CFA Testing — Identification, Primary Fit, Recommendation

Table of Contents

• Scope Boundary
• Workflow
• Decision Tree
• Required Inputs
• Code Structure
• Reporting Standards
• Method Status
• Minimal Smoke Test

Open-source skill.

Scope Boundary

Use this skill when:

• The main goal is a confirmatory measurement model for named latent constructs.
• A first-pass CFA with identification, estimator choice, and global fit reporting is the right checkpoint before validity or invariance work.

Do not use this skill when:

• The question is primarily about structural paths or mediation; use vera-data-path-reviewing.
• The focus is longitudinal change modeling across waves; use vera-data-growth-reviewing.

Workflow

Read each step file in workflow/ before executing that step.

Step	Responsibility	Executor	Document	Input	Output
Collect	Collect Inputs	Main Agent	workflow/step01-collect-inputs.md	User input	Structured SEM input summary
Diagnose	Check Measurement Setup	Main Agent	workflow/step02-check-measurement-setup.md	Prior step output	Identification + estimator decision
Test	Run Primary Cfa	Main Agent	workflow/step03-run-primary-cfa.md	Prior step output	Initial CFA fit + recommendation block

Decision Tree

1. CHECK MODEL FORM
   ├── Reflective latent factors with named indicators → CFA path
   └── Structural relations without clear latent blocks → recommend sem-full

2. CHECK ESTIMATOR
   ├── Continuous, roughly normal indicators → ML / MLR
   ├── Continuous, non-normal indicators → robust ML
   └── Ordinal indicators → WLSMV / DWLS

3. CHECK IDENTIFICATION
   ├── Each factor has 3+ indicators → standard identification
   ├── 2 indicators → require theory + equality/variance constraints
   └── 1 indicator → do not fit as free CFA factor without extra constraints

Required Inputs

Role	What to collect
Latent constructs	Factor names and theoretical meaning
Indicators	Which observed variables load on each factor
Scale type	Continuous, ordinal/Likert, binary indicators
Grouping variable	Optional; for later invariance testing
Sample size	Final analytic N and missing-data context

Code Structure

PART 0: Setup & Data Loading
PART 1: Measurement Setup Checks
PART 2: Primary CFA Fit
PART 3: Recommendation Block

Reporting Standards

1. Always report chi-square, df, CFI, TLI, RMSEA, and SRMR
2. Report standardized loadings with SE or CI when available
3. Say "fit was acceptable / borderline / poor" rather than "good" without context
4. Identification problems must be stated explicitly, never silently patched
5. Ends with a recommendation block for reliability/validity, invariance, and alternative-model comparison
6. Fit-index thresholds: CFI / TLI ≥ 0.90 (≥ 0.95 preferred); RMSEA ≤ 0.08 (≤ 0.06 preferred); SRMR ≤ 0.08. For ordinal/categorical indicators with DWLS/WLSMV, report robust (scaled/adjusted) versions of CFI, TLI, and RMSEA.

Method Status

Status	Methods
Implemented in this skill	Measurement setup checks, estimator choice, identification triage, initial CFA fit, fit-index reporting, standardized loadings
Implemented downstream in vera-data-cfa-generating	Reliability / validity summaries, invariance testing, alternative-model comparison, MI review, manuscript assembly
Out of scope in this open-source baseline	Structural SEM, longitudinal SEM, and any latent-variable family not named above

Minimal Smoke Test

• Smoke-test prompt: "Run vera-data-cfa-reviewing on a small 2-factor CFA example with 3 indicators per factor and continuous indicators. Produce the standard baseline artifacts and recommendation block."

Next step: Invoke vera-data-cfa-generating from this skillset to run the full pipeline (reliability/validity, invariance testing, alternative-model comparison, manuscript generation). See ../../CROSS-SKILL-INTERFACE.md for the shared handoff contract.