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 ≥ 3.8
• Numpy
• Scipy
• Girth
• PyMC3

Installation

Via pip

pip install girth_mcmc --upgrade

From Source

pip install . -t $PYTHONPATH --upgrade

Supports

Unidimensional

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

Multi-dimensional

• 2PL Model
• Graded Response Model
• Partial Credit Model

Usage

Subject to change but for now:

import numpy as np
from girth.synthetic import create_synthetic_irt_dichotomous
from girth_mcmc import 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.synthetic import create_synthetic_irt_polytomous
from girth_mcmc import 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)

Is some data missing? Tag it with a convenience function and run it like normal

import numpy as np
from girth.synthetic import create_synthetic_irt_dichotomous
from girth_mcmc import GirthMCMC
from girth_mcmc.utils import tag_missing_data_mcmc
                        
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)
mask = np.random.rand(*syn_data.shape) < .1
syn_data[mask] = -9999
syn_data_missing = tag_missing_data_mcmc(syn_data, [0, 1])

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

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

import numpy as np
from girth.synthetic import create_synthetic_irt_polytomous
from girth_mcmc import 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

pytest with coverage.py module

pytest --cov=girth_mcmc --cov-report term

Contact

Ryan Sanchez
ryan.sanchez@gofactr.com

Other Estimation Packages

If you are looking for Marginal Maximum Likelihood estimation routines, check out GIRTH, a graphical interface is also at GoFactr

License

MIT License

Copyright (c) 2021 Ryan C. Sanchez

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.