Full SEM Analyzing — Structural Paths, Indirect Effects, Manuscript

Open-source skill.

Read reference/specs/output-variation-protocol.md before every generation.

Workflow

Step	Responsibility	Executor	Document	Input	Output
Additional tests	Run Additional Tests	Main Agent	workflow/step04-run-additional-tests.md	Prior step output	Indirect/residual diagnostics
Subgroup	Analyze Subgroups	Main Agent	workflow/step05-analyze-subgroups.md	Prior step output	Multigroup SEM
Modeling	Fit Models	Main Agent	workflow/step06-fit-models.md	Prior step output	Alternative structural models
Comparison	Compare Models	Main Agent	workflow/step07-compare-models.md	Prior step output	Cross-model synthesis
Manuscript	Generate Manuscript	Main Agent	workflow/step08-generate-manuscript.md	Prior step output	methods.md + results.md

Additional Inputs

Collect if not already provided during testing:

• Target discipline and journal (for reporting conventions — APA 7th, Structural Equation Modeling style, etc.)
• Research question / hypothesis (directional path predictions)
• Grouping variable (for multigroup invariance testing)
• Mediation structure (which paths are hypothesized as indirect)
• Estimator preference if deviating from testing-skill default (ML, MLR, WLSMV, DWLS)

Output Structure

output/
├── methods.md
├── results.md
├── tables/              ← lavaan/semopy parameter tables, fit-index tables (Markdown + CSV)
├── figures/             ← path diagram, residual plots, multigroup comparison plots (PNG, 300 DPI)
├── references.bib
├── code.R               ← Style-varied lavaan script
└── code.py              ← Style-varied semopy script (optional)

Key References (read before generation)

File	Purpose
reference/specs/output-variation-protocol.md	Output quality variation layers
reference/specs/code-style-variation.md	Seven-dimension code style diversity
reference/patterns/sentence-bank.md	4–6 phrasings per result type
reference/rules/reporting-standards.md	Hard rules for SEM reporting

Reporting Standards

Same as vera-data-path-reviewing, plus:

• Indirect effects: always report with bias-corrected bootstrap 95% CI (≥ 5000 draws). Do not rely on Sobel z.
• Direct / indirect / total: report all three; when direct becomes non-significant after accounting for the indirect path, describe as "consistent with partial/full mediation" rather than proof of causality.
• Multigroup: report the Δχ², Δdf, Δp, ΔCFI for each invariance step (configural → metric → structural).
• Alternative models: compare with χ² difference test (nested) or AIC/BIC (non-nested); interpret ΔAIC > 10 as strong preference.
• Under MLR / Satorra–Bentler scaled estimators: Δχ² MUST be computed using the scaled difference statistic (Satorra & Bentler 2001), not by subtracting the two scaled χ² values. Simple subtraction of Satorra–Bentler-adjusted χ² gives a biased test. Use lavaan::lavTestLRT(fit1, fit2, method="satorra.bentler.2001") (or 2010 variant for negative corrections). Report the scaled difference T_d, df, p. This applies to ALL nested-model comparisons, including measurement-invariance steps.
• Modification indices: only apply when theoretically justified; report which MIs were accepted and which rejected.
• Standardized path coefficients: β with SE or CI; asterisks for significance levels discouraged — report exact p.

Cross-Skill Interface

Method Unit Contract:
├── code_r           → .R script (style-varied, lavaan)
├── code_python      → .py script (style-varied, semopy, optional)
├── methods_md       → methods.md (varied structure)
├── results_md       → results.md (varied phrasing)
├── tables/          → Markdown + CSV
├── figures/         → PNGs 300 DPI (varied layout)
├── references_bib   → .bib with cited references
└── comparison       → cross-model narrative (in results.md)

Invoked directly after vera-data-path-reviewing or orchestrated by vera-data-application-pipelining.