GIRTH: Item Response Theory
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.
Need general statistical support? Download my other project RyStats which implements commonly used statistical functions. These functions are also implemented in an interactive webapp GoFactr.com without the need to download or install software.
Item Response Theory
Unidimensional Models
Dichotomous Models
- Rasch Model
- Joint Maximum Likelihood
- Conditional Likelihood
- Marginal Maximum Likelihood
- One Parameter Logistic Models
- Joint Maximum Likelihood
- Marginal Maximum Likelihood
- Two Parameter Logistic Models
- Joint Maximum Likelihood
- Marginal Maximum Likelihood
- Mixed Expected A Prior / Marginal Maximum Likelihood
- Three Parameter Logistic Models
- Marginal Maximum Likelihood (No Optimization and Minimal Support)
Polytomous Models
- Graded Response Model
- Joint Maximum Likelihood
- Marginal Maximum Likelihood
- Mixed Expected A Prior / Marginal Maximum Likelihood
- Partial Credit Model
- Joint Maximum Likelihood
- Marginal Maximum Likelihood
- Graded Unfolding Model
- Marginal Maximum Likelihood
Ablity Estimation
- Dichotomous
- Maximum Likelihood Estimation
- Maximum a Posteriori Estimation
- Expected a Posteriori Estimation
- Polytomous
- Expected a Posteriori Estimation
Multidimensional Models
- Two Parameter Logistic Models
- Marginal Maximum Likelihood
- Graded Response Model
- Marginal Maximum Likelihood
Ablity Estimation
- Dichotomous
- Maximum a Posteriori Estimation
- Expected a Posteriori Estimation
- Polytomous
- Maximum a Posteriori Estimation
- Expected a Posteriori Estimation
Supported Synthetic Data Generation
Unidimensional
- Rasch / 1PL Models Dichotomous Models
- 2 PL Dichotomous Models
- 3 PL Dichotomous Models
- Graded Response Model Polytomous
- Partial Credit Model Polytomous
- Graded Unfolding Model Polytomous
Multidimensional
- Two Parameters Logisitic Models Dichotomous
- Graded Response Models Polytomous
Usage
Standard Estimation
To run girth with unidimensional models.
import numpy as np
from girth.synthetic import create_synthetic_irt_dichotomous
from girth import twopl_mml
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)
estimates = twopl_mml(syn_data)
discrimination_estimates = estimates['Discrimination']
difficulty_estimates = estimates['Difficulty']
Missing Data
Missing data is supported with the tag_missing_data
function.
from girth import tag_missing_data, twopl_mml
my_data = import_data(filename)
tagged_data = tag_missing_data(my_data, [0, 1])
results = twopl_mml(tagged_data)
Multidimensional Estimation
GIRTH supports multidimensional estimation but these estimation methods suffer
from the curse of dimensionality, using more than 3 factors takes a considerable amount
of time
import numpy as np
from girth.synthetic import create_synthetic_irt_dichotomous
from girth import multidimensional_twopl_mml
discrimination = np.random.uniform(-2, 2, (20, 2))
thetas = np.random.randn(2, 1000)
difficulty = np.linspace(-1.5, 1, 20)
syn_data = create_synthetic_irt_dichotomous(difficulty, discrimination, thetas)
estimates = multidimensional_twopl_mml(syn_data, 2, {'quadrature_n': 21})
discrimination_estimates = estimates['Discrimination']
difficulty_estimates = estimates['Difficulty']
Standard Errors
GIRTH does not use typical hessian based optimization routines and, therefore, currently
has limited support for standard errors. Confidence Intervals based on bootstrapping are
supported but take longer to run. Missing Data is supported in the bootstrap function as well.
The bootstrap does not support the 3PL IRT Model or the GGUM.
from girth import twopl_mml, standard_errors_bootstrap
my_data = import_data(filename)
results = standard_errors_bootstrap(my_data, twopl_mml, n_processors=4,
bootstrap_iterations=1000)
print(results['95th CI']['Discrimination'])
Factor Analysis
Factor analysis is another common method for latent variable exploration and estimation. These tools are helpful for understanding dimensionality or finding initial estimates of item parameters.
- Principal Component Analysis
- Principal Axis Factor
- Minimum Rank Factor Analysis
- Maximum Likelihood Factor Analysis
Example
import girth.factoranalysis as gfa
n_factors = 3
results = gfa.maximum_likelihood_factor_analysis(corrleation, n_factors)
print(results)
Polychoric Correlation Estimation
When collected data is ordinal, Pearson's correlation will provide biased estimates of the correlation. Polychoric correlations estimate the correlation given that the data is ordinal and normally distributed.
import girth.synthetic as gsyn
import girth.factoranalysis as gfa
import girth.common as gcm
discrimination = np.random.uniform(-2, 2, (20, 2))
thetas = np.random.randn(2, 1000)
difficulty = np.linspace(-1.5, 1, 20)
syn_data = gsyn.create_synthetic_irt_dichotomous(difficulty, discrimination, thetas)
polychoric_corr = gcm.polychoric_correlation(syn_data, start_val=0, stop_val=1)
results_fa = gfa.maximum_likelihood_factor_analysis(polychoric_corr, 2)
Support
Installation
Via pip
pip install girth --upgrade
From Source
pip install . -t $PYTHONPATH --upgrade
Dependencies
We recommend the anaconda environment which can be installed
here
Unittests
pytest with coverage.py module
pytest --cov=girth --cov-report term
Contact
Please contact me with any questions or feature requests. Thank you!
Ryan Sanchez
ryan.sanchez@gofactr.com
License
MIT License
Copyright (c) 2021 Ryan C. Sanchez
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