Add Two-Parameter IRT Model with improvements

lib/irt_ruby/two_parameter_model.rb

@@ -5,19 +5,22 @@
 module IrtRuby
   # A class representing the Two-Parameter model for Item Response Theory.
   class TwoParameterModel
-    def initialize(data, max_iter: 1000, tolerance: 1e-6)
+    def initialize(data, max_iter: 1000, tolerance: 1e-6, learning_rate: 0.01)
       @data = data
       @abilities = Array.new(data.row_count) { rand }
       @difficulties = Array.new(data.column_count) { rand }
       @discriminations = Array.new(data.column_count) { rand }
       @max_iter = max_iter
       @tolerance = tolerance
+      @learning_rate = learning_rate
     end
 
+    # Sigmoid function
     def sigmoid(x)
       1.0 / (1.0 + Math.exp(-x))
     end
 
+    # Calculate the log-likelihood of the data given the current parameters
     def likelihood
       likelihood = 0
       @data.row_vectors.each_with_index do |row, i|
@@ -33,16 +36,17 @@ def likelihood
       likelihood
     end
 
+    # Update parameters using gradient ascent
     def update_parameters
       last_likelihood = likelihood
       @max_iter.times do |_iter|
         @data.row_vectors.each_with_index do |row, i|
           row.to_a.each_with_index do |response, j|
             prob = sigmoid(@discriminations[j] * (@abilities[i] - @difficulties[j]))
             error = response - prob
-            @abilities[i] += 0.01 * error * @discriminations[j]
-            @difficulties[j] -= 0.01 * error * @discriminations[j]
-            @discriminations[j] += 0.01 * error * (@abilities[i] - @difficulties[j])
+            @abilities[i] += @learning_rate * error * @discriminations[j]
+            @difficulties[j] -= @learning_rate * error * @discriminations[j]
+            @discriminations[j] += @learning_rate * error * (@abilities[i] - @difficulties[j])
           end
         end
         current_likelihood = likelihood
@@ -52,6 +56,7 @@ def update_parameters
       end
     end
 
+    # Fit the model to the data
     def fit
       update_parameters
       { abilities: @abilities, difficulties: @difficulties, discriminations: @discriminations }