📐 IRT Model Selection Guide
Visual guide for choosing among 1PL (Rasch), 2PL, and 3PL IRT models. Load binary response data to see item p-values.
MODEL COMPARISON
| Feature | 1PL Rasch | 2PL | 3PL |
|---|---|---|---|
| Parameters | Difficulty (β) | Difficulty (β), Discrimination (α) | Difficulty (β), Discrimination (α), Guessing (γ) |
| Assumptions | Equal discrimination, no guessing | Varying discrimination, no guessing | Varying discrimination, guessing allowed |
| ICC Shape | Parallel logistic curves | Variable-slope logistic curves | Asymptotic lower bound > 0 |
| Sample Size | N ≥ 100 | N ≥ 250 | N ≥ 500 |
| Estimation | JML / CML | MML (EM) | MML (EM + priors) |
| Best For | Measurement-focused, Rasch philosophy | Exploratory psychometrics | Multiple-choice tests |
| Fit Indices | Infit/Outfit MSQ | -2LL, AIC, BIC | -2LL, AIC, BIC |
DECISION FLOWCHART
Start: Binary item response data
↓
Are items multiple-choice with plausible distractors?
Yes
↓
🔴 3PL Model
Accounts for guessing (N≥500)
Accounts for guessing (N≥500)
No
↓
Do items vary in discrimination?
Yes
↓
🔸 2PL Model
Free discrimination (N≥250)
Free discrimination (N≥250)
No / Rasch
↓
🔵 1PL Rasch
Equal discrimination (N≥100)
Equal discrimination (N≥100)
QUICK CHECK: ITEM P-VALUES
📋Paste binary response matrix (persons x items, 0/1 coded, first row = item names) to see item difficulty (p-values) and point-biserial correlations.
Data Grid
Edit cells directly. Click 'Apply to CSV' to transfer data.
🔵 1PL Rasch Model
Joint Maximum Likelihood (JML) estimation of the Rasch model. P(X=1|θ,β) = 1/(1+exp(-(θ-β))). Estimates item difficulties and person abilities with Newton-Raphson iteration.
DATA & OPTIONS
📋Binary matrix: Persons (rows) x Items (columns), coded 0/1. First row = item names. One person per row.
Data Grid
Edit cells directly. Click 'Apply to CSV' to transfer data.
📊 Statistical Interpretation
🔸 2PL Model
Marginal Maximum Likelihood (MML) estimation via EM algorithm with Gauss-Hermite quadrature (Q=21 nodes). Estimates item discrimination (α) and difficulty (β), plus EAP ability scores.
DATA & OPTIONS
📋Binary matrix: Same format as 1PL. The 2PL model frees the discrimination parameter for each item.
Data Grid
Edit cells directly. Click 'Apply to CSV' to transfer data.
📊 Statistical Interpretation
🔴 3PL Model
Three-parameter logistic model via EM with Bayesian priors on discrimination and guessing. P(X=1|θ) = γ + (1-γ)/(1+exp(-α(θ-β))). Requires larger samples (N≥500).
DATA & OPTIONS
⚠️Warning: 3PL requires N ≥ 500 for stable estimation. For smaller samples, use 1PL or 2PL.
Data Grid
Edit cells directly. Click 'Apply to CSV' to transfer data.
📊 Statistical Interpretation
⚖️ Differential Item Functioning
Detect measurement bias using Mantel-Haenszel and Logistic Regression methods. Tests whether items function differently across groups (e.g., gender, ethnicity).
DATA & OPTIONS
📋Format: Binary response matrix with an additional first column for group membership (0=reference, 1=focal). First row = headers.
Data Grid
Edit cells directly. Click 'Apply to CSV' to transfer data.
📊 Statistical Interpretation
🧩 Latent Class Analysis — Model Fit
EM algorithm for categorical latent class models with multiple random starts. Compare models with 1-K classes using AIC, BIC, SABIC, entropy, and bootstrap LRT.
DATA & OPTIONS
📋Binary response matrix: Persons (rows) x indicator variables (columns), coded 0/1. First row = variable names.
Data Grid
Edit cells directly. Click 'Apply to CSV' to transfer data.
📊 Statistical Interpretation
↔️ TOST Equivalence Testing
Two One-Sided Tests procedure (Schuirmann, 1987). Demonstrates equivalence by rejecting both H01: δ≤-Δ and H02: δ≥Δ. Supports independent means, paired means, proportions, and correlation tests.
TEST CONFIGURATION
📊 Statistical Interpretation
🔢 McDonald's ω Reliability
Factor-analytic reliability: ωtotal = (Σλ)² / [(Σλ)² + Σθ]. Extracts a single factor via ULS, computes Cronbach's α for comparison, with bootstrap 95% CI.
DATA & OPTIONS
📋Continuous data matrix: Persons (rows) x Items (columns). First row = item names. Values can be Likert-scale or continuous.
Data Grid
Edit cells directly. Click 'Apply to CSV' to transfer data.
📊 Statistical Interpretation