Adaptive Question Selector (IRT)

Item Response Theory-based adaptive testing engine that selects optimal questions based on student ability.

Features

• 2-Parameter Logistic (2PL) IRT Model
• Maximum Likelihood Estimation for ability
• Maximum Fisher Information question selection
• Real-time adaptation after each response
• Stopping rules (SE threshold, max questions)
• Simulation endpoint for testing

How It Works

P(correct) = 1 / (1 + e^(-a(θ - b)))

θ = student ability (-3 to +3)
b = question difficulty (-3 to +3)
a = discrimination (0.5 to 2.5)

The algorithm selects questions that maximize information at the student's current estimated ability level.

Quick Start

python3.12 -m venv venv
source venv/bin/activate
pip install -r requirements.txt
python -m uvicorn src.server:app --reload --port 8002

API Endpoints

Endpoint	Method	Description
/sessions	POST	Create adaptive test session
/sessions/{id}	GET	Get session status
/sessions/{id}/answer	POST	Submit answer, get next question
/simulate	GET	Run simulation with true theta
/estimate	POST	Standalone ability estimation

Usage Example

Create Session

curl -X POST http://localhost:8002/sessions \
  -H "Content-Type: application/json" \
  -d '{
    "question_pool": [
      {"id": "q1", "difficulty": -1.5, "content": "Easy"},
      {"id": "q2", "difficulty": 0.0, "content": "Medium"},
      {"id": "q3", "difficulty": 1.5, "content": "Hard"}
    ],
    "max_questions": 10,
    "stopping_se": 0.4
  }'

Submit Answer

curl -X POST http://localhost:8002/sessions/{session_id}/answer \
  -H "Content-Type: application/json" \
  -d '{"question_id": "q2", "correct": true}'

Simulate Test

curl "http://localhost:8002/simulate?true_theta=1.0&num_questions=20"

Selection Methods

Method	Description
max_info	Maximum Fisher Information (most precise)
target_50	Target 50% probability (balanced challenge)

Performance Levels

Theta Range	Level
≥ 1.5	Advanced
0.5 to 1.5	Proficient
-0.5 to 0.5	Basic
-1.5 to -0.5	Below Basic
< -1.5	Needs Support

Part of Ed-Tech Suite

Component	Repository
Question Bank MCP	Question management
Student Progress Tracker	Performance analytics
Simple Quiz Engine	Real-time quizzes
Learning Curriculum Builder	Curriculum design
Real-Time Event Pipeline	Event routing
Adaptive Question Selector	IRT-based adaptation

License

MIT

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Built by Jim Williams | GitHub