def test_log_item_gradient(self):
delta = 0.00001
y1 = 1.0
y0 = 2.0
theta = -2.0
alpha = 1.0
beta = 0.0
# simulate the gradient
true_gradient_approx_beta = (clib.log_likelihood_2PL(y1, y0, theta, alpha, beta + delta) -
clib.log_likelihood_2PL(y1, y0, theta, alpha, beta)) / delta
true_gradient_approx_alpha = (clib.log_likelihood_2PL(y1, y0, theta, alpha + delta, beta) -
clib.log_likelihood_2PL(y1, y0, theta, alpha, beta)) / delta
# calculate
calc_gradient = clib.log_likelihood_2PL_gradient(y1, y0, theta, alpha, beta)
self.assertTrue(abs(calc_gradient[0] - true_gradient_approx_beta) < 1e-4)
self.assertTrue(abs(calc_gradient[1] - true_gradient_approx_alpha) < 1e-4)
# simulate the gradient with c
c = 0.25
true_gradient_approx_beta = (clib.log_likelihood_2PL(y1, y0, theta, alpha, beta + delta, c) -
clib.log_likelihood_2PL(y1, y0, theta, alpha, beta, c)) / delta
true_gradient_approx_alpha = (clib.log_likelihood_2PL(y1, y0, theta, alpha + delta, beta, c) -
clib.log_likelihood_2PL(y1, y0, theta, alpha, beta, c)) / delta
# calculate
calc_gradient = clib.log_likelihood_2PL_gradient(y1, y0, theta, alpha, beta, c)
self.assertTrue(abs(calc_gradient[0] - true_gradient_approx_beta) < 1e-4)
self.assertTrue(abs(calc_gradient[1] - true_gradient_approx_alpha) < 1e-4)
def test_log_likelihood(self):
# raise error
# with self.assertRaisesRegexp(ValueError,'Slope/Alpha should not be zero or negative.'):
# clib.log_likelihood_2PL(0.0, 1.0, 0.0,-1.0,0.0)
# the default model, log likelihood is log(0.5)
ll = clib.log_likelihood_2PL(1.0, 0.0, 0.0, 1.0, 0.0)
self.assertEqual(ll, math.log(0.5))
ll = clib.log_likelihood_2PL(0.0, 1.0, 0.0, 1.0, 0.0)
self.assertEqual(ll, math.log(0.5))
# check the different model
ll = clib.log_likelihood_2PL(1.0, 0.0, 1.0, 1.0, 0.0)
self.assertEqual(ll, math.log(1.0 / (1.0 + math.exp(-1.0))))
ll = clib.log_likelihood_2PL(0.0, 1.0, 1.0, 1.0, 0.0)
self.assertEqual(ll, math.log(1.0 - 1.0 / (1.0 + math.exp(-1.0))))
# check a real value
ll = clib.log_likelihood_2PL(0.0, 1.0, -1.1617696779178492, 1.0, 0.0)
self.assertTrue(abs(ll + 0.27226272946920399) < 0.0000000001)
# check if it handles c correctly
ll = clib.log_likelihood_2PL(1.0, 0.0, 0.0, 1.0, 0.0, 0.25)
self.assertEqual(ll, math.log(0.625))
ll = clib.log_likelihood_2PL(0.0, 1.0, 0.0, 1.0, 0.0, 0.25)
self.assertEqual(ll, math.log(0.375))
def test_log_factor_gradient(self):
delta = 0.00001
y1 = 1.0
y0 = 2.0
theta = -2.0
alpha = 1.0
beta = 0.0
# simulate the gradient
true_gradient_approx_theta = (clib.log_likelihood_2PL(y1, y0, theta + delta, alpha, beta) -
clib.log_likelihood_2PL(y1, y0, theta, alpha, beta)) / delta
# calculate
calc_gradient = tools.log_likelihood_factor_gradient(y1, y0, theta, alpha, beta)
self.assertTrue(abs(calc_gradient - true_gradient_approx_theta) < 1e-4)
# simulate the gradient
c = 0.25
true_gradient_approx_theta = (clib.log_likelihood_2PL(y1, y0, theta + delta, alpha, beta, c) -
clib.log_likelihood_2PL(y1, y0, theta, alpha, beta, c)) / delta
# calculate
calc_gradient = tools.log_likelihood_factor_gradient(y1, y0, theta, alpha, beta, c)
self.assertTrue(abs(calc_gradient - true_gradient_approx_theta) < 1e-4)