingouin/girth, computing McDonald's omega from standardized loadings and judging fit against Hu & Bentler cutoffs. Use when the request mentions confirmatory factor analysis, structural equation modeling, a latent variable or construct model, factor loadings, IRT, or measurement invariance across groups. For deciding whether a scale is trustworthy at all prefer alterlab-ssci-measurement-gate; for plain regression prefer alterlab-statistical-analysis. Part of the AlterLab Academic Skills suite.
license	MIT
allowed-tools	Read Bash(python:*)
compatibility	Requires (declare in-session, no runtime install on Anthropic API): semopy>=2.3, factor_analyzer>=0.5, pingouin>=0.5, optionally girth (IRT) (pip). SRMR and omega are not returned by semopy — compute omega with the bundled script; IRT beyond 2PL is often better in R mirt. Runs locally via `uv run python`; no API key.
metadata	{"skill-author":"AlterLab","version":"1.0.0","depends_on":"alterlab-ssci-measurement-gate (gates whether to trust the scale), alterlab-statistical-analysis; audited by alterlab-ssci-inference-gate"}

SEM & Psychometrics — Fit the Measurement Model, Judge It Honestly

Skill type: ANALYSIS MODULE. Fits CFA / SEM / EFA / IRT and tests measurement invariance. The discipline: report fit against real cutoffs, report reliability with omega (not alpha alone), and establish invariance before comparing groups. Whether the scale should be trusted at all is the upstream call of alterlab-ssci-measurement-gate.

Core Mission

A MEASUREMENT MODEL IS ONLY DONE WHEN FIT, RELIABILITY (OMEGA), AND INVARIANCE ARE ALL REPORTED.

When to Use This Skill

• "Run a confirmatory factor analysis on my scale."
• "Fit a structural equation model / a latent-variable path model."
• "Do an exploratory factor analysis — how many factors?"
• "Fit an IRT model / get item difficulty and discrimination."
• "Test measurement invariance across countries before I compare latent means."

Does NOT Trigger

The request is really about…	Route to	Why not this skill
Whether the scale is valid/trustworthy at all (reliability≠validity discipline)	alterlab-ssci-measurement-gate	Gate decision, upstream of fitting.
Writing / wording the questionnaire items	alterlab-survey-design	Instrument construction.
Plain regression / descriptive stats	alterlab-statistical-analysis	No latent structure.
A causal treatment-effect estimate	alterlab-causal-inference	Different problem.

Verified calls (pinned)

CFA / SEM — semopy (v2.3):

from semopy import Model, calc_stats
desc = """
# measurement model
Trust =~ q1 + q2 + q3
Efficacy =~ q4 + q5 + q6
# structural path
Trust ~ Efficacy
"""
m = Model(desc); m.fit(data)          # obj='MLW' default; 'FIML' for missing
est = m.inspect(std_est=True)          # standardized loadings for omega
stats = calc_stats(m)                  # DataFrame: chi2, CFI, TLI, RMSEA, AIC, BIC ...

Note: calc_stats returns CFI/TLI/RMSEA but not SRMR — report the indices it gives and compute SRMR separately if required.

EFA — factor_analyzer (v0.5):

from factor_analyzer import FactorAnalyzer, calculate_kmo, calculate_bartlett_sphericity
kmo_all, kmo_model = calculate_kmo(X)          # sampling adequacy > .60
chi2, p = calculate_bartlett_sphericity(X)      # sphericity
fa = FactorAnalyzer(n_factors=3, rotation="promax"); fa.fit(X)
fa.loadings_; fa.get_factor_variance()          # (variance, proportional, cumulative)

ConfirmatoryFactorAnalyzer + ModelSpecificationParser.parse_model_specification_from_dict give a CFA alternative when semopy is unavailable.

Reliability — omega (not alpha alone): pingouin gives cronbach_alpha but no omega, and semopy does not return omega. Compute McDonald's omega from the standardized loadings with scripts/omega.py (ω = (Σλ)² / [(Σλ)² + Σ(1−λ²)]). Report alpha + omega together.

IRT: girth (twopl_mml, rasch_mml) for dichotomous 2PL/Rasch; py-irt for Bayesian/ scalable. For polytomous/multidimensional IRT with full fit statistics, R mirt is the practical standard — say so rather than forcing a thin Python path.

Fit cutoffs (Hu & Bentler 1999, as guidelines not gates)

CFI/TLI ≥ .95 · RMSEA ≤ .06 · SRMR ≤ .08. Use a two-index combination; do not chase a single number. Report the χ² and df alongside (χ² is sample-size sensitive, so not decisive).

Measurement invariance (before any group comparison)

Multi-group CFA sequence — configural → metric → scalar → strict — judged by ΔCFI ≤ .01 / ΔRMSEA ≤ .015, not only Δχ². Scalar invariance is the prerequisite for comparing latent means; without it a group "difference" may be a measurement artifact. Fit each nested model and compare.

Output Template

MODEL:        <CFA/SEM/EFA/IRT + the semopy/factor_analyzer spec>
FIT:          CFI= TLI= RMSEA= (chi2/df=)   vs Hu & Bentler cutoffs
RELIABILITY:  omega= (alpha= )              per factor, from standardized loadings
VALIDITY:     <AVE, HTMT if convergent/discriminant claimed>
INVARIANCE:   <configural|metric|scalar|strict established; ΔCFI reported>

References

• references/fit_and_invariance.md — omega math, fit-index nuance, the invariance sequence, IRT notes.
• scripts/omega.py — stdlib McDonald's omega from standardized loadings.

Part of the AlterLab Academic Skills suite.