Improve Rasch Model implementation with learning rate and better docu…

…mentation (#7)

lib/irt_ruby/rasch_model.rb

@@ -5,42 +5,42 @@
 module IrtRuby
   # A class representing the Rasch model for Item Response Theory.
   class RaschModel
-    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 }
       @max_iter = max_iter
       @tolerance = tolerance
+      @learning_rate = learning_rate
     end
 
+    # Sigmoid function to calculate probability
     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|
         row.to_a.each_with_index do |response, j|
           prob = sigmoid(@abilities[i] - @difficulties[j])
-          if response == 1
-            likelihood += Math.log(prob)
-          elsif response.zero?
-            likelihood += Math.log(1 - prob)
-          end
+          likelihood += response == 1 ? Math.log(prob) : Math.log(1 - prob)
         end
       end
       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(@abilities[i] - @difficulties[j])
             error = response - prob
-            @abilities[i] += 0.01 * error
-            @difficulties[j] -= 0.01 * error
+            @abilities[i] += @learning_rate * error
+            @difficulties[j] -= @learning_rate * error
           end
         end
         current_likelihood = likelihood
@@ -50,6 +50,7 @@ def update_parameters
       end
     end
 
+    # Fit the model to the data
     def fit
       update_parameters
       { abilities: @abilities, difficulties: @difficulties }

spec/irt_ruby/rasch_model_spec.rb

@@ -4,26 +4,31 @@
 
 RSpec.describe IrtRuby::RaschModel do
   let(:data) { Matrix[[1, 0, 1], [0, 1, 0], [1, 1, 1]] }
-  let(:irt_model) { IrtRuby::RaschModel.new(data, max_iter: 2000) }
+  let(:model) { IrtRuby::RaschModel.new(data, max_iter: 2000) }
+
+  describe "#initialize" do
+    it "initializes with data" do
+      expect(model.instance_variable_get(:@data)).to eq(data)
+    end
+  end
 
   describe "#sigmoid" do
-    it "calculates the sigmoid of a value" do
-      expect(irt_model.sigmoid(0)).to be_within(0.01).of(0.5)
-      expect(irt_model.sigmoid(2)).to be_within(0.01).of(0.88)
+    it "calculates the sigmoid function" do
+      expect(model.sigmoid(0)).to eq(0.5)
     end
   end
 
   describe "#likelihood" do
     it "calculates the likelihood of the data" do
-      expect(irt_model.likelihood).to be_a(Float)
+      expect(model.likelihood).to be_a(Float)
     end
   end
 
   describe "#fit" do
     it "fits the model and returns abilities and difficulties" do
-      results = irt_model.fit
-      expect(results[:abilities].size).to eq(3)
-      expect(results[:difficulties].size).to eq(3)
+      result = model.fit
+      expect(result[:abilities].size).to eq(data.row_count)
+      expect(result[:difficulties].size).to eq(data.column_count)
     end
   end
 end