Longitudinal Change Testing — Initial Growth / Change Fit

Table of Contents

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

Open-source skill.

Scope Boundary

Use this skill when:

• The goal is a latent growth or latent change baseline for repeated measurements across waves.
• A first-pass longitudinal SEM checkpoint is needed before nonlinear or multigroup extensions.

Do not use this skill when:

• The data are cross-sectional CFA or non-longitudinal SEM; use the corresponding SEM skill.
• The design is a high-frequency observed time series rather than longitudinal SEM.

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 longitudinal SEM summary
Diagnose	Check Longitudinal Setup	Main Agent	workflow/step02-check-longitudinal-setup.md	Prior step output	Wave/identification decision
Test	Run Primary Model	Main Agent	workflow/step03-run-primary-model.md	Prior step output	Initial LGM/LCSM fit + recommendation

Decision Tree

1. CHECK TIME STRUCTURE
   ├── 3+ waves of same construct → latent growth candidate
   ├── adjacent change focus → latent change score candidate
   └── only 2 waves → limited change model; report cautiously

2. CHECK MEASUREMENT
   ├── repeated observed score only → basic growth/change SEM
   └── latent construct per wave → recommend invariance-aware model

3. CHECK TRAJECTORY FORM
   ├── theory supports linear change → linear growth first
   └── theory suggests curvature → recommend nonlinear/basis model

Required Inputs

Role	What to collect
Repeated measure	Variable name measured at each wave
Time points	Number of waves, spacing (equal/unequal), time coding
Model type	Latent growth (LGM) vs latent change score (LCSM)
Scale type	Continuous, ordinal/Likert indicators per wave
Time-invariant covariates	Optional predictors of intercept/slope
Sample size	Final analytic N, attrition pattern

Code Structure

PART 0: Setup & Data Loading (wide or long format)
PART 1: Longitudinal Setup Checks (waves, identification, estimator)
PART 2: Primary Growth/Change Model Fit (intercept, slope, fit indices)
PART 3: Recommendation Block

Reporting Standards

1. Always report chi-square, df, CFI, TLI, RMSEA, and SRMR
2. Report mean and variance of intercept and slope factors
3. Report intercept-slope covariance/correlation
4. If covariates included: report their effects on intercept and slope
5. Only 2 waves: state limitation explicitly ("minimal identification")
6. Ends with recommendation block for nonlinear growth, piecewise models, time-varying covariates, and class-based trajectories
7. Fit-index thresholds: CFI / TLI ≥ 0.90 (≥ 0.95 preferred); RMSEA ≤ 0.08 (≤ 0.06 preferred); SRMR ≤ 0.08. For ordinal indicators with DWLS/WLSMV, report robust variants.
8. Measurement invariance (if repeated latent constructs across waves): test the standard sequence configural → metric (equal loadings) → scalar (equal intercepts) → strict (equal residual variances). Report ΔCFI < 0.010 and ΔRMSEA < 0.015 as thresholds for invariance at each step. Halt invariance comparison at the first level that fails and note the partial-invariance status.

Method Status

Status	Methods
Implemented in this skill	Wave-structure checks, initial LGM / LCSM fit, intercept / slope summaries, invariance-aware recommendation triggers
Implemented downstream in vera-data-growth-generating	Nonlinear trajectories, latent-basis and change-score variants, multigroup growth, parallel-process extensions, manuscript assembly
Out of scope in this open-source baseline	Cross-sectional SEM, CFA-only work, and longitudinal families not explicitly named above

Minimal Smoke Test

• Smoke-test prompt: "Run vera-data-growth-reviewing on a 3-wave repeated-measure example with equal spacing and continuous indicators. Produce the standard baseline artifacts and recommendation block."

Next step: Invoke vera-data-growth-generating from this skillset to run the full pipeline (nonlinear trajectories, latent-basis/change-score variants, multigroup growth, parallel-process models, manuscript generation). See ../../CROSS-SKILL-INTERFACE.md for the shared handoff contract.

Failure Modes

• If only 2 waves: fit basic change model but warn about minimal identification
• If model does not converge: suggest simpler specification (intercept-only)
• If cross-sectional CFA structure detected: redirect to vera-data-cfa-reviewing
• If non-longitudinal structural model: redirect to vera-data-path-reviewing