IrtRuby

IrtRuby is a Ruby gem that provides implementations of the Rasch model, the Two-Parameter (2PL) model, and the Three-Parameter (3PL) model for Item Response Theory (IRT). It allows you to estimate the abilities of individuals and the difficulties (and optionally discriminations and guessing parameters) of items based on their responses.

Installation

Add this line to your application's Gemfile:

gem 'irt_ruby'

And then execute:

bundle install

Or install it yourself as:

gem install irt_ruby

Usage

Here's a quick example using the Rasch model:

require 'irt_ruby'
require 'matrix'

# Create a sample response matrix
data = Matrix[
  [1, 0, 1],
  [0, 1, 0],
  [1, 1, 1]
]

# Initialize the Rasch model with the response data
model = IrtRuby::RaschModel.new(data)

# Fit the model to estimate abilities and difficulties
result = model.fit

# Output the estimated abilities and difficulties
puts "Abilities:    #{result[:abilities]}"
puts "Difficulties: #{result[:difficulties]}"

Using 2PL and 3PL Models

two_pl_model = IrtRuby::TwoParameterModel.new(data)
two_pl_result = two_pl_model.fit
puts two_pl_result[:abilities]
puts two_pl_result[:difficulties]
puts two_pl_result[:discriminations]

three_pl_model = IrtRuby::ThreeParameterModel.new(data)
three_pl_result = three_pl_model.fit
puts three_pl_result[:abilities]
puts three_pl_result[:difficulties]
puts three_pl_result[:discriminations]
puts three_pl_result[:guessings]

Handling Missing Data

Real-world data often has missing responses. Each model (Rasch, 2PL, 3PL) accepts a missing_strategy: option to handle nil entries:

• :ignore (default): Skip nil responses entirely in the log-likelihood and gradient calculations.
• :treat_as_incorrect: Interpret nil as 0.
• :treat_as_correct: Interpret nil as 1.

For example:

data_with_missing = [
  [1, nil, 0],
  [nil, 1,  0],
  [0,  1,  1]
]

model = IrtRuby::RaschModel.new(
  data_with_missing,
  max_iter: 300,
  learning_rate: 0.01,
  missing_strategy: :treat_as_incorrect
)
result = model.fit

puts "Abilities:    #{result[:abilities]}"
puts "Difficulties: #{result[:difficulties]}"

This flexibility helps you handle datasets where missingness might signify a skipped item or an unanswered question.

Advanced Usage

Adaptive Learning Rate & Convergence

By default, each model uses a gradient ascent with:

• An adaptive learning rate (if log-likelihood decreases, it reverts the step and reduces the rate).
• Multiple convergence checks (change in log-likelihood and average parameter updates).

You can customize:

• max_iter: The maximum number of iterations.
• tolerance and param_tolerance: Convergence thresholds for log-likelihood change and parameter updates.
• learning_rate: Initial learning rate.
• decay_factor: Factor by which the learning rate is reduced on a failed step.

Example:

IrtRuby::TwoParameterModel.new(
  data,
  max_iter: 500,
  tolerance: 1e-7,
  param_tolerance: 1e-7,
  learning_rate: 0.05,
  decay_factor: 0.5
)

Parameter Clamping

For 2PL and 3PL:

• Discriminations (a) are clamped between 0.01 and 5.0.
• Guessings (c, 3PL only) are clamped to [0.0, 0.35].

This prevents extreme or invalid parameter estimates.

Development

After checking out the repo, run bin/setup to install dependencies. Then, run rake test to run the tests. You can also run bin/console for an interactive prompt that will allow you to experiment.

To install this gem onto your local machine, run bundle exec rake install. To release a new version, update the version number in version.rb, and then run bundle exec rake release, which will create a git tag for the version, push git commits and the created tag, and push the .gem file to rubygems.org.

Contributing

Bug reports and pull requests are welcome on GitHub at https://github.com/SyntaxSpirits/irt_ruby. This project is intended to be a safe, welcoming space for collaboration, and contributors are expected to adhere to the code of conduct.

License

The gem is available as open source under the terms of the MIT License.

Code of Conduct

Everyone interacting in the IrtRuby project's codebases, issue trackers, chat rooms, and mailing lists is expected to follow the code of conduct.