Girth is a python package for estimating item response theory (IRT) parameters. In addition, synthetic IRT data generation is supported. Below is a list of available functions, for more information visit the GIRTH homepage.

Interested in Bayesian Models? Check out girth_mcmc. It provides markov chain and variational inference estimation methods.

Dichotomous Models

1. Rasch Model
   • Joint Maximum Likelihood
   • Conditional Likelihood
   • Marginal Maximum Likelihood
2. One Parameter Logistic Models
   • Joint Maximum Likelihood
   • Marginal Maximum Likelihood
3. Two Parameter Logistic Models
   • Joint Maximum Likelihood
   • Marginal Maximum Likelihood
   • Mixed Expected A Prior / Marginal Maximum Likelihood
4. Three Parameter Logistic Models
   • Marginal Maximum Likelihood (No Optimization and Minimal Support)

Polytomous Models

1. Graded Response Model
   • Joint Maximum Likelihood
   • Marginal Maximum Likelihood
   • Mixed Expected A Prior / Marginal Maximum Likelihood
2. Partial Credit Model
   • Joint Maximum Likelihood
   • Marginal Maximum Likelihood
3. Graded Unfolding Model
   • Marginal Maximum Likelihood

Ablity Estimation

1. Dichotomous
   • Marginal Likelihood Estimation
   • Maximum a Posteriori Estimation
   • Expected a Posteriori Estimation
2. Polytomous
   • Expected a Posteriori Estimation

Supported Synthetic Data Generation

1. Rasch / 1PL Models Dichotomous Models
2. 2 PL Dichotomous Models
3. 3 PL Dichotomous Models
4. Graded Response Model Polytomous
5. Partial Credit Model Polytomous
6. Graded Unfolding Model Polytomous
7. Multidimensional Dichotomous Models

Via pip

pip install girth --upgrade

From Source

python setup.py install --prefix=path/to/your/installation

We recommend the anaconda environment which can be installed here

• Python 3.7
• Numpy
• Scipy
• Numba

import numpy as np

from girth import create_synthetic_irt_dichotomous
from girth import twopl_mml

# Create Synthetic Data
difficulty = np.linspace(-2.5, 2.5, 10)
discrimination = np.random.rand(10) + 0.5
theta = np.random.randn(500)

syn_data = create_synthetic_irt_dichotomous(difficulty, discrimination, theta)

# Solve for parameters
estimates = twopl_mml(syn_data)

# Unpack estimates
discrimination_estimates = estimates['Discrimination']
difficulty_estimates = estimates['Difficulty']

Without coverage.py module

nosetests testing/

With coverage.py module

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

Ryan Sanchez
[email protected]

MIT License

Copyright (c) 2020 Ryan 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.

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