models.py

"""Overall background for the simulation:
Classes for representing items, students, simulation scenarios.
Functions for generating simulated answers."""

import math
import random
import numpy as np
from dataclasses import dataclass

def logistic(x):
    return 1 / (1 + math.exp(-x))


def get_logistic_answer(skill, difficulty):
    prob = logistic(skill - difficulty)
    return int(random.random() < prob)


def get_answer_sequences(scenario, skill, count, limit):
    items = Items(scenario)
    answer_seqs = []
    for _ in range(count):
        items.shuffle()
        answer_seqs.append(
            Student(skill, scenario.student_learnrate).
            get_answer_sequence(items, limit)
        )
    return answer_seqs


class Student:

    def __init__(self, init_skill, learning_rate=0):
        self.init_skill = init_skill
        self.skill = init_skill
        self.learning_rate = learning_rate

    def __str__(self):
        return f"Student {self.init_skill:.2f}, {self.learning_rate:.3f}"

    def get_answer(self, items, i):
        prob = items.get_answer_prob(i, self.skill)
        self.skill += self.learning_rate
        return int(random.random() < prob)

    def get_answer_sequence(self, items, length=100):
        return [self.get_answer(items, i) for i in range(length)]


class Items:

    def __init__(self, scenario):
        self.size = scenario.items_count
        self.difficulties = list(np.random.normal(loc=scenario.difficulty_mean,
                                                  scale=scenario.difficulty_std,
                                                  size=self.size))
        self.guess_chance = scenario.guess_chance

    def shuffle(self):
        random.shuffle(self.difficulties)

    def get_answer_prob(self, i, skill):
        return self.guess_chance + \
            (1 - self.guess_chance) * \
            logistic(skill - self.difficulties[i % self.size])


@dataclass
class Scenario:
    name: str
    desc: str
    guess_chance: float
    time_intensity: float
    difficulty_mean: float = 0
    difficulty_std: float = 1
    student_std: float = 1
    student_learnrate: float = 0
    items_count: int = 300