def setUp(cls):
# initialize the data
n = 10000
cls.alpha = 1.5
cls.beta = -2.0
np.random.seed(20170807)
theta_vec = np.random.normal(loc=0.0, scale=1.0, size=n)
y1 = []
y0 = []
for i in range(n):
# generate the two parameter likelihood
prob = tools.irt_fnc(theta_vec[i], cls.beta, cls.alpha)
# generate the response sequence
if prob >= np.random.uniform():
y1.append(1.0)
y0.append(0.0)
else:
y1.append(0.0)
y0.append(1.0)
# the response format follows the solver API
response_data = [y1, y0]
cls.init_theta_vec = theta_vec
cls.solver = optimizer.irt_2PL_Optimizer()
cls.solver.load_res_data(response_data)
cls.solver.set_c(0)
cls.solver.set_bounds([(-4.0, 4.0), (0.05, 2)])
def setUpClass(cls):
# initialize the data
n = 1000
cls.theta = 1.5
np.random.seed(20170807)
alpha_vec = np.random.random(n) + 1 # 1-2
beta_vec = np.random.normal(loc=0.0, scale=2.0, size=n)
c_vec = np.zeros(n)
y1 = []
y0 = []
for i in range(n):
# generate the two parameter likelihood
prob = tools.irt_fnc(cls.theta, beta_vec[i], alpha_vec[i])
# generate the response sequence
if prob >= np.random.uniform():
y1.append(1.0)
y0.append(0.0)
else:
y1.append(0.0)
y0.append(1.0)
# the response format follows the solver API
response_data = [y1, y0]
# initialize optimizer
cls.solver = optimizer.irt_factor_optimizer()
cls.solver.load_res_data(response_data)
cls.solver.set_item_parameter(alpha_vec, beta_vec, c_vec)
cls.solver.set_bounds([(-4, 4)])
def setUpClass(cls):
# simulate
np.random.seed(20170807)
thetas = np.random.rand(N,1)*theta_range - theta_range/2
cls.data = []
for i in range(N):
for t in range(T):
prob = irt_fnc(thetas[i,0], beta[t], alpha[t], c[t])
cls.data.append((i, item_ids[t] ,np.random.binomial(1,prob)))
def test_irt_fnc(self):
# make sure the shuffled sequence does not lose any elements
prob = tools.irt_fnc(0.0, 0.0, 1.0)
self.assertEqual(prob, 0.5)
# alpha should play no role
prob = tools.irt_fnc(0.0, 0.0, 2.0)
self.assertEqual(prob, 0.5)
# higher theta should have higher prob
prob = tools.irt_fnc(1.0, 0.0, 1.0)
self.assertEqual(prob, 1.0 / (1.0 + math.exp(-1.0)))
# cancel out by higher beta
prob = tools.irt_fnc(1.0, -1.0, 1.0)
self.assertEqual(prob, 0.5)
# test for c as limit situation
prob = tools.irt_fnc(-99, 0.0, 1.0, 0.25)
self.assertTrue(abs(prob - 0.25) < 1e-5)
prob = tools.irt_fnc(99, 0.0, 1.0, 0.25)
self.assertTrue(abs(prob - 1.0) < 1e-5)