GIRTH MCMC

Item Response Theory using Markov Chain Monte Carlo / Variational Inference

Dependencies

We recommend using Anaconda. Individual packages can be installed through pip otherwise.

• Python >= 3.7.6
• Numpy
• Scipy
• PyMC3

Supports

Unidimensional

• Rasch Model
• 1PL Model
• 2PL Model
• 3PL Model
• Graded Response Model

Usage

Subject to change but for now:

import numpy as np
from girth_mcmc import (create_synthetic_irt_dichotomous, 
                        GirthMCMC)
                        
discrimination = 0.89 * np.sqrt(-2 * np.log(np.random.rand(10)))
difficulty = np.random.randn(10)
theta = np.random.randn(100)

syn_data = create_synthetic_irt_dichotomous(difficulty, discrimination, 
                                            theta)

girth_model = GirthMCMC(model='2PL', 
                        options={'n_processors': 4})
results = girth_model(syn_data)
print(results)

for the graded response model, pass in the number of categories

import numpy as np
from girth_mcmc import (create_synthetic_irt_polytomous, 
                        GirthMCMC)

n_categories = 3

difficulty = np.random.randn(10, n_categories-1)
difficulty = np.sort(difficulty, 1)        
discrimination = 0.96 * np.sqrt(-2 * np.log(np.random.rand(10)))
theta = np.random.randn(150)

syn_data = create_synthetic_irt_polytomous(difficulty, discrimination, 
                                            theta, model='grm')

girth_model = GirthMCMC(model='GRM', model_args=(n_categories,),
                        options={'n_processors': 4})
results = girth_model(syn_data)
print(results)

Don't like waiting? me either. Run Variational Inference for faster but less accurate estimation.

import numpy as np
from girth_mcmc import (create_synthetic_irt_polytomous, 
                        GirthMCMC)

n_categories = 3

difficulty = np.random.randn(10, n_categories-1)
difficulty = np.sort(difficulty, 1)        
discrimination = 1.76 * np.sqrt(-2 * np.log(np.random.rand(10)))
theta = np.random.randn(150)

syn_data = create_synthetic_irt_polytomous(difficulty, discrimination, 
                                            theta, model='grm')

girth_model = GirthMCMC(model='GRM', model_args=(n_categories,),
                        options={'variational_inference': True,
                                 'variational_samples': 10000,
                                 'n_samples': 10000})
results_variational = girth_model(syn_data, progressbar=False)
print(results_variational)

Unittests

The unittests are just smoke tests for now:

Without coverage.py module

nosetests testing/

With coverage.py module

nosetests --with-coverage --cover-package=girth_mcmc testing/

Other Estimation Packages

If you are looking for Marginal Maximum Likelihood estimation routines, check out GIRTH.