3 Parameter item characteristic curve from Item response theory (IRT), written with python

item_characteristic_curve.py

from scipy.stats import norm
import numpy as np
import matplotlib.pyplot as plt

a, b, c = 1, 0, 0
D = 1.702

def normal_ogive(theta, a=1, b=0, c=0):
    return c + (1 - c) * norm.cdf(a*(theta - b))

def logistic(theta, a=1, b=0, c=0, D=1.702):
    return c + (1 - c) / (1+np.exp(-D *a * (theta - b)))

def plot_params(a=1, b=0, c=0, D=1.702):
    
    thetas = np.linspace(-3, 3)
    title = f'Discrimination(a)={a}, Diff(b)={b}, Guess(c)={c}, Scaling(D)={D}'
    plt.figure(figsize=(8, 6))
    plt.title(title)
    plt.plot(thetas, normal_ogive(thetas, a, b, c), label='Normal Ogive')
    plt.plot(thetas, logistic(thetas, a, b, c, D), label='Logistic')
    plt.legend(prop={'size': 13})
    plt.grid()
    plt.show()

plot_params()