local_clue.rb

class LocalClue
  attr_reader :aggregate
  attr_reader :left
  attr_reader :right
  attr_reader :threshold
  attr_reader :level
  attr_reader :confidence

  attr_reader :learners
  attr_reader :responses

  def initialize(learners: [], responses: [])
    @aggregate  = 0.5
    @left       = 0.0
    @right      = 1.0
    @threshold  = :below
    @level      = :medium
    @confidence = :bad

    @learners  = learners
    @responses = responses

    self._update
  end


  def _update
    learner_responses = @responses.select{|response| @learners.include? response[:learner_id]}
    if learner_responses.count >= 3
      trial_tot = learner_responses.count
      trial_suc = learner_responses.select{|response| response[:correct]}.count

      z_alpha = 0.68

      p_hat = (trial_suc + 0.5*z_alpha**2) / (trial_tot + z_alpha**2)

      var = learner_responses.map{|response| response[:correct] ? 1.0 : 0.0}
                             .map{|value| (p_hat - value)**2}
                             .inject(&:+) / (learner_responses.count - 1)

      interval = ( z_alpha * Math.sqrt(p_hat*(1-p_hat)/(trial_tot + z_alpha**2)) +
                   0.1*Math.sqrt(var) +
                   0.05 )

      @aggregate = p_hat
      @left  = [p_hat - interval, 0].max
      @right = [p_hat + interval, 1].min
    end

    if @aggregate < 0.3
      @level = :low
    elsif @aggregate < 0.8
      @level = :medium
    else
      @level = :high
    end

    if (@right-@left).abs <= 0.5
      @confidence = :good
    else
      @confidence = :bad
    end

    if learner_responses.count > 3
      @threshold = :above
    else
      @threshold = :below
    end

    # puts "[#{@aggregate} #{@left} #{@right} #{@level} #{@confidence} #{@threshold}]"
  end
end

RSpec.describe LocalClue do
  let(:local_clue) { LocalClue.new(learners: learners, responses: responses) }

  context 'no learners or responses' do
    let(:learners) { [] }
    let(:responses) { [] }

    it "'aggregate' is 0.5" do
      expect(local_clue.aggregate).to be 0.5
    end
    it "'left' is 0.0" do
      expect(local_clue.left).to be 0.0
    end
    it "'right' is 1.0" do
      expect(local_clue.right).to be 1.0
    end
    it "'level' is :medium" do
      expect(local_clue.level).to be :medium
    end
    it "'threshold' is :below" do
      expect(local_clue.threshold).to be :below
    end
    it "'confidence' is :bad" do
      expect(local_clue.confidence).to be :bad
    end
  end

  context 'single learner' do
    let(:learners) { ['lid1'] }

    context 'no responses' do
      let(:responses) { [] }

      it "'aggregate' is 0.5" do
        expect(local_clue.aggregate).to be 0.5
      end
      it "'left' is 0.0" do
        expect(local_clue.left).to be 0.0
      end
      it "'right' is 1.0" do
        expect(local_clue.right).to be 1.0
      end
      it "'level' is :medium" do
        expect(local_clue.level).to be :medium
      end
      it "'threshold' is :below" do
        expect(local_clue.threshold).to be :below
      end
      it "'confidence' is :bad" do
        expect(local_clue.confidence).to be :bad
      end
    end

    context 'few responses' do
      let(:responses) {
        [ { learner_id: 'lid1', question_id: 'qid1', correct: true},
          { learner_id: 'lid1', question_id: 'qid2', correct: false},
          { learner_id: 'lid2', question_id: 'qid1', correct: false}, ]
      }

      it "'level' is :medium" do
        expect(local_clue.level).to be :medium
      end
      it "'threshold' is :below" do
        expect(local_clue.threshold).to be :below
      end
      it "'confidence' is :bad" do
        expect(local_clue.confidence).to be :bad
      end
    end

    context 'many responses' do
      let(:responses) {
        [ { learner_id: 'lid1', question_id: 'qid1', correct: true},
          { learner_id: 'lid1', question_id: 'qid2', correct: false},
          { learner_id: 'lid1', question_id: 'qid3', correct: false},
          { learner_id: 'lid1', question_id: 'qid4', correct: true},
          { learner_id: 'lid1', question_id: 'qid5', correct: true},
          { learner_id: 'lid1', question_id: 'qid6', correct: true},
          { learner_id: 'lid1', question_id: 'qid7', correct: true},
          { learner_id: 'lid1', question_id: 'qid8', correct: true},
          { learner_id: 'lid2', question_id: 'qid2', correct: false},
          { learner_id: 'lid2', question_id: 'qid3', correct: true},
          { learner_id: 'lid3', question_id: 'qid1', correct: false}, ]
      }

      it "'threshold' is :above" do
        expect(local_clue.threshold).to be :above
      end
      it "'confidence' is :good" do
        expect(local_clue.confidence).to be :good
      end
    end
  end

  context 'multiple learners' do
    let(:learners) { ['lid1', 'lid3'] }

    context 'no responses' do
      let(:responses) { [] }

      it "'aggregate' is 0.5" do
        expect(local_clue.aggregate).to be 0.5
      end
      it "'left' is 0.0" do
        expect(local_clue.left).to be 0.0
      end
      it "'right' is 1.0" do
        expect(local_clue.right).to be 1.0
      end
      it "'level' is :medium" do
        expect(local_clue.level).to be :medium
      end
      it "'threshold' is :below" do
        expect(local_clue.threshold).to be :below
      end
      it "'confidence' is :bad" do
        expect(local_clue.confidence).to be :bad
      end
    end

    context 'few responses' do
      let(:responses) {
        [ { learner_id: 'lid1', question_id: 'qid1', correct: true},
          { learner_id: 'lid1', question_id: 'qid2', correct: false},
          { learner_id: 'lid2', question_id: 'qid1', correct: false}, ]
      }

      it "'level' is :medium" do
        expect(local_clue.level).to be :medium
      end
      it "'threshold' is :below" do
        expect(local_clue.threshold).to be :below
      end
      it "'confidence' is :bad" do
        expect(local_clue.confidence).to be :bad
      end
    end

    context 'many responses' do
      let(:responses) {
        [ { learner_id: 'lid1', question_id: 'qid1', correct: true},
          { learner_id: 'lid1', question_id: 'qid2', correct: false},
          { learner_id: 'lid1', question_id: 'qid3', correct: false},
          { learner_id: 'lid1', question_id: 'qid4', correct: true},
          { learner_id: 'lid1', question_id: 'qid5', correct: true},
          { learner_id: 'lid1', question_id: 'qid6', correct: true},
          { learner_id: 'lid1', question_id: 'qid7', correct: true},
          { learner_id: 'lid1', question_id: 'qid8', correct: true},
          { learner_id: 'lid2', question_id: 'qid2', correct: false},
          { learner_id: 'lid2', question_id: 'qid3', correct: true},
          { learner_id: 'lid3', question_id: 'qid1', correct: false}, ]
      }

      it "'threshold' is :above" do
        expect(local_clue.threshold).to be :above
      end
      it "'confidence' is :good" do
        expect(local_clue.confidence).to be :good
      end
    end
  end
end