def setUp(self):
# initialize the data
n = 10000
self.alpha = 1.5
self.beta = -2.0
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], self.beta, self.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]
# initialize optimizer
self.solver = optimizer.irt_2PL_Optimizer()
self.solver.load_res_data(response_data)
self.solver.set_theta(theta_vec)
self.solver.set_c(0)
def setUp(self):
# initialize the data
n = 1000
self.theta = 1.5
self.alpha_vec = np.random.random(n) + 1
self.beta_vec = np.random.normal(loc=0.0, scale=2.0, size=n)
self.c_vec = np.zeros(n)
y1 = []
y0 = []
for i in range(n):
# generate the two parameter likelihood
prob = tools.irt_fnc(self.theta, self.beta_vec[i], self.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
self.solver = optimizer.irt_factor_optimizer()
self.solver.load_res_data(response_data)
self.solver.set_item_parameter(self.alpha_vec, self.beta_vec, self.c_vec)
self.solver.set_bounds([(-6, 6)])
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)