mirt 0.1.1

Multidimensional Item Response Theory for Python

mirt

Multidimensional Item Response Theory for Python

A comprehensive Python implementation of Item Response Theory (IRT) models, inspired by R's mirt package.

Features

• Dichotomous Models: 1PL (Rasch), 2PL, 3PL, 4PL
• Polytomous Models: GRM, GPCM, PCM, NRM
• Estimation: EM algorithm with Gauss-Hermite quadrature
• Scoring: EAP, MAP, ML methods for person ability estimation
• Diagnostics: Item fit, person fit statistics
• Simulation: Generate response data from IRT models
• Multiple Groups: Basic multiple group analysis

Installation

pip install mirt

For development:

pip install -e ".[dev]"

Quick Start

import mirt
import numpy as np

# Simulate response data
responses = mirt.simdata(model='2PL', n_persons=500, n_items=20, seed=42)

# Fit a 2PL model
result = mirt.fit_mirt(responses, model='2PL')

# View results
print(result.summary())

# Get item parameters
params = result.coef()
print(params)

# Score respondents
scores = mirt.fscores(result, responses, method='EAP')
print(scores.to_dataframe().head())

Supported Models

Dichotomous (Binary) Models

Model	Description	Parameters
1PL/Rasch	One-parameter logistic	difficulty (b)
2PL	Two-parameter logistic	discrimination (a), difficulty (b)
3PL	Three-parameter logistic	a, b, guessing (c)
4PL	Four-parameter logistic	a, b, c, upper asymptote (d)

Polytomous (Ordinal) Models

Model	Description	Use Case
GRM	Graded Response Model	Likert scales
GPCM	Generalized Partial Credit	Partial credit items
PCM	Partial Credit Model	Rasch for polytomous
NRM	Nominal Response Model	Unordered categories

Examples

Fitting Different Models

# 1PL (Rasch) model
result_1pl = mirt.fit_mirt(responses, model='1PL')

# 3PL model with guessing
result_3pl = mirt.fit_mirt(responses, model='3PL')

# Graded Response Model for Likert data
likert_data = mirt.simdata(model='GRM', n_categories=5)
result_grm = mirt.fit_mirt(likert_data, model='GRM', n_categories=5)

Person Scoring

# Different scoring methods
eap_scores = mirt.fscores(result, responses, method='EAP')
map_scores = mirt.fscores(result, responses, method='MAP')
ml_scores = mirt.fscores(result, responses, method='ML')

# Access theta values
print(eap_scores.theta)
print(eap_scores.standard_error)

Item Analysis

# Item fit statistics
item_fit = mirt.itemfit(result, responses)
print(item_fit)

# Person fit statistics
person_fit = mirt.personfit(result, responses)
print(person_fit)

Data Simulation

# Simulate with specific parameters
a = np.random.lognormal(0, 0.3, size=20)
b = np.random.normal(0, 1, size=20)

responses = mirt.simdata(
    model='2PL',
    discrimination=a,
    difficulty=b,
    n_persons=1000,
    seed=42
)

API Reference

Main Functions

• fit_mirt(data, model, ...) - Fit an IRT model
• fscores(model, responses, method) - Compute person abilities
• simdata(model, n_persons, n_items, ...) - Simulate response data
• itemfit(result, responses) - Item fit statistics
• personfit(result, responses) - Person fit statistics

Model Classes

• TwoParameterLogistic - 2PL model class
• ThreeParameterLogistic - 3PL model class
• GradedResponseModel - GRM model class
• etc.

Comparison with R mirt

Feature	R mirt	Python mirt
Dichotomous models	1PL-4PL	1PL-4PL
Polytomous models	GRM, GPCM, PCM, NRM	GRM, GPCM, PCM, NRM
Estimation	EM, MHRM	EM
Multidimensional	Full support	Basic 2PL
Bifactor	Yes	Planned
DIF	Yes	Basic
GUI	Shiny app	-

Dependencies

• numpy >= 1.21
• scipy >= 1.7
• pandas >= 1.3

Development

# Install dev dependencies
pip install -e ".[dev]"

# Run tests
pytest

# Type checking
mypy src/mirt

# Formatting
black src tests
ruff check src tests

License

MIT License - see LICENSE

References

• Chalmers, R. P. (2012). mirt: A Multidimensional Item Response Theory Package for the R Environment. Journal of Statistical Software, 48(6), 1-29.
• Bock, R. D., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometrika, 46(4), 443-459.